- Email: [email protected]
Method for image equalization of ROI fluoroscopic images using mask localization, selection and subtraction
Computerized
Medical
Pergamon
Imaging Copyright
and Graphics, Vol. 20, No. 2, pp. 89403, 1996 0 1996 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0895-6111/96 $15.00 + .@I
PII: so895-6111(96)ooo28-6
METHOD FOR IMAGE EQUALIZATION OF ROI FLUOROSCOPIC IMAGES USING MASK LOCALIZATION, SELECTION AND SUBTRACTION
Lynn M. Fletcher, Stephen Rudin* and Daniel R. Bednarek Departments
of Biophysical Sciences and Radiology, State University of New York Medicine and Biomedical Sciences, Buffalo, NY 14215, USA (Received
25 October
at Buffalo,
School of
1995; revired 11 March 1996)
Iu regionof interest (ROI) iluoroscopy,a iilter is usedto drasticallyreducethe X-ray doseto the patient peripheral to an ROI, and masksubtractionis usedto equalizethe displayedimagebrlgbtness.Methods are describedfor an optimizedsearchto locate tbe ROI andselector constructa maskimageusinga descriptorlook up table (DLUT) basedon ROI size,relative ROI/peripbery brlgktuessaudROI shapeand orientation.After masksubtraction,the brightnessvaluesof tbe peripheryare comparableto thoseof tbe ROI provldlngfor equalizeddisplay.‘Ibis method was tested successfullyon 50 actual iluoroscopicimagesof two anthromorpldcphantoms.Tbe methodology developedfor real-time applicationswas succewhlly simulatediu PC code and full real-time implementationis underway.Copyright 0 19% ElsevierScienceLtd Key Words: Fluorosoopy, ROI fluoroscopy, Mask subtraction, Image equalization, LUT
BACKGROUND
Real-time image processing, Descriptor
temporal resolution can be sacrificed due to reduced frame rates. Removal of the grid reduces the image quality by allowing the recording of scattered radiation by the image receptor. Optical aperture enlargement increases noise throughout the image. The method of ROI fluoroscopy uses a beam attenuating filter to reduce the X-ray intensity in clinically less significant portions of the image, but leaves the ROI uneffected; thus, there is an increase in noise due to decreased quantum statistics only outside of the ROI. An image acquired with an ROI filter, if unprocessed, would appear bright in the ROI and dark in the periphery. It may be desirable to improve the appearance of the image by equalizing the displayed brightness between the ROI and the periphery using real-time image processing techniques. Since ROI fluoroscopy has been introduced by the authors, related efforts have been reported with a global image processing filtering method (13), and with an algorithmic mask technique designated as the X-ray fovea (14). Global filtering may greatly alter the image within the ROI and requires a large grey level transition region between the ROI and periphery. The ‘fovea’ method uses modeled equalization masks to preserve the ROI, and appears to offer excellent boundary matching, however, the feasibility of real-time implementation is unclear. A detailed discussion of how equalization can be accomplished in real-time ROI fluoroscopy using
AND INTRODUCTION
Fluoroscopic procedures, in general, result in much higher exposures to patients than do most types of radiographic procedures (1). Although some investigators have measured X-ray exposure levels which appear to be acceptable from a risk versus benefit perspective to patients and clinicians during fluoroscopic procedures (l+, there is continuing concern for the risks of deterministic and stochastic effects which may be associated with the exposure of X-rays (5-9). Additionally, the exposure rates can vary greatly between fluoroscopic systems (10) and between procedures. It is important to minimize examination doses whenever reasonably possible while the trade-offs between the amount of information desired from a procedure and the associated absorbed radiation dose continue to be examined. Methods to reduce fluoroscopic dose include the use of pulsed fluoroscopy (6), removal of anti-scatter grid, video camera optical aperture enlargement (1 l), and region of interest (ROI) fluoroscopy (12). Each method involves trade-offs. Pulsed progressive fluoroscopy can greatly reduce dose; however, *Correspondence should be addressed to Stephen Rudin, PhD, Division of Radiation Physics, State University of New York at Buffalo, Erie County Medical Center, 462 Grider Street, Buffalo, NY 14215, USA, Phone: (716) 898-3500; Fax: (716) 8985217; E-Mail: [email protected] 89
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both empirical and algorithmic mask subtraction follows. The methodology includes finding the ROI, determining its size, finding an appropriate mask, digitally subtracting the mask from the fluoroscopic image, adding a constant to bring the brightness values into the display range, and finally displaying the equalized image. MATERIALS
AND
METHODS
Materials, image acquisition and storage A standard fluoroscopic unit (Philips Diagnost 66) with a 35 cm image intensifier was used in the 26 cm mode. The Philips video camera signal was sent to a Targa m8 (Truevision Inc., Indianapolis, IN) 8bit frame digitizer with 512 x 512 square pixels. The automatic gain control of the video camera was disengaged so the kVp and mA could be varied without causing the video gain to change. Various uniform gadolinium filters with circular apertures were placed on top of the collimator between the X-
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ray source and the patient table. Filters varied ir ROI diameter size due to the different application! for which ROI fluoroscopy can be used. Fifty images of two standard diagnostic phan toms (Alderson Diagnostic and 3M Pelvic) were digitized and remapped using the equation of tht video calibration curve in Fig. 1 which was obtainec using bootstrap sensitometry (15). All masks ant images were linearized using this curve so that the corrected pixel values were proportional to the logarithm of X-ray intensity incident to the II-videc camera combination. This had to be done for thi! general purpose Philips unit since only video camera: used specifically for digital subtraction angiograph! are commercially calibrated linearly to the log o exposure, yielding successful subtractions. Mask images with ROIs in the center of the fielc of view (FOV) were stored in a data base and listec in the first of two descriptor look-up tables (DLUT) These mask images were digitally averaged over lt video frames to reduce the effects of noise in the
1.6 1.4 1.2 1 0.8 0.6
0.5
1
1.5
2
2.5
Log (GL-33.6) Fig. 1. Calibration curve used to linearize all images to the logarithm of light intensity incident to the video camera. The data were fit to the following equation: log(exposure) = -0.600 + 0.939 * log(GL - 33.6) - 0.0318 * log(GL - 33.6)’ where GL corresponds to pixel grey level.
Image equalization of ROI fluoroscopic images L. M. FLETCHER et al. l
subtraction process. As filters with the same material thickness were positioned on the collimator, masks were obtained with various size ROI filter holes and differing magnifications which were determined by the position of the image intensifier with respect to the X-ray source; various differences in brightness between the ROI and the periphery were obtained by varying the kVp. By prerecording these masks any one of them could be easily and quickly chosen, then subtracted from the ROI fluoroscopic image. For off-center ROI applications a second set of masks was synthetically generated and stored in the second DLUT as elliptical ROIs which are to be added to an image of a uniformly filtered FOV. These small size, stored masks are only slightly larger than the size of the ROI and they are chosen from the DLUT based on size. Due to their small size, many masks may be stored in a small amount of memory. For this experiment, 71 masks with their longest dimensions ranging from 20 to 160 pixels were made available in DLUT 2 and are listed in Table 2. These masks will be used when the ROI is found off-center in the fluoroscopic image. Due to the constant elliptical distortion in the image field for this fluoroscopic unit (found by measuring the physical attributes of the field and 22 imaged ROIs in various locations of the field), all algorithmically derived ROIs used for this experiment were created to conform to the shape and rotation parameters required (0.35 eccentricity and 6 degree rotation). The full-size or composite mask is created by superimposing the chosen, algorithmically derived ROI onto an empirical image of the uniform gadolinium filter. All code was written, compiled and executed on a 486 computer in the C programming language and a flow chart of its function is shown in Fig. 2. With this code the ROI is found and its size and shape are determined, the appropriate mask is chosen and digitally subtracted from the fluoroscopic image, a constant is added to bring the brightness values into display range and the image is digitally stored in a frame buffer before it is displayed. This method of image equalization was motivated by the speed requirements of real-time fluoroscopy. The methodology was developed with the intention of direct application to a specific hardware architecture which will support real-time image manipulation. Detailed image processing methods Find the region of interest (ROI)
in the image.
Since the brightness as represented by pixel values is expected generally to be higher in the ROI than in the periphery, regions of the images may be
91
segmented from each other through the use, of a pixel value threshold. By sampling a geometrical pattern of pixels chosen for search efficiency, and comparing those pixel values with the threshold, the ROI can be located when pixel values are found to be above the threshold. However, if there are areas within the ROI with brightness values below the threshold, these pixels could be mistakenly identified as pixels in the periphery. The chances of this problem occurring are reduced using two techniques. First, a histogram, to be determined at the time of digitization, may be easily acquired. The histogram will display the actual quantities of pixels at each brightness value and will be determined automatically with the real-time hardware. The threshold will be chosen from the range of brightness values in the valley where there is minimum frequency of occurrence between the two groups of pixels. The group with higher brightness values represents the pixels in the ROI and the group with lower brightness values represents the pixels in the periphery. Any overlap between the two groups will add to the uncertainty of the choice of the threshold; however, overlap has been minimally detected in these experiments and has not been seen yet as a major concern. The additional, second method is by oversampling, or in our case, sampling such that there will be at least two sampled pixels for any potential ROI position. The geometric search pattern used is one of three possible regular and rotationally symmetric patterns available (17)-hexagonal, triangular or square, shown in Fig. 3. The hexagonal pattern was chosen since it can cover the greatest area with the least number of points and still guarantee two search points per possible ROI location (see Fig. 4 and Appendix). The hexagonal search pattern spirals outward beginning at the center of the field of view (FOV) since the ROI is expected to be closer to the center rather than the edges of the FOV. For each point checked against the threshold, determined by the histogram, it is decided by the program whether or not the ROI has been found. In the unlikely event that the ROI is not found, when one is known to exist, the threshold may be lowered and the search will be repeated. The coordinates for the search points are precalculated and stored in a file. The calculated distances between points are based on the lowest magnified ROI projection through each physical filter hole size (smallest X-ray source to II distance) and the intrinsic nature of the hexagonal pattern. There is one search list for each filter. The calculations are consistent with the guarantee of two sample points per possible ROI location. Once the filter has
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1. From DLUTI choose mask with closest size and AB
1. Rernapitnagethrough 2.
Yes/ a ’ Subtract mask from the image
2.
Choosesearchlist
-
constant to bring image values into viewing range
3. Add
ROI centered7
No\
From DLUT2 choose ROI mask with calculated size
1. Find avg. value of ROI Find avg. vahte of periphery 3.
1
I
Subtract2froml=AB + 1. Openandread in ROI mask
No
_:::::I[::::::: Openandread in Gd uniform field image
2.
Execute search
t
I-YeS
Is X or Y length more than 15% longer than other?
t
1. Calculate avg. in uniform field image in the required ROI position
calculateconstanttobeaddedto ROI (AD - uniform field spot avg.)
2.
NC
Find edges (x, Y lengths)
3. calculatecompositemask:
uniform field with ROI mask in area of image ROI t
Fig. 2. Flow chart describing method for image equalization including ROI search, mask selection, subtraction and display.
Image equalizationof ROI fluoroscopic images L. M. l
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Fig. 3. Search patterns based on rotational symmetry: (a) triangular, (b) square and (c) hexagonal. (c) also demonstrates the “spiralling” nature of the search, where the dotted lines show points of level increment becoming repetitive after the second increment.
been chosen, the proper such Cle is selected with the necessary search list. The search was implemented on 50 images of the two phantoms (Alderson and 3M Pelvic). In the modsed program for the real-time hardware, all files of search points will be preread into RAM during the initilization section of the program to save time during access. Find the edges of the ROI. Once the ROI has been found, the boundaries must be defined. Horizontal and vertical searches are utilized from the position of the first pixel found within the ROI. A search distance of */4 the smallest video ROI diameter for the ROI filter used is the edge search increment, which by definition is smaller than the true diameter. Searching by this increment outwardly, the direction is reversed as soon as the pixel value goes below the threshold. Then every
pixel is checked inwardly until the pixel value goes above the threshold again. Once the two edges have been found in the horizontal direction, the midpoint is calculated and the search proceeds on the vertical line of the midpoint in the same manner. After the midpoint is calculated on the vertical line, the search is repeated horizontally to con&m the placement of the ROI center and to get a better measurement of the ROI diameter. If the difference between the vertical diameter and the horizontal diameter is more than 15% (a value chosen to accommodate the elliptical and slightly rotated ROI shape known to exist as a result of video chain distortions) then it is assumed that a non-R01 pixel has been misclassified as an ROI pixel. The threshold can be raised and the full edge search repeated. Calculate the difference between periphery. An average value is calculated
ROI
and
inside the
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Hexagon
1200 1000 800 600 400 200
20
40
60
80
100
120
140
160
Pixel Diameter of Smallest ROI (two search inquiries) Fig. 4. Search method comparison demonstrates that the hexagonal pattern is more efficient, requiring less points to ensnre at least two search inquiries per possible ROI location. ROI from a box of pixel values and an average value outside the ROI is determined by the average brightness collected of all the previously interrogated search points outside the ROI (below the threshold but within the FOV). The difference between these two averages is the parameter delta brightness. These values are also calculated and indexed with all oncenter stored masks (DLUT 1 shown in Table 1). A delta brightness value is subsequently calculated for the incoming fluoroscopic image and used to select or create the appropriate mask for subtraction. Mask selection
Centered case. The appropriate mask is chosen based on the ROI size and delta brightness found above. The data base is accessed through the first DLUT, functioning as a search space (Table l), and a match is found for a mask with the same attributes, if not available exactly then a best match may be made for both size and delta brightness. Since closely matching the ROI size to minimize ring artifacts is
more important than matching the delta brightness, the decision for choosing a mask is more heavily weighted by size than delta brightness. A weighted choice occurs with calculations of minimum distances between available masks and surrounding characteristic values while weighting the importance of each characteristic with cr (Fig. 5). The search space is partitioned and each segment is bound with a range of values for each characteristic. Ranges of mask characteristic values are also predetermined so as the mask needed for subtraction is searched for in the partitioned space, the mask closest to the one needed is chosen automatically. The partitions of the space, in this case twodimensional segments, do not have to be symmetric, they must, however, each contain one mask and all possible mask choices must be represented. Non-centered case. If the location of the ROI is not in the center of the FOV, but found elsewhere, an appropriate mask is chosen from the second DLUT and a full size mask is created. This DLUT is also
Image
equalization
of ROI
fluoroscopic
images
l
L. M. FLETCHER
et
95
al.
Table 1. Descriptor look up table (DLUT) categorizesavailable maskimagesfor centeredROIs ROI major Mask
number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
*For
Brightness difference (ROI -periphery)
axis (pixels)
of DLUT
number
‘I35 145 120 146 138 140 144 143 136 136 139 137 141 141 139 140 138 138 142 142 119 126 105 108 119
45 50 54 66 68 72 74 76 101 103 107 109 109 113 142 149 151 155 157 162 183 183 184 187 187
description
ROI major Mask
Brightness difference
axis (pixels)
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
(ROI-periphery)
187 189 190 190 192 192 193 196 196 196 199 200 201 201 204 204 204 211 211 211 218 218 218 227 228 228
129 129 109 118 119 129 104 105 117 127 118 127 105 113 105 116 123 105 118 124 104 115 122 127 103 117
usage see Fig. 4.
a.
b.
DLUT Diameter
Delta Brightness Delta Brightness
Mask 1
62
105
Mask 2
64
120
Mask 3
65
110
Mask 4
68
115
Mask 5 . . .
69 . . .
100 . . .
* 100
105
110
115
120...
. .
62 8 63 tif 64 a 65 66 67 68 69
Fig. 5. Pictorial demonstrationshowsthat as(a) masksare indexedin the DLUT, a minimumdistanceequation, weighted appropriately with 6, determines(b) the decisionboundariesfor maskselection.Therefore: DecisionBoundaries= MIN{[(l - U) * (d,,, - di)]’ + [cr* (AB,,, - ABi)]‘} where & =diameter of mask ROI, 4 = arbitrary diameter of ROI, A& = delta brightness of mask, ABi = arbitrary delta brightness.
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constructed as the partitioned search space above (Table 2). The masks listed in this DLUT are slightly elliptical in shape due to a small video chain distortion and have values of one inside the ROI and zero outside the ROI. All masks have been convolved with a Gaussian kernel to smooth the edges of the ROI simulating the 5-6 pixel wide edge on all fluoroscopic ROIs. The mask pixel values are no longer binary but are now stored as integer data between the values of 0 and 255. The chosen ROI mask is based on the largest measured ROI diameter, eccentricity and rotation angle. According to measurements and calculations, the eccentricities and rotation angles for all ROIs imaged with this Philips Diagnost 66 unit have had negligible differences. This allows for a more simplified model of the distorted ROI when creating a mask. It was possible to create all masks with different eccentricities and rotation angles; however, for this work it was only necessary to create ROIs with eccentricities of 0.35 and rotation angles of + 6 degrees from the vertical axis in order to characterize all ROIs imaged with this unit. Since image distortion is dependent on the image intensifier and video chain of each fluoroscopy imaging device, this analysis must be done for each unit used. Also, since very little distortion is present from the image intensifier in this case, the distortion was found to be constant and not position dependent. The mask is then created by effectively superimposing the small, ROI mask chosen onto the image with the uniform gadolinium filter. Mask subtraction. The brightness is enhanced in the periphery to match the ROI by subtracting the mask from the ROI fluoroscopic image. A constant
Table 2. DLUT 2 is used to categorize calculated ROI masks Major axis dimension
Elliptical eccentricity
ClOCkWiSe rotation
sm10356tga sm11356.tga sm12356.tga sm13356.tga sml14356.tga sm15356.tga sm16356tga sm17356.tga sm18356.tga sm19356.tga sm20356.tga
10 11 12 13 14 15 16 17 18 19 20
0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35
6 6
&0356.tga
80
0.35
k
ROI mask name
*Any variation of parameters can be applied fluoroscopic imaging system.
to a given
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determined by the average ROI image value of the mask is added to bring the brightness values into range (O-255). The subtracted image is then displayed. RESULTS
Table 3 shows a listing of all images included in the experiment described above. Also listed are the measured or actual ROI diameter, search diameter corresponding to the filter used, calculated ROI major axis, calculated ROI center, and the number of inquiries required to find each ROI. Threshold ranges were easily determined with the aid of a histogram for each image. A typical histogram is illustrated in Fig. 6 with its corresponding ROI image in Fig. 7. The histogram shows the distribution of pixels for each brightness value. The threshold can be chosen at the minimum between the two groups of pixels. There is a clear separation between groups in Fig. 6; therefore, the threshold for this image can range between values 110 and 130. Figure 7 is a single frame fluoroscopic image of the 3M pelvic phantom with an off-center ROI. The filter attenuates about 90% of the exposure in the periphery yielding a greatly reduced image intensity in the periphery. There is increased noise in the periphery due to reduced quantum statistics while the ROI image quality is preserved. An example of image equalization for the case where the ROI is found to be in the center of the FOV is displayed in Fig. 8. The single frame image with the ROI is in Fig. 8a while the closest size video mask shown in Fig. 8b was chosen from DLUT 1. The subtracted result is shown in Fig. 8c. Note the very small white ring around the ROI exhibiting a match which is not exactly the size of the image ROI. A search demonstration of an offcenter ROI image is shown in Fig. 9. The white dots indicate searched points which did not locate the ROI whereas the search point marked with the black dot found the ROI and then stopped searching. For this particular image the search required 27 queries before recognizing the ROI. With the real-time image processing hardware the search will be continuous, constantly compensating for new ROI sizes, positions and the difference in patient thickness. The process by which the composite mask was created is shown in Fig. 10. A uniformly filtered image, used as the base for the composite mask, Fig. lOa, is joined with the small mask of the closest size ROI, Fig. lob. The small mask is shifted to the proper location where all values are divided by 255 to obtain values between
Image Table Actual ROI diameter of filter (cm)
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.704 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.588 1.588 1.588 1.588 0.704 0.704 0.704 0.704 0.704 0.704 0.704 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27
3. Results
equalization
of ROI
of hexagonal Search diameter (smallest mag. of tilter ROI)
fluoroscopic
search,
images
algorithmic
Calculated ROI major axis
20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 50 50 50 50 50 50 50 50
34 88 75 76 81 55 49 52 54 68 45 45 61 68
N/A 101 100
N/A 97 45 43 42 45 49 47 45 58 64 55 61 54 32 76 82 40 79 73 63 68 76 86 74 95 84 86 70 101 108 105 101
l
L. M. FLETCHER
characterization
et al. and
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subtraction
Calculated ROI center (row, column) 229,277 316,341 312,329 311,329 351,240 211,269 204,301 206.242 2181296 210,291 216.270 238;293 354,231 307.23 1 Complete ROI 248,278 248,278 Complete ROI 248,278 271,259 157,266 241.245 268;260 272,253 272.252 272;252 296,344 299,363 366,365 215.386 218;378 283,366 131,236 343,287 220.130 340;285 305,163 232,258 378,335 235.258 3451289 192,286 249.235 406;278 410,278 233,246 214,322 245.234 NO;174 196,171
# Search inquiries
not within
not within
‘Alderson phantom images (1-19) exhibit comparable results to tbc 3M pelvic phantom images (20-50). As the filter was changed to offer a different range of possible ROI sixes, a new search list was ac(‘Rssed as shown. center of the FOV and all calculated ROI centers indicate the distance from the center, tberefore, corresponding required to find the ROI.
0 and 1 then multiplied by the desired difference in brightness. Then the uniform image value of that pixel is added to the result of the previous multiplication. The result of this calculation is that everywhere where there was a 0 in the small mask, the original value of the uniform image is substituted; wherever there was a 1, the brightness
85 39 40 15 19 21 46 21 19 19 21 19 12 2 FOV 1 1 FOV 1 5 47 1 5 1 1 1 16 40 74 44 81 42 49 13 25 13 26 1 37 1 13 20 I 35 35 1 18 1 6 6
Coordinate (248,278) is the to the number of inquiries
difference is added to the uniform image value. Once completed, this full size mask is ready for subtraction from the fluoroscopic image (Fig. 1Oc). The images in Fig. 11 are ROI fluoroscopic images of the pelvic phantom before and after subtraction using the mask created in Fig. 10. Again it is clear that the image quality in the ROI
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j30.14 -4 5 0.12 5
0.1
1 0.08 ‘4 0.06 s % O-O4 ‘aj 0.02 ti 0
..............periphery
50
......... ROI _............................................................................~
100
.......................................... ..~.....................
150
250
Brightness Value Note: Periphery and ROI pixel quantities are not to the same scale. Fig. 6. Histogram used to find search threshold for the image in Fig. 7 shows the distribution of pixels for each brightness value.
of the subtracted image is preserved while the image quality in the periphery is degraded due to reduced photon statistics, or quantum mottle.
Fig. 7. Single frame fluoroscopic image of 3M pelvic phantom with an ROI off-center. The ROI pixels are bright compared to the pixels in the periphery thus they belong to the group of pixels with high brightness values in the histogram shown in Fig. 6. Similarly, the pixels in the periphery can be seen in the group with low pixel values.
DISCUSSION
The results of the experiment in Table 3 show that all ROIs were found with the hexagonal search pattern described above except for image numbers 15 and 18 of the Alderson phantom sequence. Tbis result was expected since these ROIs were not completely within the FOV, therefore not circular. Since the fluoroscopic images digitized from the Philips Diagnost unit all had the same distortion effects, this search algorithm was successfully implemented to expect a shape resembling a circle but allowing for a 15% difference between the two measured diameters. The allowance approximates the difference between the major and minor axis of the elliptical shape found in these images. On another imager the expectations might change and in that case the algorithm would need to be modified. Also, when the amount of distortion begins to depend on position, as it would with most image intensifiers where pin-cushion distortion increases further from the center (18), a more sophisticated approach will be required to characterize the specific shape of the ROI. It may be possible to employ an ellipse detection technique such as the one suggested by Yin and Chen (19) using the symmetry of the ellipse and only five points to characterize its five parameters. This, however, was obviously not necessary for these conditions since the Philips image intensiher
Image equalization of ROI fluoroscopic images l L. M. FLETCHBR et al.
99
Fig. 9. Demonstration of the hexagonal search patten as it locates an off-center ROI in a fluoroscopic image. White dots indicate the locations of search while the black dot indicates the search point which found the ROI.
Fii ;. 8. Mask subtraction using mask chosen from DLUT. (4 Single frame fluoroscopic image of 3M pelvic phantom Wil :h an ROI in the center of the FOV. (b) Video mask chchen from the DLUT, 10 averaged frames and matched fo1 . size and brightness difference. (c) ROI image corrected by subtracting mask in (b). Note the small artifactual ring around the ROI caused by an inexact match.
used in this study had one of the smallest pin-cushion distortions of image intensifiers commercially available (18). Thresholds for segmentation were successfully determined through a user-interfaced histogram acquisition program which prompted the user to enclose the ROI in a circle. These thresholds varied since the automatic brightness control was disabled and due to the content of each ROI. For most images no overlap was observed between the two regions as in the example Fig. 6 corresponding to the image in Fig. 7. However, there was a slight amount of overlap in three of the images which did not seem to affect the performance of the ROI search since they were all located. Overlap does indicate possible error in choosing the threshold, but the number of pixels in the overlap region are so few that they do not seem to be of major concern. The Datacube hardware architecture to be used in future ROI fluoroscopy implementation is capable of utilizing a non-user interfaced analysis which will calculate a single histogram with pixel quantities and brightness values for each image. It is anticipated that it will be easy to automatically lind the minimum between peaks in the histogram once it has been acquired. Once an appropriate threshold was selected the search was executed with the list of search points corresponding to the filter hole size. If the center of the ROI was found in the center of the FOV, a mask was chosen from DLUT 1. Figure 8a shows a typical image with a mask in the center of the FOV. The
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Fig. 10. A full size mask is created for an off-center ROI by joining (a) a uniformly f&red image and (b) a small mask consisting of an ROI chosen from a DLUT based on size, elliptical eccentricity and rotation angle. The composite, algorithmic mask (c) may be subtracted from the image for which it was created.
closest size mask chosen from DLUT 1 is shown in Fig. 8b and the subtracted result is shown in Fig. 8c. Note the very small white ring around the ROI in Fig. 8c exhibiting a match which is not exactly the size of the image ROI. A white ring is present when the ROI of the chosen mask is slightly smaller than the ROI of the fluoroscopic image. Conversely, a black ring is noticed when the chosen mask ROI is slightly larger than the ROI of the image. Either type of ring is expected when selecting a closest fit mask from the DLUT. Although the image field is nonuniform due to the Heel effect, inverse square law and X-ray II defects, mask subtraction corrects for these non-uniformities of the X-ray field. Also introduced after either subtraction is increased noise in the periphery due to reduced photon statistics and pixel quantitization from S-bit digitization. The latter problem should be reduced when the 1Zbit digitizer is in use with the Datacube hardware.
Fig. 11. Mask subtraction using mask created in Fig. 1Oc. (a) Single frame fluoroscopic image of the pelvic phantom to be equalized. (b) The corrected ROI image. Figure 9 is a demonstration of the search method on an image with an ROI off-center. Once the search has completed one full rotation the search distance is incremented outwardly at the upper left portion of the FOV. Clearly, the ROI was found with the first pixel that entered the ROI boundary or the 27* inquiry. This number is very small compared to the result of a loop test previously reported for a Datacube image processor used with a Sun Sparcstation 10 controller (20). The time required to retrieve any one pixel from video was found to be less than 12 ps. Therefore, 27 retrievals will take about 0.3 ms, which is much less than 33.3 ms, the time required to display one video frame. The time required for random retrievals should not be confused with the
Image equalization
of ROI fluoroscopic images l L. M. FLETCHER et al.
time required for image processing calculations to follow since these operations will be completed with pipeline processing which take place at much faster per pixel speeds. Since the ROI was found off-center, a full-size mask was created from the uniform image shown in Fig. 10a and the ROI mask shown in Fig. lob. The small ROI mask was translated to the calculated ROI position of the fluoroscopic image and superimposed, yielding the mask in Fig. 1Oc. This method of mask creation, although algorithmic, combines the empirical uniform image with the algorithmic ROI yielding a mask which, as in Fig. 8, removes the nonuniformities of the X-ray FOV mentioned above for the centered ROI case. The results of the subtraction are shown in Fig. 11 and are comparable to the subtractions of oncentered masks, indicating that the new mask creation method is successful. The one difference which can be seen in Fig. 1 lb compared to Fig. 8c is in the shading of the ring around the ROI. The ROI in Fig. 1lb has a ring which is half dark and half bright demonstrating a half-pixel error in the y-axis placement of the ROI in the mask. This error is minimal and difficult to correct when the ROI has an even dimension hence no one pixel on which to center the ROI. Also, a small variation in ROI dimension measurements has been seen while varying the search thresholds. Therefore, a nonoptimized threshold may cause some error in the dimension measurements, resulting in error with the mask selection or creation since this problem is independent of position. Again, this problem may be present but it does not appear to be a major concern as long as a reasonable mask is used leaving only a few pixel wide boundary between the ROI and the periphery. The true impact of these minor artifacts upon clinical procedures will require further detailed study; however, initial qualitative data indicates high tolerance of clinicians to this type of geometric artifact. SUMMARY A method was developed for ROI localization, mask selection and mask subtraction. It was then implemented via simulation code written for the PC intended for transfer to a SUN workstation interfacing with Datacube fast acquisition image hardware. The method was tested on 50 images and the results show that it was successfully implemented. All ROIs were found with fewer than 86 search points corresponding to 1.03 ms, except for the two noncircular ROIs which were partially outside the FOV. The maximum time for search on these images
101
should be 1 ms, which is less than one video frame time, using real-time image processors. Through this method fluoroscopic images may be equalized after the ROI attenuation filter is applied during ROI fluoroscopy. The reduction of exposure area product to the patient while using the ROI filter device ranges from 60 to 89% based on filter hole sixes between 40 and 150 pixels in diameter. The method of image equalization provides the fluoroscopist with images which have comparable levels of brightness in the ROI and the periphery. This method may be used whenever an increase in quantum noise in the periphery is acceptable such as during interventional procedures where the periphery is needed only for guidance or reference. Additionally, the methods described for a larger sized centered ROI appear to be applicable to a broad range of diagnostic fluoroscopic procedures.
work was supported in part by NIH
Acknowledgement-This
Grant No. ROlNS31883.
RETERENCXS 1. National Council on Radiation Protection, report 100. 31; 1989. 2. Lindsay, B.D.; Eichling, J.O.; Ambos, H.D.; Cain, M.E. Radiation exposure to patients and medical personnel during radiofrequency catheter ablation for supraventricular tachycardia. Am. J. Cardiol. 70:218-223; 1992. 3. Bergeron, P.; Carrier, R.; Roy, D.; Blabs, N.; Raymond, J. Radiation doses to patients in neurointerventional procedures. Am. J. Neurorad. 151809-1812; 1994. 4. Goldstone, K.E.; Wright, I.H.; Cohen, B. Radiation exposure to the hands of orthopaedic surgeons during procedures under fluoroscopic X-ray control. Brit. J. Radiol. 66(790):899-901; 1992. 5. Geterud, K.; Larsson, A.; Mattson, S. Radiation doses to patients and personnel during Buoroscopy at percutaneous renal stone extraction. Acta. Radiologica 30:201-206; 1989. 6. Holmes, D.R.; Wondrow, M.A.; Gray, J.E.; Vetter, R.J.; Fellows, J.L.; Julsrud, P.R. Effect of pulsed progressive fluoroscopy on reduction of radiation dose in the cardiac catheterization laboratory. Am. Col. Cardiol. 15(1):159-162; 1990. 7. Vehmas, T.; Tikkanen, H. Measuring radiation during ,/percutaneous drainages: can shoulder dosemeters be used to estimate finger doses?. Brit. J. Radiol. 65(779):1007-1010; 1992. 8. Cagnon, C.H.; Benedict, S.H.; Mankovich. N.J.; Bushberg, J.T.: Seubert, J.A.; Whitina. J.S. Exnosure rates in hiah-levelcontrol fluoroscopy for imige enhancement. Radiol. 178643 646; 1991. 9. Food and Drug Administration: Advoidance of serious x-ray induced skin injuries to patients during fluoroscopically guided procedures. F.D.A. Pub. Health Advis. 30 September 1994. Reprinted in Cerebrovas. Surg. l(2), 34, 1995. 10. Boone, J.M.: Pfeiffer. D.E.: Strauss. K.J.: Rossi. R.P.: Lin. P.P.; Shepard, J.S.; Conway, B.J. A survey of tluoroscopic exposure rates: AAPM task group no. 11 report. Med. Phys. 20(3):789-794; 1993.
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11. Rudin, S.; Bednarek, D.R.; Miller, J.A. Dose reduction during fluoroscopic placement of feeding tubes. Radiol. 178(3):647651; 1991. 12. Rudin, S.; Bedaarek, D.R. Region of interest fluoroscopy. Med. Phys. 19(5):1183-1189; 1992. 13. Rowland, J.A.; Rieppo, P.M.; Ji, G. Region of interest fluoroscopy with dynamic filtering. RSNA 1993, paper #648. SUDD~to Radiol. 189(P):216: 1993. 14. Lab-be, M.S.; Chiu, ‘M.; R&sxotarski, MS.; Bani-Hashemi, A.R.; Wilson, D.L. The X-ray fovea, a device for reducing Xray dose in fluoroscopy. Med. Phys. 21(3):471-481; 1994. 15. Bedaarek, D.R.; Rudin, S. Modified bootstrap sensitometry in radiography. Opt. Eag. 20(2):271-274; 1981. 16. Bednarek, D.R.; Rudin, S.; Wong, R. Assessment of patient exposure for barium enema examinations. Invest&t. Radiol. 18(5):452-458; 1983. 17. Bronofski J. The Ascent of Man. Little, Brown aad Co., Boston, 1973, 176. 18. Rudin, S.; Bednarek, D.R.; Wong, R. Accurate characterixation of image intensifier distortion. Med. Phys. 18(6):11451151; 1991. 19. Yin, P.Y.; Chen, L.H. New method for ellipse detection by means of symmetry. J. Electron. Imag. 3(1):20-29; 1994. 20. Rudia, S.; Fletcher, L.M.; Bedaarek, D.R. Rapid selection of the image mask in Region of Interest Fluoroscopy. RSNA 1994, paper #1243c. Suppl to Radiol. 193(P):333; 1994. About the Author-LM. FLETCHER-HBATH received the B.S. in Imaging Science from the Rochester Institute of Technology, Roche&r;New York in 1992 and the M.S. in Biophysics from the State Universitv of New York at Buffalo in 1995. Her research interests are data analysis methods of medical images including segmentation algorithms. About the AU~~OF-STEPHIEN Rurn~ has been on the Faculty of the University at Buffalo (SUNY), School of Medicine and Biomedical Scinces since 1977 and is a Professor in the Departments of Radiology, Neurosurgery and Biophysical Sciences. He has been a practicing medical physicist since 1968 involved in all aspects of teaching and research in medical diagnostic imaging.Dr Rudia’s research interests have been in the fields of rapid sequence aad scanning beam radiology, digital imaging, computerized iastrumeatation, tele-radiography, radiation dose measurement and reduction and various other areas in radiological aad health physics. About the Author-DAraaL R. BEDNAREK received a PhD in Medical Physics from the Pritxker School of Medicine of the University of Chicago in 1978. He is currently aa Associate Professor of Radiology and Research Associate Professor of Biophysics and of Neurosurgery at the State University of New York at Buffalo.
March-April/l996,
Volume 20, Number 2
shape, however, it is impossible to allow only two points per ROI location. The minimum number of points . inside a diameter of this size, with four per triangle, is three. The results of this pattern are 0 expected to be higher than any pattern which can guarantee the two points desired for this search method. The total number of points (P) required to fill the FOV, where: D,=
distance between points, x-direction
and
D,, = distance between points, y-direction
p=(&)*(k) P=
(f) *;$)d*
5
n2 = 4’62 i?
Assume square inscribed into a circular ROI of diameter d The distance between points in each direction is seen best in this orientation where D, = D, = f To guarantee two points per possible ROI l location, a fifth point must be placed in the center of the circle. Unlike the triangular 0 shape, the square does allow a minumum of two points per ROI. The total number of points required to fill the FOV:
COMPARISON OF SEARCH PATTERN GEOMETRIES BY CALCULATION
Assuming a circular (diameter d) ROI with an inscribed equilateral triangle n = number of pixels in a row of column of the image then: height of triangle = f d + f d = i d side of triangle
= $d+$d=$d
Requiring at least two points per possible ROI location, a fourth point is needed in the center of the circle as shown above. Intrinsic to this geometric
Assume hexagon inscribed into a circular ROI of diameter d s = side of hexagon $ guarantee pain:’ per possible 2: location, only the six points are required. Intrinsic to the hexagonal shape, either no pixels are guaranteed to fall with in the circle (only if the
Image equalization of ROI fluoroscopic images L. M. FLETCHER ef al. l
hexagon size does not fit on or inside the circle) or at least two points are guaranteed to fall within each possible ROI position. Note: the hexagon is made up of six small equilateral triangles. D, = average of 4 and d = $ d D, = height of one small triangle
= &$
The total number FOV:
of points required
103
to fill the
Medical
Pergamon
Imaging Copyright
and Graphics, Vol. 20, No. 2, pp. 89403, 1996 0 1996 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0895-6111/96 $15.00 + .@I
PII: so895-6111(96)ooo28-6
METHOD FOR IMAGE EQUALIZATION OF ROI FLUOROSCOPIC IMAGES USING MASK LOCALIZATION, SELECTION AND SUBTRACTION
Lynn M. Fletcher, Stephen Rudin* and Daniel R. Bednarek Departments
of Biophysical Sciences and Radiology, State University of New York Medicine and Biomedical Sciences, Buffalo, NY 14215, USA (Received
25 October
at Buffalo,
School of
1995; revired 11 March 1996)
Iu regionof interest (ROI) iluoroscopy,a iilter is usedto drasticallyreducethe X-ray doseto the patient peripheral to an ROI, and masksubtractionis usedto equalizethe displayedimagebrlgbtness.Methods are describedfor an optimizedsearchto locate tbe ROI andselector constructa maskimageusinga descriptorlook up table (DLUT) basedon ROI size,relative ROI/peripbery brlgktuessaudROI shapeand orientation.After masksubtraction,the brightnessvaluesof tbe peripheryare comparableto thoseof tbe ROI provldlngfor equalizeddisplay.‘Ibis method was tested successfullyon 50 actual iluoroscopicimagesof two anthromorpldcphantoms.Tbe methodology developedfor real-time applicationswas succewhlly simulatediu PC code and full real-time implementationis underway.Copyright 0 19% ElsevierScienceLtd Key Words: Fluorosoopy, ROI fluoroscopy, Mask subtraction, Image equalization, LUT
BACKGROUND
Real-time image processing, Descriptor
temporal resolution can be sacrificed due to reduced frame rates. Removal of the grid reduces the image quality by allowing the recording of scattered radiation by the image receptor. Optical aperture enlargement increases noise throughout the image. The method of ROI fluoroscopy uses a beam attenuating filter to reduce the X-ray intensity in clinically less significant portions of the image, but leaves the ROI uneffected; thus, there is an increase in noise due to decreased quantum statistics only outside of the ROI. An image acquired with an ROI filter, if unprocessed, would appear bright in the ROI and dark in the periphery. It may be desirable to improve the appearance of the image by equalizing the displayed brightness between the ROI and the periphery using real-time image processing techniques. Since ROI fluoroscopy has been introduced by the authors, related efforts have been reported with a global image processing filtering method (13), and with an algorithmic mask technique designated as the X-ray fovea (14). Global filtering may greatly alter the image within the ROI and requires a large grey level transition region between the ROI and periphery. The ‘fovea’ method uses modeled equalization masks to preserve the ROI, and appears to offer excellent boundary matching, however, the feasibility of real-time implementation is unclear. A detailed discussion of how equalization can be accomplished in real-time ROI fluoroscopy using
AND INTRODUCTION
Fluoroscopic procedures, in general, result in much higher exposures to patients than do most types of radiographic procedures (1). Although some investigators have measured X-ray exposure levels which appear to be acceptable from a risk versus benefit perspective to patients and clinicians during fluoroscopic procedures (l+, there is continuing concern for the risks of deterministic and stochastic effects which may be associated with the exposure of X-rays (5-9). Additionally, the exposure rates can vary greatly between fluoroscopic systems (10) and between procedures. It is important to minimize examination doses whenever reasonably possible while the trade-offs between the amount of information desired from a procedure and the associated absorbed radiation dose continue to be examined. Methods to reduce fluoroscopic dose include the use of pulsed fluoroscopy (6), removal of anti-scatter grid, video camera optical aperture enlargement (1 l), and region of interest (ROI) fluoroscopy (12). Each method involves trade-offs. Pulsed progressive fluoroscopy can greatly reduce dose; however, *Correspondence should be addressed to Stephen Rudin, PhD, Division of Radiation Physics, State University of New York at Buffalo, Erie County Medical Center, 462 Grider Street, Buffalo, NY 14215, USA, Phone: (716) 898-3500; Fax: (716) 8985217; E-Mail: [email protected] 89
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Computerized Medical Imaging and Graphics
both empirical and algorithmic mask subtraction follows. The methodology includes finding the ROI, determining its size, finding an appropriate mask, digitally subtracting the mask from the fluoroscopic image, adding a constant to bring the brightness values into the display range, and finally displaying the equalized image. MATERIALS
AND
METHODS
Materials, image acquisition and storage A standard fluoroscopic unit (Philips Diagnost 66) with a 35 cm image intensifier was used in the 26 cm mode. The Philips video camera signal was sent to a Targa m8 (Truevision Inc., Indianapolis, IN) 8bit frame digitizer with 512 x 512 square pixels. The automatic gain control of the video camera was disengaged so the kVp and mA could be varied without causing the video gain to change. Various uniform gadolinium filters with circular apertures were placed on top of the collimator between the X-
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ray source and the patient table. Filters varied ir ROI diameter size due to the different application! for which ROI fluoroscopy can be used. Fifty images of two standard diagnostic phan toms (Alderson Diagnostic and 3M Pelvic) were digitized and remapped using the equation of tht video calibration curve in Fig. 1 which was obtainec using bootstrap sensitometry (15). All masks ant images were linearized using this curve so that the corrected pixel values were proportional to the logarithm of X-ray intensity incident to the II-videc camera combination. This had to be done for thi! general purpose Philips unit since only video camera: used specifically for digital subtraction angiograph! are commercially calibrated linearly to the log o exposure, yielding successful subtractions. Mask images with ROIs in the center of the fielc of view (FOV) were stored in a data base and listec in the first of two descriptor look-up tables (DLUT) These mask images were digitally averaged over lt video frames to reduce the effects of noise in the
1.6 1.4 1.2 1 0.8 0.6
0.5
1
1.5
2
2.5
Log (GL-33.6) Fig. 1. Calibration curve used to linearize all images to the logarithm of light intensity incident to the video camera. The data were fit to the following equation: log(exposure) = -0.600 + 0.939 * log(GL - 33.6) - 0.0318 * log(GL - 33.6)’ where GL corresponds to pixel grey level.
Image equalization of ROI fluoroscopic images L. M. FLETCHER et al. l
subtraction process. As filters with the same material thickness were positioned on the collimator, masks were obtained with various size ROI filter holes and differing magnifications which were determined by the position of the image intensifier with respect to the X-ray source; various differences in brightness between the ROI and the periphery were obtained by varying the kVp. By prerecording these masks any one of them could be easily and quickly chosen, then subtracted from the ROI fluoroscopic image. For off-center ROI applications a second set of masks was synthetically generated and stored in the second DLUT as elliptical ROIs which are to be added to an image of a uniformly filtered FOV. These small size, stored masks are only slightly larger than the size of the ROI and they are chosen from the DLUT based on size. Due to their small size, many masks may be stored in a small amount of memory. For this experiment, 71 masks with their longest dimensions ranging from 20 to 160 pixels were made available in DLUT 2 and are listed in Table 2. These masks will be used when the ROI is found off-center in the fluoroscopic image. Due to the constant elliptical distortion in the image field for this fluoroscopic unit (found by measuring the physical attributes of the field and 22 imaged ROIs in various locations of the field), all algorithmically derived ROIs used for this experiment were created to conform to the shape and rotation parameters required (0.35 eccentricity and 6 degree rotation). The full-size or composite mask is created by superimposing the chosen, algorithmically derived ROI onto an empirical image of the uniform gadolinium filter. All code was written, compiled and executed on a 486 computer in the C programming language and a flow chart of its function is shown in Fig. 2. With this code the ROI is found and its size and shape are determined, the appropriate mask is chosen and digitally subtracted from the fluoroscopic image, a constant is added to bring the brightness values into display range and the image is digitally stored in a frame buffer before it is displayed. This method of image equalization was motivated by the speed requirements of real-time fluoroscopy. The methodology was developed with the intention of direct application to a specific hardware architecture which will support real-time image manipulation. Detailed image processing methods Find the region of interest (ROI)
in the image.
Since the brightness as represented by pixel values is expected generally to be higher in the ROI than in the periphery, regions of the images may be
91
segmented from each other through the use, of a pixel value threshold. By sampling a geometrical pattern of pixels chosen for search efficiency, and comparing those pixel values with the threshold, the ROI can be located when pixel values are found to be above the threshold. However, if there are areas within the ROI with brightness values below the threshold, these pixels could be mistakenly identified as pixels in the periphery. The chances of this problem occurring are reduced using two techniques. First, a histogram, to be determined at the time of digitization, may be easily acquired. The histogram will display the actual quantities of pixels at each brightness value and will be determined automatically with the real-time hardware. The threshold will be chosen from the range of brightness values in the valley where there is minimum frequency of occurrence between the two groups of pixels. The group with higher brightness values represents the pixels in the ROI and the group with lower brightness values represents the pixels in the periphery. Any overlap between the two groups will add to the uncertainty of the choice of the threshold; however, overlap has been minimally detected in these experiments and has not been seen yet as a major concern. The additional, second method is by oversampling, or in our case, sampling such that there will be at least two sampled pixels for any potential ROI position. The geometric search pattern used is one of three possible regular and rotationally symmetric patterns available (17)-hexagonal, triangular or square, shown in Fig. 3. The hexagonal pattern was chosen since it can cover the greatest area with the least number of points and still guarantee two search points per possible ROI location (see Fig. 4 and Appendix). The hexagonal search pattern spirals outward beginning at the center of the field of view (FOV) since the ROI is expected to be closer to the center rather than the edges of the FOV. For each point checked against the threshold, determined by the histogram, it is decided by the program whether or not the ROI has been found. In the unlikely event that the ROI is not found, when one is known to exist, the threshold may be lowered and the search will be repeated. The coordinates for the search points are precalculated and stored in a file. The calculated distances between points are based on the lowest magnified ROI projection through each physical filter hole size (smallest X-ray source to II distance) and the intrinsic nature of the hexagonal pattern. There is one search list for each filter. The calculations are consistent with the guarantee of two sample points per possible ROI location. Once the filter has
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1. From DLUTI choose mask with closest size and AB
1. Rernapitnagethrough 2.
Yes/ a ’ Subtract mask from the image
2.
Choosesearchlist
-
constant to bring image values into viewing range
3. Add
ROI centered7
No\
From DLUT2 choose ROI mask with calculated size
1. Find avg. value of ROI Find avg. vahte of periphery 3.
1
I
Subtract2froml=AB + 1. Openandread in ROI mask
No
_:::::I[::::::: Openandread in Gd uniform field image
2.
Execute search
t
I-YeS
Is X or Y length more than 15% longer than other?
t
1. Calculate avg. in uniform field image in the required ROI position
calculateconstanttobeaddedto ROI (AD - uniform field spot avg.)
2.
NC
Find edges (x, Y lengths)
3. calculatecompositemask:
uniform field with ROI mask in area of image ROI t
Fig. 2. Flow chart describing method for image equalization including ROI search, mask selection, subtraction and display.
Image equalizationof ROI fluoroscopic images L. M. l
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Fig. 3. Search patterns based on rotational symmetry: (a) triangular, (b) square and (c) hexagonal. (c) also demonstrates the “spiralling” nature of the search, where the dotted lines show points of level increment becoming repetitive after the second increment.
been chosen, the proper such Cle is selected with the necessary search list. The search was implemented on 50 images of the two phantoms (Alderson and 3M Pelvic). In the modsed program for the real-time hardware, all files of search points will be preread into RAM during the initilization section of the program to save time during access. Find the edges of the ROI. Once the ROI has been found, the boundaries must be defined. Horizontal and vertical searches are utilized from the position of the first pixel found within the ROI. A search distance of */4 the smallest video ROI diameter for the ROI filter used is the edge search increment, which by definition is smaller than the true diameter. Searching by this increment outwardly, the direction is reversed as soon as the pixel value goes below the threshold. Then every
pixel is checked inwardly until the pixel value goes above the threshold again. Once the two edges have been found in the horizontal direction, the midpoint is calculated and the search proceeds on the vertical line of the midpoint in the same manner. After the midpoint is calculated on the vertical line, the search is repeated horizontally to con&m the placement of the ROI center and to get a better measurement of the ROI diameter. If the difference between the vertical diameter and the horizontal diameter is more than 15% (a value chosen to accommodate the elliptical and slightly rotated ROI shape known to exist as a result of video chain distortions) then it is assumed that a non-R01 pixel has been misclassified as an ROI pixel. The threshold can be raised and the full edge search repeated. Calculate the difference between periphery. An average value is calculated
ROI
and
inside the
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Hexagon
1200 1000 800 600 400 200
20
40
60
80
100
120
140
160
Pixel Diameter of Smallest ROI (two search inquiries) Fig. 4. Search method comparison demonstrates that the hexagonal pattern is more efficient, requiring less points to ensnre at least two search inquiries per possible ROI location. ROI from a box of pixel values and an average value outside the ROI is determined by the average brightness collected of all the previously interrogated search points outside the ROI (below the threshold but within the FOV). The difference between these two averages is the parameter delta brightness. These values are also calculated and indexed with all oncenter stored masks (DLUT 1 shown in Table 1). A delta brightness value is subsequently calculated for the incoming fluoroscopic image and used to select or create the appropriate mask for subtraction. Mask selection
Centered case. The appropriate mask is chosen based on the ROI size and delta brightness found above. The data base is accessed through the first DLUT, functioning as a search space (Table l), and a match is found for a mask with the same attributes, if not available exactly then a best match may be made for both size and delta brightness. Since closely matching the ROI size to minimize ring artifacts is
more important than matching the delta brightness, the decision for choosing a mask is more heavily weighted by size than delta brightness. A weighted choice occurs with calculations of minimum distances between available masks and surrounding characteristic values while weighting the importance of each characteristic with cr (Fig. 5). The search space is partitioned and each segment is bound with a range of values for each characteristic. Ranges of mask characteristic values are also predetermined so as the mask needed for subtraction is searched for in the partitioned space, the mask closest to the one needed is chosen automatically. The partitions of the space, in this case twodimensional segments, do not have to be symmetric, they must, however, each contain one mask and all possible mask choices must be represented. Non-centered case. If the location of the ROI is not in the center of the FOV, but found elsewhere, an appropriate mask is chosen from the second DLUT and a full size mask is created. This DLUT is also
Image
equalization
of ROI
fluoroscopic
images
l
L. M. FLETCHER
et
95
al.
Table 1. Descriptor look up table (DLUT) categorizesavailable maskimagesfor centeredROIs ROI major Mask
number
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
*For
Brightness difference (ROI -periphery)
axis (pixels)
of DLUT
number
‘I35 145 120 146 138 140 144 143 136 136 139 137 141 141 139 140 138 138 142 142 119 126 105 108 119
45 50 54 66 68 72 74 76 101 103 107 109 109 113 142 149 151 155 157 162 183 183 184 187 187
description
ROI major Mask
Brightness difference
axis (pixels)
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
(ROI-periphery)
187 189 190 190 192 192 193 196 196 196 199 200 201 201 204 204 204 211 211 211 218 218 218 227 228 228
129 129 109 118 119 129 104 105 117 127 118 127 105 113 105 116 123 105 118 124 104 115 122 127 103 117
usage see Fig. 4.
a.
b.
DLUT Diameter
Delta Brightness Delta Brightness
Mask 1
62
105
Mask 2
64
120
Mask 3
65
110
Mask 4
68
115
Mask 5 . . .
69 . . .
100 . . .
* 100
105
110
115
120...
. .
62 8 63 tif 64 a 65 66 67 68 69
Fig. 5. Pictorial demonstrationshowsthat as(a) masksare indexedin the DLUT, a minimumdistanceequation, weighted appropriately with 6, determines(b) the decisionboundariesfor maskselection.Therefore: DecisionBoundaries= MIN{[(l - U) * (d,,, - di)]’ + [cr* (AB,,, - ABi)]‘} where & =diameter of mask ROI, 4 = arbitrary diameter of ROI, A& = delta brightness of mask, ABi = arbitrary delta brightness.
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constructed as the partitioned search space above (Table 2). The masks listed in this DLUT are slightly elliptical in shape due to a small video chain distortion and have values of one inside the ROI and zero outside the ROI. All masks have been convolved with a Gaussian kernel to smooth the edges of the ROI simulating the 5-6 pixel wide edge on all fluoroscopic ROIs. The mask pixel values are no longer binary but are now stored as integer data between the values of 0 and 255. The chosen ROI mask is based on the largest measured ROI diameter, eccentricity and rotation angle. According to measurements and calculations, the eccentricities and rotation angles for all ROIs imaged with this Philips Diagnost 66 unit have had negligible differences. This allows for a more simplified model of the distorted ROI when creating a mask. It was possible to create all masks with different eccentricities and rotation angles; however, for this work it was only necessary to create ROIs with eccentricities of 0.35 and rotation angles of + 6 degrees from the vertical axis in order to characterize all ROIs imaged with this unit. Since image distortion is dependent on the image intensifier and video chain of each fluoroscopy imaging device, this analysis must be done for each unit used. Also, since very little distortion is present from the image intensifier in this case, the distortion was found to be constant and not position dependent. The mask is then created by effectively superimposing the small, ROI mask chosen onto the image with the uniform gadolinium filter. Mask subtraction. The brightness is enhanced in the periphery to match the ROI by subtracting the mask from the ROI fluoroscopic image. A constant
Table 2. DLUT 2 is used to categorize calculated ROI masks Major axis dimension
Elliptical eccentricity
ClOCkWiSe rotation
sm10356tga sm11356.tga sm12356.tga sm13356.tga sml14356.tga sm15356.tga sm16356tga sm17356.tga sm18356.tga sm19356.tga sm20356.tga
10 11 12 13 14 15 16 17 18 19 20
0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35
6 6
&0356.tga
80
0.35
k
ROI mask name
*Any variation of parameters can be applied fluoroscopic imaging system.
to a given
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determined by the average ROI image value of the mask is added to bring the brightness values into range (O-255). The subtracted image is then displayed. RESULTS
Table 3 shows a listing of all images included in the experiment described above. Also listed are the measured or actual ROI diameter, search diameter corresponding to the filter used, calculated ROI major axis, calculated ROI center, and the number of inquiries required to find each ROI. Threshold ranges were easily determined with the aid of a histogram for each image. A typical histogram is illustrated in Fig. 6 with its corresponding ROI image in Fig. 7. The histogram shows the distribution of pixels for each brightness value. The threshold can be chosen at the minimum between the two groups of pixels. There is a clear separation between groups in Fig. 6; therefore, the threshold for this image can range between values 110 and 130. Figure 7 is a single frame fluoroscopic image of the 3M pelvic phantom with an off-center ROI. The filter attenuates about 90% of the exposure in the periphery yielding a greatly reduced image intensity in the periphery. There is increased noise in the periphery due to reduced quantum statistics while the ROI image quality is preserved. An example of image equalization for the case where the ROI is found to be in the center of the FOV is displayed in Fig. 8. The single frame image with the ROI is in Fig. 8a while the closest size video mask shown in Fig. 8b was chosen from DLUT 1. The subtracted result is shown in Fig. 8c. Note the very small white ring around the ROI exhibiting a match which is not exactly the size of the image ROI. A search demonstration of an offcenter ROI image is shown in Fig. 9. The white dots indicate searched points which did not locate the ROI whereas the search point marked with the black dot found the ROI and then stopped searching. For this particular image the search required 27 queries before recognizing the ROI. With the real-time image processing hardware the search will be continuous, constantly compensating for new ROI sizes, positions and the difference in patient thickness. The process by which the composite mask was created is shown in Fig. 10. A uniformly filtered image, used as the base for the composite mask, Fig. lOa, is joined with the small mask of the closest size ROI, Fig. lob. The small mask is shifted to the proper location where all values are divided by 255 to obtain values between
Image Table Actual ROI diameter of filter (cm)
8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
0.704 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.588 1.588 1.588 1.588 0.704 0.704 0.704 0.704 0.704 0.704 0.704 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.008 1.27 1.27 1.27 1.27 1.27 1.27 1.27 1.27
3. Results
equalization
of ROI
of hexagonal Search diameter (smallest mag. of tilter ROI)
fluoroscopic
search,
images
algorithmic
Calculated ROI major axis
20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 50 50 50 50 50 50 50 50
34 88 75 76 81 55 49 52 54 68 45 45 61 68
N/A 101 100
N/A 97 45 43 42 45 49 47 45 58 64 55 61 54 32 76 82 40 79 73 63 68 76 86 74 95 84 86 70 101 108 105 101
l
L. M. FLETCHER
characterization
et al. and
97
subtraction
Calculated ROI center (row, column) 229,277 316,341 312,329 311,329 351,240 211,269 204,301 206.242 2181296 210,291 216.270 238;293 354,231 307.23 1 Complete ROI 248,278 248,278 Complete ROI 248,278 271,259 157,266 241.245 268;260 272,253 272.252 272;252 296,344 299,363 366,365 215.386 218;378 283,366 131,236 343,287 220.130 340;285 305,163 232,258 378,335 235.258 3451289 192,286 249.235 406;278 410,278 233,246 214,322 245.234 NO;174 196,171
# Search inquiries
not within
not within
‘Alderson phantom images (1-19) exhibit comparable results to tbc 3M pelvic phantom images (20-50). As the filter was changed to offer a different range of possible ROI sixes, a new search list was ac(‘Rssed as shown. center of the FOV and all calculated ROI centers indicate the distance from the center, tberefore, corresponding required to find the ROI.
0 and 1 then multiplied by the desired difference in brightness. Then the uniform image value of that pixel is added to the result of the previous multiplication. The result of this calculation is that everywhere where there was a 0 in the small mask, the original value of the uniform image is substituted; wherever there was a 1, the brightness
85 39 40 15 19 21 46 21 19 19 21 19 12 2 FOV 1 1 FOV 1 5 47 1 5 1 1 1 16 40 74 44 81 42 49 13 25 13 26 1 37 1 13 20 I 35 35 1 18 1 6 6
Coordinate (248,278) is the to the number of inquiries
difference is added to the uniform image value. Once completed, this full size mask is ready for subtraction from the fluoroscopic image (Fig. 1Oc). The images in Fig. 11 are ROI fluoroscopic images of the pelvic phantom before and after subtraction using the mask created in Fig. 10. Again it is clear that the image quality in the ROI
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j30.14 -4 5 0.12 5
0.1
1 0.08 ‘4 0.06 s % O-O4 ‘aj 0.02 ti 0
..............periphery
50
......... ROI _............................................................................~
100
.......................................... ..~.....................
150
250
Brightness Value Note: Periphery and ROI pixel quantities are not to the same scale. Fig. 6. Histogram used to find search threshold for the image in Fig. 7 shows the distribution of pixels for each brightness value.
of the subtracted image is preserved while the image quality in the periphery is degraded due to reduced photon statistics, or quantum mottle.
Fig. 7. Single frame fluoroscopic image of 3M pelvic phantom with an ROI off-center. The ROI pixels are bright compared to the pixels in the periphery thus they belong to the group of pixels with high brightness values in the histogram shown in Fig. 6. Similarly, the pixels in the periphery can be seen in the group with low pixel values.
DISCUSSION
The results of the experiment in Table 3 show that all ROIs were found with the hexagonal search pattern described above except for image numbers 15 and 18 of the Alderson phantom sequence. Tbis result was expected since these ROIs were not completely within the FOV, therefore not circular. Since the fluoroscopic images digitized from the Philips Diagnost unit all had the same distortion effects, this search algorithm was successfully implemented to expect a shape resembling a circle but allowing for a 15% difference between the two measured diameters. The allowance approximates the difference between the major and minor axis of the elliptical shape found in these images. On another imager the expectations might change and in that case the algorithm would need to be modified. Also, when the amount of distortion begins to depend on position, as it would with most image intensifiers where pin-cushion distortion increases further from the center (18), a more sophisticated approach will be required to characterize the specific shape of the ROI. It may be possible to employ an ellipse detection technique such as the one suggested by Yin and Chen (19) using the symmetry of the ellipse and only five points to characterize its five parameters. This, however, was obviously not necessary for these conditions since the Philips image intensiher
Image equalization of ROI fluoroscopic images l L. M. FLETCHBR et al.
99
Fig. 9. Demonstration of the hexagonal search patten as it locates an off-center ROI in a fluoroscopic image. White dots indicate the locations of search while the black dot indicates the search point which found the ROI.
Fii ;. 8. Mask subtraction using mask chosen from DLUT. (4 Single frame fluoroscopic image of 3M pelvic phantom Wil :h an ROI in the center of the FOV. (b) Video mask chchen from the DLUT, 10 averaged frames and matched fo1 . size and brightness difference. (c) ROI image corrected by subtracting mask in (b). Note the small artifactual ring around the ROI caused by an inexact match.
used in this study had one of the smallest pin-cushion distortions of image intensifiers commercially available (18). Thresholds for segmentation were successfully determined through a user-interfaced histogram acquisition program which prompted the user to enclose the ROI in a circle. These thresholds varied since the automatic brightness control was disabled and due to the content of each ROI. For most images no overlap was observed between the two regions as in the example Fig. 6 corresponding to the image in Fig. 7. However, there was a slight amount of overlap in three of the images which did not seem to affect the performance of the ROI search since they were all located. Overlap does indicate possible error in choosing the threshold, but the number of pixels in the overlap region are so few that they do not seem to be of major concern. The Datacube hardware architecture to be used in future ROI fluoroscopy implementation is capable of utilizing a non-user interfaced analysis which will calculate a single histogram with pixel quantities and brightness values for each image. It is anticipated that it will be easy to automatically lind the minimum between peaks in the histogram once it has been acquired. Once an appropriate threshold was selected the search was executed with the list of search points corresponding to the filter hole size. If the center of the ROI was found in the center of the FOV, a mask was chosen from DLUT 1. Figure 8a shows a typical image with a mask in the center of the FOV. The
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Fig. 10. A full size mask is created for an off-center ROI by joining (a) a uniformly f&red image and (b) a small mask consisting of an ROI chosen from a DLUT based on size, elliptical eccentricity and rotation angle. The composite, algorithmic mask (c) may be subtracted from the image for which it was created.
closest size mask chosen from DLUT 1 is shown in Fig. 8b and the subtracted result is shown in Fig. 8c. Note the very small white ring around the ROI in Fig. 8c exhibiting a match which is not exactly the size of the image ROI. A white ring is present when the ROI of the chosen mask is slightly smaller than the ROI of the fluoroscopic image. Conversely, a black ring is noticed when the chosen mask ROI is slightly larger than the ROI of the image. Either type of ring is expected when selecting a closest fit mask from the DLUT. Although the image field is nonuniform due to the Heel effect, inverse square law and X-ray II defects, mask subtraction corrects for these non-uniformities of the X-ray field. Also introduced after either subtraction is increased noise in the periphery due to reduced photon statistics and pixel quantitization from S-bit digitization. The latter problem should be reduced when the 1Zbit digitizer is in use with the Datacube hardware.
Fig. 11. Mask subtraction using mask created in Fig. 1Oc. (a) Single frame fluoroscopic image of the pelvic phantom to be equalized. (b) The corrected ROI image. Figure 9 is a demonstration of the search method on an image with an ROI off-center. Once the search has completed one full rotation the search distance is incremented outwardly at the upper left portion of the FOV. Clearly, the ROI was found with the first pixel that entered the ROI boundary or the 27* inquiry. This number is very small compared to the result of a loop test previously reported for a Datacube image processor used with a Sun Sparcstation 10 controller (20). The time required to retrieve any one pixel from video was found to be less than 12 ps. Therefore, 27 retrievals will take about 0.3 ms, which is much less than 33.3 ms, the time required to display one video frame. The time required for random retrievals should not be confused with the
Image equalization
of ROI fluoroscopic images l L. M. FLETCHER et al.
time required for image processing calculations to follow since these operations will be completed with pipeline processing which take place at much faster per pixel speeds. Since the ROI was found off-center, a full-size mask was created from the uniform image shown in Fig. 10a and the ROI mask shown in Fig. lob. The small ROI mask was translated to the calculated ROI position of the fluoroscopic image and superimposed, yielding the mask in Fig. 1Oc. This method of mask creation, although algorithmic, combines the empirical uniform image with the algorithmic ROI yielding a mask which, as in Fig. 8, removes the nonuniformities of the X-ray FOV mentioned above for the centered ROI case. The results of the subtraction are shown in Fig. 11 and are comparable to the subtractions of oncentered masks, indicating that the new mask creation method is successful. The one difference which can be seen in Fig. 1 lb compared to Fig. 8c is in the shading of the ring around the ROI. The ROI in Fig. 1lb has a ring which is half dark and half bright demonstrating a half-pixel error in the y-axis placement of the ROI in the mask. This error is minimal and difficult to correct when the ROI has an even dimension hence no one pixel on which to center the ROI. Also, a small variation in ROI dimension measurements has been seen while varying the search thresholds. Therefore, a nonoptimized threshold may cause some error in the dimension measurements, resulting in error with the mask selection or creation since this problem is independent of position. Again, this problem may be present but it does not appear to be a major concern as long as a reasonable mask is used leaving only a few pixel wide boundary between the ROI and the periphery. The true impact of these minor artifacts upon clinical procedures will require further detailed study; however, initial qualitative data indicates high tolerance of clinicians to this type of geometric artifact. SUMMARY A method was developed for ROI localization, mask selection and mask subtraction. It was then implemented via simulation code written for the PC intended for transfer to a SUN workstation interfacing with Datacube fast acquisition image hardware. The method was tested on 50 images and the results show that it was successfully implemented. All ROIs were found with fewer than 86 search points corresponding to 1.03 ms, except for the two noncircular ROIs which were partially outside the FOV. The maximum time for search on these images
101
should be 1 ms, which is less than one video frame time, using real-time image processors. Through this method fluoroscopic images may be equalized after the ROI attenuation filter is applied during ROI fluoroscopy. The reduction of exposure area product to the patient while using the ROI filter device ranges from 60 to 89% based on filter hole sixes between 40 and 150 pixels in diameter. The method of image equalization provides the fluoroscopist with images which have comparable levels of brightness in the ROI and the periphery. This method may be used whenever an increase in quantum noise in the periphery is acceptable such as during interventional procedures where the periphery is needed only for guidance or reference. Additionally, the methods described for a larger sized centered ROI appear to be applicable to a broad range of diagnostic fluoroscopic procedures.
work was supported in part by NIH
Acknowledgement-This
Grant No. ROlNS31883.
RETERENCXS 1. National Council on Radiation Protection, report 100. 31; 1989. 2. Lindsay, B.D.; Eichling, J.O.; Ambos, H.D.; Cain, M.E. Radiation exposure to patients and medical personnel during radiofrequency catheter ablation for supraventricular tachycardia. Am. J. Cardiol. 70:218-223; 1992. 3. Bergeron, P.; Carrier, R.; Roy, D.; Blabs, N.; Raymond, J. Radiation doses to patients in neurointerventional procedures. Am. J. Neurorad. 151809-1812; 1994. 4. Goldstone, K.E.; Wright, I.H.; Cohen, B. Radiation exposure to the hands of orthopaedic surgeons during procedures under fluoroscopic X-ray control. Brit. J. Radiol. 66(790):899-901; 1992. 5. Geterud, K.; Larsson, A.; Mattson, S. Radiation doses to patients and personnel during Buoroscopy at percutaneous renal stone extraction. Acta. Radiologica 30:201-206; 1989. 6. Holmes, D.R.; Wondrow, M.A.; Gray, J.E.; Vetter, R.J.; Fellows, J.L.; Julsrud, P.R. Effect of pulsed progressive fluoroscopy on reduction of radiation dose in the cardiac catheterization laboratory. Am. Col. Cardiol. 15(1):159-162; 1990. 7. Vehmas, T.; Tikkanen, H. Measuring radiation during ,/percutaneous drainages: can shoulder dosemeters be used to estimate finger doses?. Brit. J. Radiol. 65(779):1007-1010; 1992. 8. Cagnon, C.H.; Benedict, S.H.; Mankovich. N.J.; Bushberg, J.T.: Seubert, J.A.; Whitina. J.S. Exnosure rates in hiah-levelcontrol fluoroscopy for imige enhancement. Radiol. 178643 646; 1991. 9. Food and Drug Administration: Advoidance of serious x-ray induced skin injuries to patients during fluoroscopically guided procedures. F.D.A. Pub. Health Advis. 30 September 1994. Reprinted in Cerebrovas. Surg. l(2), 34, 1995. 10. Boone, J.M.: Pfeiffer. D.E.: Strauss. K.J.: Rossi. R.P.: Lin. P.P.; Shepard, J.S.; Conway, B.J. A survey of tluoroscopic exposure rates: AAPM task group no. 11 report. Med. Phys. 20(3):789-794; 1993.
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11. Rudin, S.; Bednarek, D.R.; Miller, J.A. Dose reduction during fluoroscopic placement of feeding tubes. Radiol. 178(3):647651; 1991. 12. Rudin, S.; Bedaarek, D.R. Region of interest fluoroscopy. Med. Phys. 19(5):1183-1189; 1992. 13. Rowland, J.A.; Rieppo, P.M.; Ji, G. Region of interest fluoroscopy with dynamic filtering. RSNA 1993, paper #648. SUDD~to Radiol. 189(P):216: 1993. 14. Lab-be, M.S.; Chiu, ‘M.; R&sxotarski, MS.; Bani-Hashemi, A.R.; Wilson, D.L. The X-ray fovea, a device for reducing Xray dose in fluoroscopy. Med. Phys. 21(3):471-481; 1994. 15. Bedaarek, D.R.; Rudin, S. Modified bootstrap sensitometry in radiography. Opt. Eag. 20(2):271-274; 1981. 16. Bednarek, D.R.; Rudin, S.; Wong, R. Assessment of patient exposure for barium enema examinations. Invest&t. Radiol. 18(5):452-458; 1983. 17. Bronofski J. The Ascent of Man. Little, Brown aad Co., Boston, 1973, 176. 18. Rudin, S.; Bednarek, D.R.; Wong, R. Accurate characterixation of image intensifier distortion. Med. Phys. 18(6):11451151; 1991. 19. Yin, P.Y.; Chen, L.H. New method for ellipse detection by means of symmetry. J. Electron. Imag. 3(1):20-29; 1994. 20. Rudia, S.; Fletcher, L.M.; Bedaarek, D.R. Rapid selection of the image mask in Region of Interest Fluoroscopy. RSNA 1994, paper #1243c. Suppl to Radiol. 193(P):333; 1994. About the Author-LM. FLETCHER-HBATH received the B.S. in Imaging Science from the Rochester Institute of Technology, Roche&r;New York in 1992 and the M.S. in Biophysics from the State Universitv of New York at Buffalo in 1995. Her research interests are data analysis methods of medical images including segmentation algorithms. About the AU~~OF-STEPHIEN Rurn~ has been on the Faculty of the University at Buffalo (SUNY), School of Medicine and Biomedical Scinces since 1977 and is a Professor in the Departments of Radiology, Neurosurgery and Biophysical Sciences. He has been a practicing medical physicist since 1968 involved in all aspects of teaching and research in medical diagnostic imaging.Dr Rudia’s research interests have been in the fields of rapid sequence aad scanning beam radiology, digital imaging, computerized iastrumeatation, tele-radiography, radiation dose measurement and reduction and various other areas in radiological aad health physics. About the Author-DAraaL R. BEDNAREK received a PhD in Medical Physics from the Pritxker School of Medicine of the University of Chicago in 1978. He is currently aa Associate Professor of Radiology and Research Associate Professor of Biophysics and of Neurosurgery at the State University of New York at Buffalo.
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shape, however, it is impossible to allow only two points per ROI location. The minimum number of points . inside a diameter of this size, with four per triangle, is three. The results of this pattern are 0 expected to be higher than any pattern which can guarantee the two points desired for this search method. The total number of points (P) required to fill the FOV, where: D,=
distance between points, x-direction
and
D,, = distance between points, y-direction
p=(&)*(k) P=
(f) *;$)d*
5
n2 = 4’62 i?
Assume square inscribed into a circular ROI of diameter d The distance between points in each direction is seen best in this orientation where D, = D, = f To guarantee two points per possible ROI l location, a fifth point must be placed in the center of the circle. Unlike the triangular 0 shape, the square does allow a minumum of two points per ROI. The total number of points required to fill the FOV:
COMPARISON OF SEARCH PATTERN GEOMETRIES BY CALCULATION
Assuming a circular (diameter d) ROI with an inscribed equilateral triangle n = number of pixels in a row of column of the image then: height of triangle = f d + f d = i d side of triangle
= $d+$d=$d
Requiring at least two points per possible ROI location, a fourth point is needed in the center of the circle as shown above. Intrinsic to this geometric
Assume hexagon inscribed into a circular ROI of diameter d s = side of hexagon $ guarantee pain:’ per possible 2: location, only the six points are required. Intrinsic to the hexagonal shape, either no pixels are guaranteed to fall with in the circle (only if the
Image equalization of ROI fluoroscopic images L. M. FLETCHER ef al. l
hexagon size does not fit on or inside the circle) or at least two points are guaranteed to fall within each possible ROI position. Note: the hexagon is made up of six small equilateral triangles. D, = average of 4 and d = $ d D, = height of one small triangle
= &$
The total number FOV:
of points required
103
to fill the