Development and application of a three-dimensional artificial visual system

Section III MEDICAL IMAGING

Computer Methods and Programs in Biomedicine 22 (1986) 69-77

69

Elsevier CPB 00751

Development and application of a three-dimensional artificial visual system J a m e s M. C o g g i n s

1,2, F r e d r i c

S. F a y 2 a n d K e v i n E. F o g a r t y 2

r Computer Science Department, Worcester Polytechnic Institute, Worcester, MA 01609 and 2 Biomedical Imaging Group, Department of Physiology, University of Massachusetts Medical School 55 Lake Avenue North, Worcester, MA 01605, U.S.A.

A three-dimensional artificial visual system has been developed to aid in the analysis of 3-D fluorescence images of smooth muscle cells. The system consists of three sets of 3-D spatial filters that decompose the image to enable a simple recombination algorithm to locate the discrete bodies of protein concentration in a cell, classify the concentration bodies as globular or oval, and determine the 3-D orientation of the oval bodies. A graphic model of the protein concentration is created from the data provided by the artificial visual system. Patterns of organization in the distribution of the protein bodies are investigated using an interactive graphics system. Computer vision Interactive computer graphics Image analysis Fluorescence digital imaging microscopy Three-dimensional imagery

1. Introduction

2. Smooth muscle cells

Image processing, pattern recognition and computer graphics techniques have been c o m b i n e d with immunocytochemistry and fluorescence microscopy to provide a powerful new tool for analysis of cellular and subcellular structures, including the distributions of molecules within a single cell. This paper describes an artificial visual system (AVS) that is used to create a graphics model of the distribution of a protein (a-actinin) within a single smooth muscle cell. This paper will present an overview of the biological problem of interest, after which the AVS and the three-dimensional interactive graphics system will be described. We will present a progress report on the project and discuss other potential biomedical applications of the AVS.

The contractile mechanism in striated muscle cells is fairly well understood; strands of proteins (actin and myosin) are anchored by structures called z-disks that are rich in the protein a-actinin. During contraction, the protein strands slide relative to each other, exerting force against .'the z-disks and thereby contracting the cell [1]. The contractile mechanism of smooth muscle cells is not well understood. S m o o t h muscle cells lack the striations and z-disks of striated muscle cells, but do contain discrete bodies rich in aactinin and strands of myosin and actin. These proteins are presumed to interact in smooth muscle cells as they interact in striated muscle cells [2,3], but this notion has not been verified, partly because of the difficulty of identifying long-range structural patterns in the placement of the aactinin bodies, which do not appear to be ordered in any two-dimensional image [4,5].

0169-2607/86/$03.50 © 1986 Elsevier Science Publishers B.V. (Biomedical Division)

70 We do know, however, that a-actinin is distributed through the cell in two types of discrete bodies of concentration: irregular plaques attached to the cell membrane, and small oblong bodies in the cytoplasm. Some fluorescence images suggest that the oblong dense bodies occur in regular strands twisting through the cell in three dimensions. Since these bodies apparently serve to anchor filaments of actin along the lines of force in the cell, the positions and orientations of the a-actinin bodies provide cues regarding how force is generated and transmitted through the cell. Some dense bodies are visible in electron micrographs, but the images do not provide enough information to discern long-range three-dimensional organization [4]. Also, the cells must be fixed before making electron micrographs, and we would like to develop an imaging method that could be used on living cells. The a-actinin dense bodies can be imaged in either living or fixed cells by using fluorescence digital imaging microscopy [6]. Fluorescencelabelled antibodies specific to a-actinin are introduced into the cell and then fluorescence images are acquired. Three-dimensional information is obtained by optical sectioning. The three-dimensional image data is preprocessed to minimize image noise, nonuniformities in the optical system's gain, and distortion due to the optical system [7]. The problem now is to locate in the three-dimensional image all of the a-actinin dense bodies a n d to determine the orientation of the oblong bodies. In the imaging system we have developed, the oblong dense bodies are one pixel wide and about five pixels tong (corresponding to a width of 0.25/~m and a length of 1.25/~m). The long axes of oblong bodies have been observed to lie within 30 ° of the long axis of relaxed cells [7]. Attempts to locate and determine orientations of the bodies by visual inspection of the image planes proved impractical because of the large number of bodies and because of the difficulty of correlating traces of obliquely oriented bodies through multiple image planes in the presence of noise and distortion. A smudge in one plane could indicate a dense body, an out-of-focus structure from a nearby image plane, or a 'hot spot' of fluorescence unrelated to the dense bodies being

sought. Nevertheless, one cell was manually processed, giving positions and limited orientation data on the bodies. The data was used to create a rotating graphic model viewable from a fixed point in space [7], but it proved too awkward for the level of interaction desired. Stereo images created by solid modelling of the 3-D image proved too abstract for stereopsis to be effective, and occlusion of data was a serious problem [7]. We then committed to developing an artificial visual system to simplify the image data and harness interactive graphics capabilities for the physiological analysis.

3. A three-dimensional visual system

Recent insights into the operation of early stages of the human visual system suggest that the visual system decomposes a stimulus image into a series of quasi-independent spatial frequency channels [8-11]. The information separated by the channels is then recombined to begin stereopsis and the interpretation of the image. This insight has suggested a class of procedures that are amenable to comprter implementation based on spatial filtering [12-16]. An 'artificial visual system' is a set of spatial filters and a recombination algorithm that maps the filter outputs into a representation space [12]. The mapping of a stimulus into the representation space can then be operated upon using standard pattern recognition tools [12,17]. Mappings of image regions to an abstract feature space have been applied previously for image segmentation based on heuristic feature measurements on local areas of an image [18,19]. In the smooth;muscle study, the filter design reflects the a priori knowledge concerning the expected orientation and sizes of the dense bodies as well as the uncertainty in that knowledge and the measurement precision desired. Incorporating this knowledge into the filter design makes the AVS filters more sensitive and specific, so fewer filters can be used than would be required in a more generalized, unguided analysis. The AVS perceives the dense bodies in three dimensions, so that all image information relating to a dense body can be analyzed in a single step. No intermediate steps

71

are necessary to correlate two-dimensional traces from different image planes (as is necessary when the images are analyzed by human observers). Thus, the three-dimensional AVS is based on principles underlying human vision but extends those principles beyond their implementation in the human visual system.

of each point (x, y, z) are obtained by the following equations:

R ( x , y, z ) = s q r t ( x 2 + y2 + z 2) O(x,y,z)=90

if y = 0

= arctan(sqrt(x 2 + y2 )/i 4. Filter definitions

The filters making up the AVS are created in the spatial domain by integrating weighting functions that depend on the representation of image points in spherical coordinates. The spherical coordinates

y t)

otherwise ~(x, y , z ) = 9 0 =270

ifx=0andz>=0 ifx=0andz<0

= arctan(z/x)

otherwise.

Fig. 1. Schematic diagram of AVS filters. This diagram gives an intuitive sense of the shapes of the filters, although the intensity of the real filters fades away gradually, unlike the sharp borders of the models. A, The R series filters locate the dense bodies and provide a measurement of the length of the bodies. The responses of the rest of the filters are examined only at the locations of local m a x i m u m responses to the R filters. B, The T-series filters measure the declination angle of the bodies. C, The P series filters measure the azimuth angle of the bodies.

72 Notice that the 0 function reflects points with negative y coordinates about the x-z plane so the range of the 0 function is 0 to 90 °. The range of the q~ function is 0 to 360 °. The weighting functions are defined as follows: W R ( x , y , z; r ) = l

i f R ( x , y, z)~
= m a x ( 0 , 1 - ( R ( x , y, x ) - r ) ) otherwise W T ( x , y, z; t ) =

max(O,1- [lO(x, y, z)-t[/lO]) W T l ( x , y , z; t ) = l

if0(x,y,

z)<~t

= WT(x, y, z; t)

otherwise

W P ( x , y, z; p ) =

max(0,1- [[q,(x, y, z)-p[/60]) Now we use the weighting functions to define the filters. RI(x, R2(x, R3(x, R4(x,

y, y, y, y,

z) = WR(x, z) = WR(x, z) = WR(x, z) = WR(x,

y, y, y, y,

z; 1.5)z; 2.5)" z; 3.5)" z; 4.5)"

WTI(x, WTI(x, WTI(x, WTI(x,

y, y, y, y,

z; z; z; z;

Tl(x, T2(x, T3(x, T4(x, T5(x, T6(x,

y, y, y, y, y, y,

z ) = R4(x, z ) = R4(x, z) = R4(x, z ) = R4(x, z) = R4(x, z ) = R4(x,

y, y, y, y, y, y,

z). z). z)" z). z). z).

WT(x, WT(x, WT(x, WT(x, WT(x, WT(x,

y, y, y, y, y, y,

z; z; z; z; z; z;

O) 10) 20) 30) 40) 50)

Pl(x, P2(x, P3(x, P4(x, P5(x, P6(x,

y, y, y, y, y, y,

z ) = R4(x, z) = R4(x, z ) = R4(x, z ) = R4(x, z ) = R4(x, z ) = R4(x,

y, y, y, y, y, y,

z). z). z). z). z). z).

WP(x, WP(x, WP(x, WP(x, WP(x, WP(x,

y, y, y, y, y, y,

z; z; z; z; z; z;

O) 60) 120) 180) 240) 300)

50) 50) 50) 50)

The R filters resemble truncated cones (Fig. 1A) and are used to locate the dense bodies in space. When the image is convolved with these

filters, locally maximum responses.occur whenever a maximum volume of a dense body is inside the filter's volume. Of course, the filters respond to objects other than the bodies we seek, but since the oblong bodies are symmetrical and oriented within 30 ° of the y axis in our image, the local maxima in the filtered images include the center points of the oblong bodies, plus some noise and responses to the irregular plaques. Most of the noise maxima are eliminated by thresholding; filter responses to the organized light sources representing protein concentrations are always much higher than responses to random noise phenomena. Another type of noise maximum occurs when an R-filter overlaps two separate bodies that are close together; the local maximum is located in the empty region between the bodies. This case is eliminated by rejecting maxima that do not have corresponding maxima in all smaller R filters. The orientation of the oblong bodies (in terms of the angles 0 and q,) and the identification of the plaques are determined by the T series and P series filters. The filters are designed based on the principle that a stimulus value can be located along a continuum by a suitable set of overlapping filters [20]. Both the T and P series filters are constructed by subdividing filter R4 into overlapping filters whose sum is filter R4. The T series filters (Fig. 1B) determines the declination angle, 0, between the long axis of the cell (which we arranged to coincide with the y axis of the image) and the long axis of the body and resemble overlapping 'hollow cones' whose intensity falls off linearly from the center orientation. The P series (Fig. 1C) determines the azimuthal angle, q~, and resemble wedge-shaped sections cut from filter R4.

5. Procedure

Several steps are performed during and after image acquisition to minimize noise and distortion in the image, including an iterative, constrained restoration procedure which partially corrects for distortion introduced by the imaging system's optics (for details, see [7]). Next, we convolve the filters with the enhanced three-dimensional fluorescence image. The filters partition the image information

73 a l o n g the R, 0, a n d ¢ dimensions. W e will now specify the r e c o m b i n a t i o n a l g o r i t h m that c o m pletes the analysis of the image. C o n c e n t r a t i o n b o d i e s are l o c a t e d b y analysis of the responses to the R filters. Local m a x i m a are identified a n d t h r e s h o l d e d at the m e a n intensity of all of the local m a x i m a in each channel. Since n o n u n i f o r m i t i e s in the intensity of fluorescence within a b o d y can affect slightly the location of the local m a x i m u m , m a x i m a in different filtered images at c o r r e s p o n d i n g o r a d j a c e n t l o c a t i o n s are c o n s i d e r e d together. A n estimate of the size of the b o d y is p r o v i d e d b y the sequence of m a x i m u m intensities from all of the R channels: the intensity of the m a x i m a increase with the filter size until the filter is larger t h a n the dense b o d y . T h e size o f the largest filter whose response intensity is still increasing is the e s t i m a t e of the size of the b o d y . T o d e t e r m i n e the o r i e n t a t i o n of the bodies, we m a p each b o d y into a 12-dimensional feature space where the features are the responses ( n o r m a l i z e d b y the response o f the largest a c c e p t e d R filter) of

93°

~°

2

the T a n d P series filters at the l o c a t i o n o f the b o d y as d e t e r m i n e d above. W e have s t u d i e d this feature space extensively using an artificial i m a g e c o n t a i n i n g m o d e l b o d i e s s a m p l i n g the range of relevant sizes a n d o r i e n t a t i o n s for the cell study. Since the test b o d i e s are generated from a regular s a m p l i n g of the 0 a n d ep angles relevant to the dense bodies, the filter responses to these b o d i e s are o r d e r e d a n d can b e used to w a r p the feature space to m a k e a n o r m a l E u c l i d e a n distance m e t r i c serve as a m e a s u r e of the closeness of bodies, or even to m a k e possible a direct m e a s u r e m e n t of the 0 a n d ¢ values of a b o d y using angles a n d distances in the w a r p e d space. I n o r d e r to m a k e the s t u d y of m o d e l images c o m p a r a b l e to real cell images, the artificial i m a g e was d i s t o r t e d using an e m p i r i c a l estimate of the p o i n t s p r e a d function of the i m a g i n g system [7] a n d a n a l y z e d using the AVS. Since two p a r a m e t e r s d e t e r m i n e the p a t t e r n of the test bodies, a n d these two p a r a m e t e r s are exactly the m e a s u r e m e n t s m a d e b y the A V S filters, we sought a t w o - d i m e n s i o n a l

9

0

Fig. 2. Projection of model bodies onto a plane. This is a 2-D projection of the 6-D data derived from the responses of the P series filters to a set of model bodies. The model bodies have 0 angles of 0, 5, 10, 15, 20, 25 and 30°. For each 0 value except 0, there are bodies with ~b angles of 0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300 and 330°. A, The model bodies map onto concentric ovals, where larger ovals correspond to larger 0 values, q, = 0 ° is to the right with larger angles proceeding counterclockwise. The projection is not circular due to image distortions that cause the filter components in the 90 and 270° directions (vertical in the diagram) to be less sensitive than the 0 and 180° directions (horizontal). B, Boosting the 90 and 270° responses yields a nearly circular pattern so that measurements of distance and angle in this feature space accurately represent the orientations of the bodies. Interactions between 0 and 'k enable the 0 angle to be deduced from the output of the qb filters alone.

74 plane onto which the points could be projected. One such plane is determined by the points corresponding to bodies at the following orientations (expressed as (0, ~) ordered pairs): (0,0), (5.0), (5,90). The residual image distortion, which decreases the sensitivity of the filters in the direction of the distortion (~ = 90 and ~ = 270), causes the projection to be flattened (Fig. 2A). By boosting the responses in those directions, we obtain a planar projection in which the bodies map into points on concentric circles: the radius of the circle indicates the 8 angle of the body, and the orientation of a point from a reference vector indicates the ~ angle of the body (Fig. 2B). This relationship is caused primarily by the interdependence of ~ and 0 measurements. As the 8 angle

increases, the ~ preference of a~ body is more pronounced, leading to a stronger response in the filters and thus a circle of larger radius. Thus, by warping the feature space to counteract the known image distortion, we can measure the 8 and values directly in terms of distances and angles between points in the feature space. We are continuing to refine this feature space in further studies involving modifications to the filters as well as additional warping of the feature space.

6. Interactive graphics model When the artificial visual system is applied to a real cell, the (x, y, z) positions of all of the a-

Fig. 3. Computer graphics images of a real cell. The data extracted by the artificial visual system is used to create a simplifiedimage using computer graphics techniques. The graphic model can be examined from (A) the viewpoint of the microscope, or (B) the viewpoint can be moved into the cell, enabling 3-D interaction in order to study long-range structural patterns.

75 actinin bodies and the (0, ~) orientations of the oblong bodies are recorded. A graphic model is then constructed in which the irregular blobs are represented as spheres at the appropriate locations, and the oblong bodies are represented as oblong structures with the position and orientation as determined by the artificial visual system from the cell data. The graphic images are created by mathematically projecting a prototype sphere or oblong body into the location and orientation in space where a real dense body was found and then applying a viewing transformation. The resulting figure (if it is inside the viewing volume) is shaded using a cosine shading algorithm and sent to a three-dimensional graphics system that performs polygon filling and handles superposition using a z-buffer algorithm (for graphics algorithms, see [21]). Fig. 3 shows two images of the graphic model. The viewpoint of Fig. 3A is similar to that of the microscope, but the graphic image is not affected by blurring or depth-of-field limitations. Using the graphic model, dramatic images can be produced from viewpoints corresponding to locations inside the cell as shown in Fig. 3B. Such images allow examination of the long-range patterns of dense bodies from vantage points that are entirely impractical when working with real cells. Also, the graphic images can be examined without interference from noise or optical distortions. Interaction with the graphic model is provided by a three-dimensional cursor in the form of a wire-frame arrow. A three-dimensional joystick provides control of the cursor's roll, pitch, yaw, and three-axis translation. The closest body to the cursor can be marked for reference by changing its color. Using colors to mark different strands, we can follow the t~-actinin strands through the cell and record the patterns obtained. The three-dimensional cursor can be reoriented to point along the direction of the currently marked body. The view of the cell can also be regenerated with a new viewpoint corresponding to the position and orientation of either the cursor or a body. Thus, we can change our viewpoint to sight along a particular body to find the next body in its strand.

7. Project status

We are currently refining the AVS by creating new filters from weighted sums of cylinders. Since the cylinder is a better approximation to the shape of a dense body than a line, the resulting filters should be better-tuned to the dense bodies and less prone to spurious extremes. Preliminary tests of cylinder-based filters support this hypothesis. We are also testing whether the residual optical system distortion can be decreased by stretching the filters themselves in the direction of the distortion, thereby incorporating knowledge of the distortion into the AVS itself. We are also refining the pattern-recognition techniques for interpreting the orientation of the oblong bodies. The point spread function of the optical system is not symmetrical, so the planar projection is not exactly circular. We are attempting to compensate for the aberration in order to improve the projection. We are also testing the robustness of the AVS by adding noise to the restored images and observing the degradation of the orientation estimates. The graphics system is complete and ready for production work when the AVS refinements are complete. We will incorporate an array processor into the graphics system when production is ready to begin.

8. Discussion

The filter-based AVS has proven particularly useful due to several properties of the filtering approach, as follows: (1) Spatial filtering is intuitively understandable, so filters appropriate for quantifying various continua can be created easily. (2) A priori knowledge can be effectively incorporated into the design of the filters and the recombination algorithm. (3) Since the AVS characteristics are determined mainly by the filters, experiments may be performed with a minimum of reprogramming and algorithm development. In addition, since a few simple algorithms suffice for much of the processing requirements, special devices

76 such as array processors can be brought to bear to enhance the speed of execution. (4) Fast algorithms exist for performing spatial filtering. These algorithms are amenable to parallel processing to enhance execution speeds. (5) The most important property of spatial filtering is that a suitably constructed ensemble of filters can be used to decompose an image along any of several continua (e.g. size, orientation, spatial frequency, shape, etc.) [20]. Thus, the ensemble of filters in a visual system can be constructed so as to define a meaningful feature space [12]

9. Applications to other medical imagery The three-dimensional artificial visual system can be applied to other forms of three-dimensional medical imagery. The filters must be redesigned to embody different objectives and different a priori knowledge concerning the objects under study, and a recombination algorithm must be developed for the particular analysis required. For example, a three-dimensional visual system could prove very useful in analyzing nuclear medicine imagery. In nuclear medicine, the images are often very coarse and noisy. Detection of structures in a body through separate analysis of two-dimensional sections can be very difficult. An abnormality that is below the detection threshold for human observers in two-dimensional sections can become clearly detectable if the images of the abnormality in several image planes can reinforce each other. A three-dimensional visual system can make detection decisions based on the entire three-dimensional image structure, resulting in enhanced sensitivity for detecting abnormalities in three dimensions. The three-dimensional visual system can also be used to identify known structures, making image registrations and interpretations easier. Identification of known structures can enhance confidence and speed in making diagnostic judgements from ultrasound or CT images. Filter-based AVSs can also be applied to twodimensional images. Two-dimensional filter sets

are easier to define and less expensive in storage and computing time than three-dimensional filter sets, thus a more complete sampling of the continua of interest can be performed in two dimensions with a corresponding increase in sensitivity and reliability of the results. Cell classification and cell counting present immediate possibilities for applications. For cell detection, only the approximate apparent size of the target cells needs to be specified and incorporated into the filter set. Cell differentiation by size, profile, color or internal visual texture are all possible with the filtering framework. Heuristic approaches to cell image analysis have been reported [e.g. 22-24], but these involve highly idiosyncratic algorithms which must be completely redesigned for any new application or variation in the problem.

10. Conclusion An AVS has been developed to locate protein bodies in fluorescence micrographs of smooth muscle cells. The results obtained have been used to create an interactive graphic model portraying the protein distribution in the cell. These capabilities have provided new tools for analysis of the contractile mechanism of smooth muscle. The problem solved by the AVS involved identification of small objects in a noisy, distorted three-dimensional image. The success obtained in this difficult application suggests that filter-based visual systems could prove valuable in other image interpretation tasks in two or three dimensions. The flexibility and comprehensibility of filter-based visual systems could prove to be of great value in a number of important clinical and research applications.

Acknowledgement This work was supported in part by grants from the NIH (HL14523) and the Muscular Dystrophy Association of America. We also wish to acknowledge equipment grants from Digital Equipment Corporation, Lexidata Corporation, and Analogics

77 Incorporated. WPI Computer Science students S u s a n A b r a m s o n a n d E l i z a b e t h P h a l e n m a d e sign i f i c a n t c o n t r i b u t i o n s to the d e v e l o p m e n t o f the i n t e r a c t i v e g r a p h i c s system. T h i s a r t i c l e is b a s e d o n ' D e v e l o p m e n t a n d A p plication of a Three-Dimensional Artificial Visual S y s t e m ' b y J a m e s M. C o g g i n s , W o r c e s t e r P o l y t e c h n i c I n s t i t u t e , K e v i n E. F o g a r t y a n d F r e d r i c S. Fay, University of Massachusetts Medical School, W o r c e s t e r , M A a p p e a r i n g in Ninth Annual Sym-

posium on Computer Applications in Medical Care,, B a l t i m o r e , M D , N o v e m b e r 1 0 - 1 3 , 1985, pp. 686. © 1985 I E E E .

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