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An automatic method for colon segmentation in CT colonography
Computerized Medical Imaging and Graphics 33 (2009) 325–331
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Computerized Medical Imaging and Graphics journal homepage: www.elsevier.com/locate/compmedimag
An automatic method for colon segmentation in CT colonography Alberto Bert a,∗ , Ivan Dmitriev b,1 , Silvano Agliozzo a,2 , Natalia Pietrosemoli b,1 , Mark Mandelkern c,3 , Teresa Gallo d,4 , Daniele Regge d,4 a
im3D S.p.A. Medical Imaging Lab, Via Lessolo 3, 10153 Torino, Italy Institute for Scientific Interchange Foundation, Viale S. Severo 65, 10133 Torino, Italy c Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USA d Institute for Cancer Research and Treatment, Strada Provinciale 142 km 3,95, 10060 Candiolo, Torino, Italy b
a r t i c l e
i n f o
Article history: Received 5 July 2006 Received in revised form 15 January 2009 Accepted 23 February 2009 Keywords: CT colonography Colon cancer Segmentation CAD
a b s t r a c t An automatic method for the segmentation of the colonic wall is proposed for abdominal computed tomography (CT) of the cleansed and air-inflated colon. This multistage approach uses an adaptive 3D region-growing algorithm, with a self-adjusting growing condition depending on local variations of the intensity at the air-tissue boundary. The method was evaluated using retrospectively collected CT scans based on visual segmentation of the colon by expert radiologists. This evaluation showed that the procedure identifies 97% of the colon segments, representing 99.8% of the colon surface, and accurately replicates the anatomical profile of the colonic wall. The parameter settings and performance of the method are relatively independent of the scanner and acquisition conditions. The method is intended for application to the computer-aided detection of polyps in CT colonography. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Colon cancer currently ranks as the third leading cause of cancer-related deaths in the world [1]. Most colorectal cancers arise from initially adenomatous polyps, and studies show that early detection and removal of colonic polyps can reduce the risk of colon cancer, thus decreasing the mortality rate [2]. Unfortunately, conventional methods for the detection of colonic polyps are invasive and uncomfortable and have associated morbidity [3–5]. Computed tomographic colonography (CTC) or virtual colonoscopy has emerged as a potential alternative screening method for colonic polyps and masses [6]. It combines helical CT scanning of the abdomen with visualization tools for non-invasive assessment of the colonic mucosa. However, the interpretation of CTC exams is time-consuming and the accuracy of polyp detection may depend on the display methods adopted [7].
∗ Corresponding author. Tel.: +39 011 1950 8773; fax: +39 011 1950 8968. E-mail addresses: [email protected] (A. Bert), [email protected] (I. Dmitriev), [email protected] (S. Agliozzo), [email protected] (N. Pietrosemoli), [email protected] (M. Mandelkern), [email protected] (T. Gallo), [email protected] (D. Regge). 1 Tel.: +39 011 660 3090; fax: +39 011 660 0049. 2 Tel.: +39 011 1950 8773; fax: +39 011 1950 8968. 3 Tel.: +1 949 824 6944; fax: +1 949 824 2174. 4 Tel.: +39 011 993 3111; fax: +39 011 993 3225. 0895-6111/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compmedimag.2009.02.004
In recent years, computer-aided diagnosis (CAD) systems have been proposed in order to overcome the drawbacks of CTC [8,9]. The aim of CAD systems is to automatically detect polyps and masses, and to provide the locations of suspicious regions of the colon. Radiologists can thus focus on a reduced number of small areas, while quickly surveying the larger portion of the colon. The drastic reduction of the time required for interpretation will increase throughput and may improve diagnostic performance. The processing required for CAD usually includes a segmentation step dedicated to the extraction of the colon from the CT dataset. This step precedes colonic wall characterization, and strongly affects overall CAD performance. Both semi- and fully automated colon segmentation algorithms have been proposed [8,10–16,19–23]. Automatic approaches generally use a combination of tissue classification and knowledgeguided region growing. Classification methods include simple thresholding [12–14] and principal component analysis [15]. Thresholding, morphological operations, and connected component analysis are used in [16,19,20]. A centerline-based method was adopted by [21]. Deformable models have also been applied to colon segmentation [22,23]. In this work, a multistage method for the extraction of the colon surface is reported. First the air surrounding the body and contained in the lungs is masked, by replacing the corresponding CT data with out-of-range values. Three-dimensional region growing is then performed, automatically locating seed points without using prior knowledge of the colon geometry. The region-growing process
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uses a self-adjusting growth condition, which changes according to the local variation of the intensity at the air-tissue boundary. We adopted this technique in order to obtain a more accurate segmented colon surface than that obtainable using a global threshold and also to obtain a significant saving in computation time compared to methods employing deformable models [23]. A partial and preliminary version of this work was presented previously [24]. 2. Material Thirty CT colonography cases were retrospectively randomly collected from CT colonography examinations at the Institute for the Cancer Research and Treatment, Candiolo, Torino, Italy. Bowel cleansing was performed in all cases by oral administration of 4 l of a commercially available polyethylene glycolelectrolyte solution, approximately 12 h before the examination. A 40 mg intravenous bolus of hyoscine-n-butyl bromide (Buscopan, Boehringer Ingelman; Paris, France) was administered immediately prior to beginning CTC in order to reduce peristaltic artifacts, intestinal motility and spasms. Colon distension was obtained by the introduction of room air through a rectal tube with a balloon connected to a pump by a valve mechanism. Air was introduced by manual compression, and insufflation was interrupted when the patient complained of abdominal tension, generally after 1.5 l of insufflated air. A CT s cout examination of the abdomen and pelvis was then acquired to assess the degree of colon distension, and additional air was insufflated if required. The scans extend from the lower chest just above the diaphragm to below the anus, so the top 25 mm of each scan contains lung tissue. Data were collected with two different machines: a CT scanner HighSpeed CT/i (GE Medical Systems, Milwaukee, Wisconsin, USA) and a LightSpeed 16 scanner (GE Medical Systems, Milwaukee, Wisconsin, USA). The first of these is a single-slice scanner and the following parameters were used: slice collimation 5 mm, kVp 120, current 120 mA and pitch 2 mm. The second is a 16 slice scanner, used with slice collimation of 1.25 mm, kVp 120, current 80 mA and pitch 1.375 mm. While the in-plane matrix is always 512 × 512 pixels, different inter-slice distances (ranging from 0.6 to 2.0 mm) and orientations (prone, supine) were selected in order to have a wide range of different conditions. The algorithm was implemented in the ANSI standard C++ programming language [25], so that it can be executed under operating systems like GNU/Linux and Microsoft Windows. Computation was performed on a Intel Pentium IV 2.8 GHz CPU running GNU/Linux, and the program was compiled using GNU gcc. 3. The segmentation scheme The segmentation scheme consists of three stages: (1) external segmentation, which masks air outside the body surface, (2) lung segmentation, which masks air in the lungs, and (3) colon segmentation, which extracts colon segments. As part of the development of the algorithm, the 30 scans were reviewed independently by two radiologists with substantial CTC expertise, who were asked to identify colon segments in the original transaxial images. This input was used to set thresholds used to distinguish colon from non-colon segments and to evaluate the accuracy of the algorithm as described below. Both radiologists agreed on the identification of 64 segments. 3.1. External segmentation The first stage of the segmentation algorithm recognizes and masks the air surrounding the body of the subject, referred to here
Fig. 1. Normalized histogram of the volume dataset in the range of CT values between T0 and 200 HU. Maxima of air (T0 , −700 HU) and fat (−300, 0 HU) values are marked with circles. Te (equal to − 541 HU in this case) is also shown.
as the e xternal air. This segmentation is performed in two steps. The first is a thresholding procedure and the second is a 3D regiongrowing process to mask the external air remaining after the first step. Lower and upper CT threshold values, T0 and Te , are used for both steps. T0 is the lowest possible CT value, − 1000 Hounsfield unit (HU) and Te is derived from the histogram of the CT volume as the average of the maxima of CT air values (ranging between T0 and −700 HU) and CT fat values (ranging between − 300 and 0 HU) [16]. Fig. 1 shows an example, for which Te is equal to −541 HU. Once T0 and Te are defined, the first step of the external air segmentation is performed as follows. In thresholding algorithms, the image is scanned, and all voxel with values between two thresholds are masked. In our case, starting from the top of the image, rows are scanned in the left-to-right direction, and values between T0 and Te , i.e. air values, are masked. However, unlike traditional thresholding, when a value higher than Te is found in a certain row, i.e. the body surface is reached, the scan stops. In those cases a second scan is started in the same row, from the right side of the image (right-to-left direction), in order to mask the air at the right of the body. All points where the scans reach the body and stop are collected in order to be used as seeds for the second step. An example of the output of the algorithm is shown in Fig. 2(b). Unlike the traditional thresholding algorithm, this approach does not consider all the voxels of the image. The air contained in the body and a small part of the external air are not taken into account at all (see Fig. 2(b)). The missed external air is segmented by 3D region growing (by six-neighbor voxel connectivity) in the second segmentation step, starting from the seeds produced by the first step and using T0 and Te as lower and upper thresholds. At the end of the described thresholding step of this external segmentation stage, the air component of the histogram is drastically decreased (see Figs. 1 and 3), and is mostly composed of air in the lungs and bowel. 3.2. Lung segmentation Lung tissue was always present in the first 25 mm of the scan (Section 2). The associated histogram, reported in Fig. 4, shows a single air peak attributable to the lungs. The same component, marked with a circle in Fig. 3, is found in the histogram of the whole dataset. The CT value at that peak, called Tl , is used in the lung segmentation stage as follows. All voxels lying in the first slice, having CT values between T0 and Tl , are taken as seeds for 3D region growing and are applied to the full data set. Region growing is performed using T0 and Tl as lower and upper thresholds. Voxels belonging to the extracted segments
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Fig. 2. Output of the first (b) and the second (c) steps of the external air segmentation on an example slice (a). The segmented air is marked with an out-of-range value (visible as white), while the unsegmented air keeps its original values (visible as black).
are masked by setting them to a CT value out of the normal range. In case the colon lumen is included in the first slice of the dataset, seeds are placed also in the colon air, which causes colon segments to be extracted. To identify colon segments, we use the parameter s pecific area, s. Specific area is defined as the ratio between the number of surface voxels to that of volume voxels of a segment, and it is an alternative to sphericity to expresses the compactness of shape. Due to the irregular shape of air spaces in the lung, lung segments usually have much larger s than (tube-like) colon segments. Segments having s smaller than a threshold, Ls , are classified as non-lung, and unmasked. Ls was empirically determined as follows:
first we calculated the s value for the segments found by the lung segmentation stage and for the colon segments identified by the radiologists; then we set Ls to the average between the minimum lung s and the maximum colon s. Fig. 5 shows how the s distributions of lung and colon segments are separated by the threshold Ls , which resulted to be equal to 0.3.
Fig. 3. Normalized histogram of the volume dataset taken after the external segmentation, with CT values ranging between T0 and 200 HU. The peak corresponding to the lung air is marked with a circle.
Fig. 4. Normalized histogram of CT values for slices containing lung tissue (the first 25 mm axially), after external segmentation. Tl is the CT value of the air (T0 , −700 HU) peak and is equal to −876 HU in this case.
3.3. Colon segmentation Once external and lung air are masked, the colon segments can be identified. First, a new histogram of the volume dataset is
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Fig. 7. Histogram reported in Fig. 6 zoomed in the CT value range of T0 and Tl HU. In the reported case m, Tc and Ts (also shown) are equal to −955, − 906 and −979 HU, respectively.
Fig. 5. s distribution of colon and lung segments. Each distribution is individually normalized to one, in order to represent both of them on the same scale. Note how the discrimination value, Ls , clearly separates lung from colon tissue.
calculated (see Fig. 6); now CT values ranging between T0 and Tl correspond to the air contained in the colon and in the small bowel. This range is shown in detail in Fig. 7 and is referred to as the bowel component of the histogram. The seed threshold is defined as Ts = m − , where m and are respectively the mean and standard deviation of the bowel component (see Fig. 7). The whole dataset is scanned, and voxels having CT values between T0 and Ts are selected as seeds for the subsequent 3D 6-connected breadth-first region-growing process [17,18]. The lower and upper thresholds of the region-growing are T0 and Tc , respectively, where Tc = m + 2. During the region-growing process, when a voxel V, with a CT value higher than Tc , is found, a new threshold defining the colon surface, Ta , is calculated based on the local CT values of the colon wall, as follows. A ray of length l mm is projected forward from V along the direction from which V was reached, and the maximum CT value of the ray, Mr , is identified. If Mr is lower than a threshold, Tw , we assume that the ray does not intersect a wall, where Tw = m + 4. All voxels touched by the ray are classified as air voxels, and the region-growing process is continued. If Mr is higher than Tw , the value of the local surface threshold is incremented by the fraction
Fig. 6. Normalized histogram of the volume dataset with CT values ranging between T0 and 200 HU, taken after the lung segmentation. In this example Tl and Tm (peak of muscular tissue) are equal to − 876 and 46 HU, respectively.
q of the difference between Mr and Tc , i.e. Ta = Tc + q(Mr − Tc ). The first voxel of the ray having CT value higher than Ta is classified as a surface voxel. The region-growing process is then continued. The set of surface voxels so found constitutes the one-voxel-thick surface of a segment. If the ray is sufficiently long, and if there are dense structures (like bones) close to the colonic wall, Mr might be artificially high, compromising the surface definition. In order to avoid this behavior, an upper bound Tm for Mr is defined as the CT value of the muscle peak, seen as the maximum of the histogram between 0 and 200 HU (see Fig. 6). Together with colon segments, several segments of small bowel and lung may be extracted in this stage. However, most of these segments can be distinguished using specific area, s, and segment volume, v. The small bowel is generally neither well inflated by the air, nor well cleansed, resulting in small segments with high specific area. As demonstrated above, lung segments have very high specific area. Fig. 8 gives the scatterplot of v vs. s for colon and non-colon segments, as identified by the radiologists (see Section 3). An enlargement of the lower left area of the graph is shown as an
Fig. 8. Specific area (s) and volume (v, in mm3 ) of segments extracted by the colonsegmentation stage. Colon and non-colon segments, as identified by the radiologists, are represented by crosses and circles, respectively. The lower left corner of the figure is expanded, and the average of the threshold values, Ds and Dv , are shown with dashed lines (0.36 and 11,633 mm3 , respectively).
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inset. The figure shows that colon and non-colon segments (represented by crosses and circles, respectively) lie in well-defined areas, allowing us to distinguish them in the s-v space. We determined discrimination thresholds for s and v (Ds and Dv , respectively) in order to classify and remove the non-colon segments. To determine Ds and Dv , we split the thirty scans into two groups of 20 and 10 scans, here referred to as the training and testing sets. Segments with s < Ds and v > Dv are classified as colon. As a cross-validation procedure, the splitting of the data was performed three times, rotating the scans in the two sets. For each splitting, Ds and Dv were chosen in order to minimize the number of misclassified segments in the training set, and then applied to the testing set. Fig. 8 contains a scatterplot of v vs. s, where, for illustrative purposes, the averages of the three values of Ds and Dv are shown as dashed lines. An approach similar to our use of a ray in this stage was suggested by Wyatt et al. for the electronic cleansing of the colon prepared with tagging agents [13]. 4. Results and discussion 4.1. External segmentation The external segmentation is effective with rare exceptions. One of these is when, because of poor positioning or an inadequate field of view, part of the colon is not fully contained in the field making colon air appear contiguous with external air. In this case, as a result, part of the colon is masked during the external segmentation. An alternate method for external segmentation is based on region growing starting from the corners of the volume, as proposed in [13]. We implemented and tested this alternative, and our approach obtains exactly the same result approximately 11 times faster. Since the external air segmentation is the most computationally intensive stage of the segmentation scheme, this outcome is particularly significant. 4.2. Lung segmentation An example of lung segmentation is reported in Fig. 9. The first slice of the dataset is shown before (left) and after (right) segmentation, and the extracted air is shown as white. As explained in Section 3.2, the segmentation is performed using region growing with Tl as the upper bound. The way thresholds for region-growing are determined is similar to that employed by Näppi et al. [19]. We observed that in cases where sections of the colonic wall are very close to the lungs, setting Tl too high can cause the lung segment to invade the colonic lumen. The choice of Tl as the peak value of the lung-CT histogram makes it low enough to avoid colon
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invasion. This strategy might cause some parts of the lungs to be left unmasked. However, segments containing lung tissue found in the subsequent colon-segmentation stage are readily discarded based on their large values of specific area s as described in Section 3.3. The s distributions of lung and colon segments are well separated (Fig. 5). Only three colon segments have s higher than the lowest observed lung s value, and these correspond to cases affected by movement artifacts. 4.3. Colon segmentation The values of the thresholds used in the colon-segmentation stage are empirically chosen, according to the role they play in the algorithm (Section 3.3). For example, Tc , the upper threshold of the region-growing step, must be low enough to avoid penetration of the relatively low-density surfaces delimiting the colonic lumen, such as thin walls and haustra. However, during the empirical search for optimal values, we observed that deviations within a few percents from the optimal values do not significantly compromise the segmentation results, i.e. no visible defects are introduced in the reconstructed surface. Detection of the colonic surface is determined by Ta , which is an adaptive threshold, defined according to the CT values of the local colonic wall. The local character of Ta prevents, for example, the generation of holes in thin surfaces like haustra during the surfacedetection step. At the same time, it makes possible the drawing of a surface profile close to the real wall when dense structures are close to the colon. The parameters l and q are used to determine the local Ta and thus influence the quality of the resulting surface. l is the length of the ray along which the profile of the CT values of the colonic wall is obtained. This ray must be long enough to penetrate the tissue surrounding the colonic lumen, and the optimal l was empirically found to be 7 mm. The value of q determines the placement of the surface voxels in the transition region at the air-tissue boundary of the colonic wall, where small q places the surface near the lumen. We have found that the resulting surface does not depend critically on the actual value of q; in the present case q = 0.1 The quality of the surface obtained with a local threshold approach shows a marked improvement over surfaces generated by procedures based on the use of a global threshold. After triangulation this surface can be effectively used for the 3D visualization of the colon. Fig. 10 shows the 3D rendering of two examples of segmented colon. The segments extracted by the colon-segmentation stage include a small number of extraneous segments derived from the small bowel and lung. We refer to these segments as non-colon findings. As described above, the thresholds Dv and Ds were used to
Fig. 9. Output of the lung segmentation (b) on the first slice of a sample case (a). The extracted air is marked with an out-of-range value (visible as white).
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Fig. 10. Examples of the 3D rendering of the colon segmented by our algorithm. In case (a) all the non-colon air-filled structures of the scan were successfully identified and discarded; while in (b) we show a case where two non-colon segments were misidentified.
classify and remove these extraneous segments. These thresholds were validated by splitting the data into training sets and testing sets in three different ways. The results of the classification are reported in Table 1. The algorithm correctly classified 62 out of 64 colon segments (97%) yielding 99.8% of the colon surface and 300 of 329 non-colon segments (91%), yielding a misclassified noncolonic surface area equal to 6.3% of that of the colon. The results are consistent for the three splittings. All large colon segments were recognized and the two missed ones represent 0.1% and 0.4% of the colon area, respectively. Nearly all false positives derive from the small bowel; because the small bowel is not well-cleansed and not well-insufflated, these segments are especially prone to false-positive findings. Among the segments found and rejected in this stage are large lung segments with v > 3 × 105 mm3 (see Fig. 8), which are missed by the lung-extraction stage because they are not connected to the first slice, where the seeds for region growing are placed (Section 3.2). The overall algorithm would not be affected by the use of fecal tagging, since we neither consider nor process the region of CT values corresponding to tagged feces. Thus electronic cleansing, facilitated by using contrast agents, can either precede or follow segmentation [26]. Our results compare favorably with the results of [19], where 98% of the colonic surface was recognized and 10–15% of the segmented surface was extra-colonic, and the results of [13], where agreement between automatic and manual segmentation was reported
as 40–80%. Iordanescu et al. [14] report that 83% of the cases segmented completely and 10% segmented partially, out of 292 cases. With calculations based on the number of segmented colon voxels, Frimmel et al. [21] reported a sensitivity of 97% out of 38 CTC datasets. Li and Santago [20], combining prone and supine scans, obtained an average colon coverage of 88%, out of 100 datasets. In all cases the results of the automatic algorithms are compared with those obtained by expert radiologists performing manual selection of colon segments.
Table 1 Performance of the classification method on the testing sets. For each splitting of the scans, we report the optimal classification parameters Ds and Dv , the number of colon segments classified correctly (true positives, TP), the corresponding percentage of recognized colon surface (RCS), the number of non-colon segments classified correctly (true negatives, TN), and the ratio of the surface of the misclassified non-colon segments (false positives) to that of the colon surface, expressed as a percentage (EFM). The average values of the three splittings are also reported.
5. Conclusions
Ds Dv (mm3 ) TP RCS (%) TN EFM (%)
Splitting 1
Splitting 2
Splitting 3
Average
0.365 11,000 20/21 99.9 97/112 8.6
0.360 11,000 26/27 99.6 130/140 7.2
0.360 12,900 16/16 100 73/77 3.1
62/64 (97%) 99.8 300/329 (91%) 6.3
4.4. Computational efficiency The overall segmentation takes less than 4 s for low resolution scans, and less than 9 s for the scans acquired by the multi-slice scanner (see Section 2). In particular, the procedure for external air segmentation, which is the most computationally intensive stage of the segmentation scheme, is faster than that described in [13] by a factor 10. The computation time of our algorithm compares favorably with the fastest segmentation algorithms reported in the literature to date [14,21]. The allocated RAM memory corresponds to the size of the whole dataset, approximately 100 MB for the GE CT/i and approximately 300 MB for the GE Light Speed 16. The data structures created by the algorithm are less than 30 MB.
We described a novel automatic colon-segmentation method for CT colonography, intended for application to the computer-aided detection of colorectal polyps. First, the air surrounding the body and contained in the lungs were automatically recognized and masked. 3D region growing using a self-adjusting stopping criterion was then performed, starting from automatically placed seeds, without preprocessing or using any prior knowledge of colon geometry. The distinctive local character of the region-growing process prevented the generation of holes in thin walls, while ensuring a surface profile close to that of the actual tissue. Colon segments were distinguished from other air-filled structures by means of their size and specific area.
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The algorithm was developed using 30 retrospectively collected CT datasets (either prone or supine scan), and tested by comparison with the blind review of two expert radiologists. We recognized 99.8% of the colonic surface. Findings misclassified as colon amounted to 6% of the colonic surface. The method is computationally efficient. The overall segmentation takes 9 s for high resolution data on an Intel Pentium IV 2.8 GHz CPU. As a next step, our algorithm will be tested with a larger number of cases, including exams prepared with tagging agents, and inserted in the CAD system currently being developed by our group. 6. Summary Colon cancer currently ranks as the third leading cause of cancer-related deaths in the world. Most colorectal cancers arise from adenomatous polyps. Studies show that early detection and removal of colonic polyps can reduce the risk of colon cancer, thus decreasing the mortality rate. Computed tomographic colonography (CTC) has emerged as a promising screening method for colonic polyps and masses. In recent years, computer-aided diagnosis (CAD) systems have been proposed in order to improve the performance of CTC. The aim of CAD systems is to automatically detect polyps and masses, and to provide the locations of suspicious regions of the colon. The processing required for CAD includes a segmentation step that extracts the colon. Most previous colon-segmentation algorithms are based on user-defined seed points, from which extraction of the colonic volume is started. An automatic method for segmentation of the colonic wall was proposed for abdominal computed tomography (CT) of the cleansed and air-inflated colon. First, the air surrounding the body and contained in the lungs is automatically recognized and masked. Then, 3D region growing using a self-adjusting stopping criterion was performed, starting from automatically placed seeds, without preprocessing or using any prior knowledge of colon geometry. The distinctive local character of the region-growing process prevents the generation of holes in thin walls, while ensuring a surface profile close to that of the actual tissue. Colon segments were distinguished from other air-filled structures by means of their size and specific area. The method was evaluated using retrospectively collected CT scans based on visual segmentation of the colon by expert radiologists. This evaluation showed that the procedure identifies 97% of the colon segments representing 99.8% of the colon surface. The parameter settings and performance of the method are relatively independent of the scanner used and acquisition conditions. The method is computationally efficient. The overall segmentation takes 9 s for high resolution data on an Intel Pentium IV 2.8 GHz CPU.
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Acknowledgment This work has been partially founded by MIUR (CNR Sezione Oncologia, legge 449/97–99) and Fondazione CRT. References [1] World Health Organization Fact sheet N.297, July 2008. http://www.who.int/ mediacentre/factsheets/fs297/en/.
Silvano Agliozzo is a researcher at im3D S.p.A. Medical Imaging Lab, Torino, Italy. Natalia Pietrosemoli is a researcher at ISI, Torino, Italy. Mark Mandelkern is a professor of physics at the University of California, Irvine, Irvine, CA, USA. Teresa Gallo is a radiologist at the IRCC, Candiolo, Torino, Italy. Daniele Regge is the Director of the Radiology Unit at the IRCC, Candiolo, Torino, Italy.
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Computerized Medical Imaging and Graphics journal homepage: www.elsevier.com/locate/compmedimag
An automatic method for colon segmentation in CT colonography Alberto Bert a,∗ , Ivan Dmitriev b,1 , Silvano Agliozzo a,2 , Natalia Pietrosemoli b,1 , Mark Mandelkern c,3 , Teresa Gallo d,4 , Daniele Regge d,4 a
im3D S.p.A. Medical Imaging Lab, Via Lessolo 3, 10153 Torino, Italy Institute for Scientific Interchange Foundation, Viale S. Severo 65, 10133 Torino, Italy c Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USA d Institute for Cancer Research and Treatment, Strada Provinciale 142 km 3,95, 10060 Candiolo, Torino, Italy b
a r t i c l e
i n f o
Article history: Received 5 July 2006 Received in revised form 15 January 2009 Accepted 23 February 2009 Keywords: CT colonography Colon cancer Segmentation CAD
a b s t r a c t An automatic method for the segmentation of the colonic wall is proposed for abdominal computed tomography (CT) of the cleansed and air-inflated colon. This multistage approach uses an adaptive 3D region-growing algorithm, with a self-adjusting growing condition depending on local variations of the intensity at the air-tissue boundary. The method was evaluated using retrospectively collected CT scans based on visual segmentation of the colon by expert radiologists. This evaluation showed that the procedure identifies 97% of the colon segments, representing 99.8% of the colon surface, and accurately replicates the anatomical profile of the colonic wall. The parameter settings and performance of the method are relatively independent of the scanner and acquisition conditions. The method is intended for application to the computer-aided detection of polyps in CT colonography. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Colon cancer currently ranks as the third leading cause of cancer-related deaths in the world [1]. Most colorectal cancers arise from initially adenomatous polyps, and studies show that early detection and removal of colonic polyps can reduce the risk of colon cancer, thus decreasing the mortality rate [2]. Unfortunately, conventional methods for the detection of colonic polyps are invasive and uncomfortable and have associated morbidity [3–5]. Computed tomographic colonography (CTC) or virtual colonoscopy has emerged as a potential alternative screening method for colonic polyps and masses [6]. It combines helical CT scanning of the abdomen with visualization tools for non-invasive assessment of the colonic mucosa. However, the interpretation of CTC exams is time-consuming and the accuracy of polyp detection may depend on the display methods adopted [7].
∗ Corresponding author. Tel.: +39 011 1950 8773; fax: +39 011 1950 8968. E-mail addresses: [email protected] (A. Bert), [email protected] (I. Dmitriev), [email protected] (S. Agliozzo), [email protected] (N. Pietrosemoli), [email protected] (M. Mandelkern), [email protected] (T. Gallo), [email protected] (D. Regge). 1 Tel.: +39 011 660 3090; fax: +39 011 660 0049. 2 Tel.: +39 011 1950 8773; fax: +39 011 1950 8968. 3 Tel.: +1 949 824 6944; fax: +1 949 824 2174. 4 Tel.: +39 011 993 3111; fax: +39 011 993 3225. 0895-6111/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compmedimag.2009.02.004
In recent years, computer-aided diagnosis (CAD) systems have been proposed in order to overcome the drawbacks of CTC [8,9]. The aim of CAD systems is to automatically detect polyps and masses, and to provide the locations of suspicious regions of the colon. Radiologists can thus focus on a reduced number of small areas, while quickly surveying the larger portion of the colon. The drastic reduction of the time required for interpretation will increase throughput and may improve diagnostic performance. The processing required for CAD usually includes a segmentation step dedicated to the extraction of the colon from the CT dataset. This step precedes colonic wall characterization, and strongly affects overall CAD performance. Both semi- and fully automated colon segmentation algorithms have been proposed [8,10–16,19–23]. Automatic approaches generally use a combination of tissue classification and knowledgeguided region growing. Classification methods include simple thresholding [12–14] and principal component analysis [15]. Thresholding, morphological operations, and connected component analysis are used in [16,19,20]. A centerline-based method was adopted by [21]. Deformable models have also been applied to colon segmentation [22,23]. In this work, a multistage method for the extraction of the colon surface is reported. First the air surrounding the body and contained in the lungs is masked, by replacing the corresponding CT data with out-of-range values. Three-dimensional region growing is then performed, automatically locating seed points without using prior knowledge of the colon geometry. The region-growing process
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uses a self-adjusting growth condition, which changes according to the local variation of the intensity at the air-tissue boundary. We adopted this technique in order to obtain a more accurate segmented colon surface than that obtainable using a global threshold and also to obtain a significant saving in computation time compared to methods employing deformable models [23]. A partial and preliminary version of this work was presented previously [24]. 2. Material Thirty CT colonography cases were retrospectively randomly collected from CT colonography examinations at the Institute for the Cancer Research and Treatment, Candiolo, Torino, Italy. Bowel cleansing was performed in all cases by oral administration of 4 l of a commercially available polyethylene glycolelectrolyte solution, approximately 12 h before the examination. A 40 mg intravenous bolus of hyoscine-n-butyl bromide (Buscopan, Boehringer Ingelman; Paris, France) was administered immediately prior to beginning CTC in order to reduce peristaltic artifacts, intestinal motility and spasms. Colon distension was obtained by the introduction of room air through a rectal tube with a balloon connected to a pump by a valve mechanism. Air was introduced by manual compression, and insufflation was interrupted when the patient complained of abdominal tension, generally after 1.5 l of insufflated air. A CT s cout examination of the abdomen and pelvis was then acquired to assess the degree of colon distension, and additional air was insufflated if required. The scans extend from the lower chest just above the diaphragm to below the anus, so the top 25 mm of each scan contains lung tissue. Data were collected with two different machines: a CT scanner HighSpeed CT/i (GE Medical Systems, Milwaukee, Wisconsin, USA) and a LightSpeed 16 scanner (GE Medical Systems, Milwaukee, Wisconsin, USA). The first of these is a single-slice scanner and the following parameters were used: slice collimation 5 mm, kVp 120, current 120 mA and pitch 2 mm. The second is a 16 slice scanner, used with slice collimation of 1.25 mm, kVp 120, current 80 mA and pitch 1.375 mm. While the in-plane matrix is always 512 × 512 pixels, different inter-slice distances (ranging from 0.6 to 2.0 mm) and orientations (prone, supine) were selected in order to have a wide range of different conditions. The algorithm was implemented in the ANSI standard C++ programming language [25], so that it can be executed under operating systems like GNU/Linux and Microsoft Windows. Computation was performed on a Intel Pentium IV 2.8 GHz CPU running GNU/Linux, and the program was compiled using GNU gcc. 3. The segmentation scheme The segmentation scheme consists of three stages: (1) external segmentation, which masks air outside the body surface, (2) lung segmentation, which masks air in the lungs, and (3) colon segmentation, which extracts colon segments. As part of the development of the algorithm, the 30 scans were reviewed independently by two radiologists with substantial CTC expertise, who were asked to identify colon segments in the original transaxial images. This input was used to set thresholds used to distinguish colon from non-colon segments and to evaluate the accuracy of the algorithm as described below. Both radiologists agreed on the identification of 64 segments. 3.1. External segmentation The first stage of the segmentation algorithm recognizes and masks the air surrounding the body of the subject, referred to here
Fig. 1. Normalized histogram of the volume dataset in the range of CT values between T0 and 200 HU. Maxima of air (T0 , −700 HU) and fat (−300, 0 HU) values are marked with circles. Te (equal to − 541 HU in this case) is also shown.
as the e xternal air. This segmentation is performed in two steps. The first is a thresholding procedure and the second is a 3D regiongrowing process to mask the external air remaining after the first step. Lower and upper CT threshold values, T0 and Te , are used for both steps. T0 is the lowest possible CT value, − 1000 Hounsfield unit (HU) and Te is derived from the histogram of the CT volume as the average of the maxima of CT air values (ranging between T0 and −700 HU) and CT fat values (ranging between − 300 and 0 HU) [16]. Fig. 1 shows an example, for which Te is equal to −541 HU. Once T0 and Te are defined, the first step of the external air segmentation is performed as follows. In thresholding algorithms, the image is scanned, and all voxel with values between two thresholds are masked. In our case, starting from the top of the image, rows are scanned in the left-to-right direction, and values between T0 and Te , i.e. air values, are masked. However, unlike traditional thresholding, when a value higher than Te is found in a certain row, i.e. the body surface is reached, the scan stops. In those cases a second scan is started in the same row, from the right side of the image (right-to-left direction), in order to mask the air at the right of the body. All points where the scans reach the body and stop are collected in order to be used as seeds for the second step. An example of the output of the algorithm is shown in Fig. 2(b). Unlike the traditional thresholding algorithm, this approach does not consider all the voxels of the image. The air contained in the body and a small part of the external air are not taken into account at all (see Fig. 2(b)). The missed external air is segmented by 3D region growing (by six-neighbor voxel connectivity) in the second segmentation step, starting from the seeds produced by the first step and using T0 and Te as lower and upper thresholds. At the end of the described thresholding step of this external segmentation stage, the air component of the histogram is drastically decreased (see Figs. 1 and 3), and is mostly composed of air in the lungs and bowel. 3.2. Lung segmentation Lung tissue was always present in the first 25 mm of the scan (Section 2). The associated histogram, reported in Fig. 4, shows a single air peak attributable to the lungs. The same component, marked with a circle in Fig. 3, is found in the histogram of the whole dataset. The CT value at that peak, called Tl , is used in the lung segmentation stage as follows. All voxels lying in the first slice, having CT values between T0 and Tl , are taken as seeds for 3D region growing and are applied to the full data set. Region growing is performed using T0 and Tl as lower and upper thresholds. Voxels belonging to the extracted segments
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Fig. 2. Output of the first (b) and the second (c) steps of the external air segmentation on an example slice (a). The segmented air is marked with an out-of-range value (visible as white), while the unsegmented air keeps its original values (visible as black).
are masked by setting them to a CT value out of the normal range. In case the colon lumen is included in the first slice of the dataset, seeds are placed also in the colon air, which causes colon segments to be extracted. To identify colon segments, we use the parameter s pecific area, s. Specific area is defined as the ratio between the number of surface voxels to that of volume voxels of a segment, and it is an alternative to sphericity to expresses the compactness of shape. Due to the irregular shape of air spaces in the lung, lung segments usually have much larger s than (tube-like) colon segments. Segments having s smaller than a threshold, Ls , are classified as non-lung, and unmasked. Ls was empirically determined as follows:
first we calculated the s value for the segments found by the lung segmentation stage and for the colon segments identified by the radiologists; then we set Ls to the average between the minimum lung s and the maximum colon s. Fig. 5 shows how the s distributions of lung and colon segments are separated by the threshold Ls , which resulted to be equal to 0.3.
Fig. 3. Normalized histogram of the volume dataset taken after the external segmentation, with CT values ranging between T0 and 200 HU. The peak corresponding to the lung air is marked with a circle.
Fig. 4. Normalized histogram of CT values for slices containing lung tissue (the first 25 mm axially), after external segmentation. Tl is the CT value of the air (T0 , −700 HU) peak and is equal to −876 HU in this case.
3.3. Colon segmentation Once external and lung air are masked, the colon segments can be identified. First, a new histogram of the volume dataset is
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Fig. 7. Histogram reported in Fig. 6 zoomed in the CT value range of T0 and Tl HU. In the reported case m, Tc and Ts (also shown) are equal to −955, − 906 and −979 HU, respectively.
Fig. 5. s distribution of colon and lung segments. Each distribution is individually normalized to one, in order to represent both of them on the same scale. Note how the discrimination value, Ls , clearly separates lung from colon tissue.
calculated (see Fig. 6); now CT values ranging between T0 and Tl correspond to the air contained in the colon and in the small bowel. This range is shown in detail in Fig. 7 and is referred to as the bowel component of the histogram. The seed threshold is defined as Ts = m − , where m and are respectively the mean and standard deviation of the bowel component (see Fig. 7). The whole dataset is scanned, and voxels having CT values between T0 and Ts are selected as seeds for the subsequent 3D 6-connected breadth-first region-growing process [17,18]. The lower and upper thresholds of the region-growing are T0 and Tc , respectively, where Tc = m + 2. During the region-growing process, when a voxel V, with a CT value higher than Tc , is found, a new threshold defining the colon surface, Ta , is calculated based on the local CT values of the colon wall, as follows. A ray of length l mm is projected forward from V along the direction from which V was reached, and the maximum CT value of the ray, Mr , is identified. If Mr is lower than a threshold, Tw , we assume that the ray does not intersect a wall, where Tw = m + 4. All voxels touched by the ray are classified as air voxels, and the region-growing process is continued. If Mr is higher than Tw , the value of the local surface threshold is incremented by the fraction
Fig. 6. Normalized histogram of the volume dataset with CT values ranging between T0 and 200 HU, taken after the lung segmentation. In this example Tl and Tm (peak of muscular tissue) are equal to − 876 and 46 HU, respectively.
q of the difference between Mr and Tc , i.e. Ta = Tc + q(Mr − Tc ). The first voxel of the ray having CT value higher than Ta is classified as a surface voxel. The region-growing process is then continued. The set of surface voxels so found constitutes the one-voxel-thick surface of a segment. If the ray is sufficiently long, and if there are dense structures (like bones) close to the colonic wall, Mr might be artificially high, compromising the surface definition. In order to avoid this behavior, an upper bound Tm for Mr is defined as the CT value of the muscle peak, seen as the maximum of the histogram between 0 and 200 HU (see Fig. 6). Together with colon segments, several segments of small bowel and lung may be extracted in this stage. However, most of these segments can be distinguished using specific area, s, and segment volume, v. The small bowel is generally neither well inflated by the air, nor well cleansed, resulting in small segments with high specific area. As demonstrated above, lung segments have very high specific area. Fig. 8 gives the scatterplot of v vs. s for colon and non-colon segments, as identified by the radiologists (see Section 3). An enlargement of the lower left area of the graph is shown as an
Fig. 8. Specific area (s) and volume (v, in mm3 ) of segments extracted by the colonsegmentation stage. Colon and non-colon segments, as identified by the radiologists, are represented by crosses and circles, respectively. The lower left corner of the figure is expanded, and the average of the threshold values, Ds and Dv , are shown with dashed lines (0.36 and 11,633 mm3 , respectively).
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inset. The figure shows that colon and non-colon segments (represented by crosses and circles, respectively) lie in well-defined areas, allowing us to distinguish them in the s-v space. We determined discrimination thresholds for s and v (Ds and Dv , respectively) in order to classify and remove the non-colon segments. To determine Ds and Dv , we split the thirty scans into two groups of 20 and 10 scans, here referred to as the training and testing sets. Segments with s < Ds and v > Dv are classified as colon. As a cross-validation procedure, the splitting of the data was performed three times, rotating the scans in the two sets. For each splitting, Ds and Dv were chosen in order to minimize the number of misclassified segments in the training set, and then applied to the testing set. Fig. 8 contains a scatterplot of v vs. s, where, for illustrative purposes, the averages of the three values of Ds and Dv are shown as dashed lines. An approach similar to our use of a ray in this stage was suggested by Wyatt et al. for the electronic cleansing of the colon prepared with tagging agents [13]. 4. Results and discussion 4.1. External segmentation The external segmentation is effective with rare exceptions. One of these is when, because of poor positioning or an inadequate field of view, part of the colon is not fully contained in the field making colon air appear contiguous with external air. In this case, as a result, part of the colon is masked during the external segmentation. An alternate method for external segmentation is based on region growing starting from the corners of the volume, as proposed in [13]. We implemented and tested this alternative, and our approach obtains exactly the same result approximately 11 times faster. Since the external air segmentation is the most computationally intensive stage of the segmentation scheme, this outcome is particularly significant. 4.2. Lung segmentation An example of lung segmentation is reported in Fig. 9. The first slice of the dataset is shown before (left) and after (right) segmentation, and the extracted air is shown as white. As explained in Section 3.2, the segmentation is performed using region growing with Tl as the upper bound. The way thresholds for region-growing are determined is similar to that employed by Näppi et al. [19]. We observed that in cases where sections of the colonic wall are very close to the lungs, setting Tl too high can cause the lung segment to invade the colonic lumen. The choice of Tl as the peak value of the lung-CT histogram makes it low enough to avoid colon
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invasion. This strategy might cause some parts of the lungs to be left unmasked. However, segments containing lung tissue found in the subsequent colon-segmentation stage are readily discarded based on their large values of specific area s as described in Section 3.3. The s distributions of lung and colon segments are well separated (Fig. 5). Only three colon segments have s higher than the lowest observed lung s value, and these correspond to cases affected by movement artifacts. 4.3. Colon segmentation The values of the thresholds used in the colon-segmentation stage are empirically chosen, according to the role they play in the algorithm (Section 3.3). For example, Tc , the upper threshold of the region-growing step, must be low enough to avoid penetration of the relatively low-density surfaces delimiting the colonic lumen, such as thin walls and haustra. However, during the empirical search for optimal values, we observed that deviations within a few percents from the optimal values do not significantly compromise the segmentation results, i.e. no visible defects are introduced in the reconstructed surface. Detection of the colonic surface is determined by Ta , which is an adaptive threshold, defined according to the CT values of the local colonic wall. The local character of Ta prevents, for example, the generation of holes in thin surfaces like haustra during the surfacedetection step. At the same time, it makes possible the drawing of a surface profile close to the real wall when dense structures are close to the colon. The parameters l and q are used to determine the local Ta and thus influence the quality of the resulting surface. l is the length of the ray along which the profile of the CT values of the colonic wall is obtained. This ray must be long enough to penetrate the tissue surrounding the colonic lumen, and the optimal l was empirically found to be 7 mm. The value of q determines the placement of the surface voxels in the transition region at the air-tissue boundary of the colonic wall, where small q places the surface near the lumen. We have found that the resulting surface does not depend critically on the actual value of q; in the present case q = 0.1 The quality of the surface obtained with a local threshold approach shows a marked improvement over surfaces generated by procedures based on the use of a global threshold. After triangulation this surface can be effectively used for the 3D visualization of the colon. Fig. 10 shows the 3D rendering of two examples of segmented colon. The segments extracted by the colon-segmentation stage include a small number of extraneous segments derived from the small bowel and lung. We refer to these segments as non-colon findings. As described above, the thresholds Dv and Ds were used to
Fig. 9. Output of the lung segmentation (b) on the first slice of a sample case (a). The extracted air is marked with an out-of-range value (visible as white).
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Fig. 10. Examples of the 3D rendering of the colon segmented by our algorithm. In case (a) all the non-colon air-filled structures of the scan were successfully identified and discarded; while in (b) we show a case where two non-colon segments were misidentified.
classify and remove these extraneous segments. These thresholds were validated by splitting the data into training sets and testing sets in three different ways. The results of the classification are reported in Table 1. The algorithm correctly classified 62 out of 64 colon segments (97%) yielding 99.8% of the colon surface and 300 of 329 non-colon segments (91%), yielding a misclassified noncolonic surface area equal to 6.3% of that of the colon. The results are consistent for the three splittings. All large colon segments were recognized and the two missed ones represent 0.1% and 0.4% of the colon area, respectively. Nearly all false positives derive from the small bowel; because the small bowel is not well-cleansed and not well-insufflated, these segments are especially prone to false-positive findings. Among the segments found and rejected in this stage are large lung segments with v > 3 × 105 mm3 (see Fig. 8), which are missed by the lung-extraction stage because they are not connected to the first slice, where the seeds for region growing are placed (Section 3.2). The overall algorithm would not be affected by the use of fecal tagging, since we neither consider nor process the region of CT values corresponding to tagged feces. Thus electronic cleansing, facilitated by using contrast agents, can either precede or follow segmentation [26]. Our results compare favorably with the results of [19], where 98% of the colonic surface was recognized and 10–15% of the segmented surface was extra-colonic, and the results of [13], where agreement between automatic and manual segmentation was reported
as 40–80%. Iordanescu et al. [14] report that 83% of the cases segmented completely and 10% segmented partially, out of 292 cases. With calculations based on the number of segmented colon voxels, Frimmel et al. [21] reported a sensitivity of 97% out of 38 CTC datasets. Li and Santago [20], combining prone and supine scans, obtained an average colon coverage of 88%, out of 100 datasets. In all cases the results of the automatic algorithms are compared with those obtained by expert radiologists performing manual selection of colon segments.
Table 1 Performance of the classification method on the testing sets. For each splitting of the scans, we report the optimal classification parameters Ds and Dv , the number of colon segments classified correctly (true positives, TP), the corresponding percentage of recognized colon surface (RCS), the number of non-colon segments classified correctly (true negatives, TN), and the ratio of the surface of the misclassified non-colon segments (false positives) to that of the colon surface, expressed as a percentage (EFM). The average values of the three splittings are also reported.
5. Conclusions
Ds Dv (mm3 ) TP RCS (%) TN EFM (%)
Splitting 1
Splitting 2
Splitting 3
Average
0.365 11,000 20/21 99.9 97/112 8.6
0.360 11,000 26/27 99.6 130/140 7.2
0.360 12,900 16/16 100 73/77 3.1
62/64 (97%) 99.8 300/329 (91%) 6.3
4.4. Computational efficiency The overall segmentation takes less than 4 s for low resolution scans, and less than 9 s for the scans acquired by the multi-slice scanner (see Section 2). In particular, the procedure for external air segmentation, which is the most computationally intensive stage of the segmentation scheme, is faster than that described in [13] by a factor 10. The computation time of our algorithm compares favorably with the fastest segmentation algorithms reported in the literature to date [14,21]. The allocated RAM memory corresponds to the size of the whole dataset, approximately 100 MB for the GE CT/i and approximately 300 MB for the GE Light Speed 16. The data structures created by the algorithm are less than 30 MB.
We described a novel automatic colon-segmentation method for CT colonography, intended for application to the computer-aided detection of colorectal polyps. First, the air surrounding the body and contained in the lungs were automatically recognized and masked. 3D region growing using a self-adjusting stopping criterion was then performed, starting from automatically placed seeds, without preprocessing or using any prior knowledge of colon geometry. The distinctive local character of the region-growing process prevented the generation of holes in thin walls, while ensuring a surface profile close to that of the actual tissue. Colon segments were distinguished from other air-filled structures by means of their size and specific area.
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The algorithm was developed using 30 retrospectively collected CT datasets (either prone or supine scan), and tested by comparison with the blind review of two expert radiologists. We recognized 99.8% of the colonic surface. Findings misclassified as colon amounted to 6% of the colonic surface. The method is computationally efficient. The overall segmentation takes 9 s for high resolution data on an Intel Pentium IV 2.8 GHz CPU. As a next step, our algorithm will be tested with a larger number of cases, including exams prepared with tagging agents, and inserted in the CAD system currently being developed by our group. 6. Summary Colon cancer currently ranks as the third leading cause of cancer-related deaths in the world. Most colorectal cancers arise from adenomatous polyps. Studies show that early detection and removal of colonic polyps can reduce the risk of colon cancer, thus decreasing the mortality rate. Computed tomographic colonography (CTC) has emerged as a promising screening method for colonic polyps and masses. In recent years, computer-aided diagnosis (CAD) systems have been proposed in order to improve the performance of CTC. The aim of CAD systems is to automatically detect polyps and masses, and to provide the locations of suspicious regions of the colon. The processing required for CAD includes a segmentation step that extracts the colon. Most previous colon-segmentation algorithms are based on user-defined seed points, from which extraction of the colonic volume is started. An automatic method for segmentation of the colonic wall was proposed for abdominal computed tomography (CT) of the cleansed and air-inflated colon. First, the air surrounding the body and contained in the lungs is automatically recognized and masked. Then, 3D region growing using a self-adjusting stopping criterion was performed, starting from automatically placed seeds, without preprocessing or using any prior knowledge of colon geometry. The distinctive local character of the region-growing process prevents the generation of holes in thin walls, while ensuring a surface profile close to that of the actual tissue. Colon segments were distinguished from other air-filled structures by means of their size and specific area. The method was evaluated using retrospectively collected CT scans based on visual segmentation of the colon by expert radiologists. This evaluation showed that the procedure identifies 97% of the colon segments representing 99.8% of the colon surface. The parameter settings and performance of the method are relatively independent of the scanner used and acquisition conditions. The method is computationally efficient. The overall segmentation takes 9 s for high resolution data on an Intel Pentium IV 2.8 GHz CPU.
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Acknowledgment This work has been partially founded by MIUR (CNR Sezione Oncologia, legge 449/97–99) and Fondazione CRT. References [1] World Health Organization Fact sheet N.297, July 2008. http://www.who.int/ mediacentre/factsheets/fs297/en/.
Silvano Agliozzo is a researcher at im3D S.p.A. Medical Imaging Lab, Torino, Italy. Natalia Pietrosemoli is a researcher at ISI, Torino, Italy. Mark Mandelkern is a professor of physics at the University of California, Irvine, Irvine, CA, USA. Teresa Gallo is a radiologist at the IRCC, Candiolo, Torino, Italy. Daniele Regge is the Director of the Radiology Unit at the IRCC, Candiolo, Torino, Italy.