A novel approach to extract colon lumen from ct images for virtual colonoscopy - medical imaging, ieee transactions on

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 12, DECEMBER 2000 A Novel Approach to Extract Colon Lumen from CT Images for Virtual Colonoscopy Dongqing Chen*, Member, IEEE, Zhengrong Liang, Member, IEEE, Mark R. Wax, Lihong Li, Student Member, IEEE, Bin Li, and Arie E. Kaufman, Member, IEEE Abstract—An automatic method has been developed for
ease of performance, degree of patient compliance, expense, segmentation of abdominal computed tomography (CT) images
and diagnostic accuracy. Among these methods, only optical for virtual colonoscopy obtained after a bowel preparation of a
colonoscopy and barium enema might be able to examine low-residue diet with ingested contrast solutions to enhance the
the entire colon. Optical colonoscopy requires intravenous image intensities of residual colonic materials. Removal of the
enhanced materials was performed electronically by a computer
sedation, takes approximately one hour to perform, has dif- algorithm. The method is a multistage approach that employs
ficulty in examing the cecum, the most distal portion, and a modified self-adaptive on-line vector quantization technique
is expensive. Barium enema requires a great deal of patient for a low-level image classification and utilizes a region-growing
physical cooperation to obtain X-rays at different views, and strategy for a high-level feature extraction. The low-level clas-
has a low sensitivity. In recent years, virtual colonoscopy sification labels each voxel based on statistical analysis of its
three-dimensional intensity vectors consisting of nearby voxels.
technology has been developed as an alternative method of The high-level processing extracts the labeled stool, fluid and air
massive population screening for examining the entire colon voxels within the colon, and eliminates bone and lung voxels which
for early cancer detection This have similar image intensities as the enhanced materials and air,
technology uses a computer system to navigate through the but are physically separated from the colon. This method was
colon model reconstructed from the patient's abdominal CT evaluated by volunteer studies based on both objective and sub-
jective criteria. The validation demonstrated that the method has
images. It has been shown that this technology is effective in a high reproducibility and repeatability and a small error due to
imaging colonic polyps as small as 3 mm in diameter partial volume effect. As a result of this electronic colon cleansing,
All techniques that examine the colon require a clean lumen, routine physical bowel cleansing prior to virtual colonoscopy may
eliminating residual materials that can falsely be interpreted as not be necessary.
colonic masses. Prior to any of these examinations, patients Index Terms—Bowel preparation, electronic colon cleansing,
undergo a bowel cleansing preparation which includes either image segmentation, virtual colonoscopy.
washing the colon with a large amount of liquids or adminis-tering medications and enemas to induce bowel movements This bowel preparation is often more unpleasant than theexamination itself. An alternative method of cleansing the colon COLORECTAL carcinoma is the second leading cause of would be very attractive. In virtual colonoscopy, contrast solu-
cancer-related deaths in the United States with 56 000 tions can be ingested to enhance the image intensities of the deaths reported in 1998 and an estimated 131 600 new cases stool and fluid. By applying image segmentation algorithms, were diagnosed Colonic polyps that are 10 mm or larger these colonic materials can be virtually removed from the im- in diameter are considered to be clinically significant, since ages without the patient undergoing physical bowel washing.
they have a high probability of being malignant Detection This paper will focus on the development of an automatic seg- and removal of smaller sized polyps can eliminate over 90% of mentation method to remove the contrasted colonic materials colon cancer cases.
for virtual colonoscopy.
Currently available colorectal cancer screening procedures include digital rectal examination, fecal occult blood test, flex-ible sigmoidoscopy, barium enema, and optical colonoscopy.
II. METHODS AND MATERIALS These diagnostic tests differ greatly with respect to safety, A. Bowel Preparation and Imaging Protocol Manuscript received May 4, 1999; revised August 18, 2000. This work was Five volunteers were recruited for this study with written con- supported by the National Institutes of Health (NIH) under Grant CA79180 of sents. Some of these subjects were used as training samples for the National Cancer Institute; Grant HL54166 of the National Heart, Lung and validating the hypothesis of the method and all of them were Blood Institute; Grant NS33853 of the National Institute of Neurological Dis-order and Stroke; and Established Investigator Award of the American Heart used for evaluating the performance of the method. The training Association. The Associate EWditor responsible for coordinating the review of samples were chosen for an equal distribution in gender with a this paper and recommending its publication was W. Higgins. Asterisk indicates wide age range, see Table I, where three patients were added to *D. Chen is with the Departments of Radiology, State University of New include variation in a large population. All volunteers had the York, Stony Brook, NY 11794 USA (e-mail: [email protected].).
following bowel preparation. During the day prior to CT scan, Z. Liang, M. R. Max, L. Li, B. Li, and A. E. Kaufman are with the Depart- the volunteers took a high fluid, low residue diet for the meals. In ments of Radiology and Computer Science, State University of New York, StonyBrook, NY 11794 USA.
order to enhance residual colonic materials, they ingested con- Publisher Item Identifier S 0278-0062(00)10613-5.
trast solutions of 250 cc barium sulfate suspension (2.1% w/v, 0278–0062/00$10.00 2000 IEEE CHEN et al.: A NOVEL APPROACH TO EXTRACT COLON LUMEN FROM CT IMAGES FOR VIRTUAL COLONOSCOPY SUBJECT INFORMATION, WHERE F AND M STAND FOR THE FEMALE AND MALE, AND V AND P FOR THE VOLUNTEER AND PATIENT E-Z-EM, Inc.) with each meal and 120 ml of MD-Gastroview Depiction of the local volume for a voxel.
(diatriuzoate meglumine and diatriozoate sodium solutions) inequal 60 ml amounts during the evening and in the morningbefore the CT scan. All patients used the same bowel prepara- component analysis (PCA) was then applied to the local tion with addition of magnesium citrate laxative and bisacodyl vector series to determine the dimension of the feature vectors tablets and suppository for physical colon cleansing.
and the associated orthogonal transformation matrix [i.e., the Prior to acquiring CT images, 1.0 mg of Glucagon was given Karhunen–Loeve (K–L) transformation matrix]. The PCA on intravenously in order to reduce colonic motion and spasm, fol- the datasets of the training samples showed that a reasonable lowed by introducing approximately 1000 cc of CO through a dimension of the feature vectors was 5, where the summation small bore rectal tube to inflate the colon. All CT images were of the first five principal components' variances was more than acquired in less than 40 s during a single breath hold. Using a 92% of the total variance.
GE/CTI spiral CT scanner, 5mm collimation with pitch between It is computationally costly to determine K–L matrix for each 1.5–2.0 : 1, depending upon the span of the colon as determined dataset. A general K–L matrix was then determined by the training from a digital scout radiograph, was performed. Scan parame- samples and used for segmenting all datasets acquired from the ters included 120 kVp, 180–280 mA (lower mA for volunteers) same source, i.e., from the same scanner with the same imaging and field of view (FOV) between 34–40 cm based on the ab- protocol described previously. To provide evidence for using the dominal size. The acquired data were reconstructed at 1-mm in- general K–L matrix for all datasets acquired from the same source, tervals with a 512 512 array, resulting in 300–450 slices for the Kolomogorve–Smirnov test was performed which aims each dataset. Both supine and prone positions were scanned for to prove that all datasets from the same source could be regarded validation purpose. For the same purpose, each volunteer was as a sample set from an identical probability distribution. A supine also scanned in the following day after the first CT scan and a dataset was chosen from each of the training samples. The as- day of low-residue diet, resulting in four datasets.
sociated cumulative distribution function (CDF) was obtainedand denoted by (some volunteers have B. Feature Analysis of Image Data two supine scans acquired in two consecutive days). By utilizingall datasets (both supine and prone) in the training samples, a To minimize computing time, the voxels outside the body general CDF, denoted by , was also computed. This contour were first eliminated. The remaining is called body was regarded as the estimation of the source CDF. Then, the voxels. This was achieved by a boundary-search algorithm are identical distributions may be Similar to Markov random field (MRF) models tested against hypothesis H1: are not identical, we assume that a three–dimensional (3-D) object of a . The differences of greatest magnitude similar tissue type in a CT image should be in a contiguous were listed in Table II.
3-D volume, naturally including partial volume effect. It is The table Table VIII] gives the critical value with a reasonable to classify the body voxels based on the intensity two-tail test at a nominal 1% significance level of 0.45. All similarity within certain spatial range. The diameter of the local differences listed in Table II are less than 0.45 (the largest range for a given voxel should be less than 5 mm considering sample size Table VIII] is 20, where the critical value the partial volume effect and the 5-mm-thick collimation. By is associated to this sample size). Hence, we accept H0, i.e., the acquisition protocol described above, each voxel was 1 all datasets can be regarded as coming from an identical mm thick with size in the – axial plane varying from 0.64 probability distribution. Therefore, the general K–L matrix to 0.94 mm depending on the FOV. The chosen local volume determined by the training samples can be applied to segment is depicted in Fig. 1. Its diameter is less than 4.6 mm in all all the datasets acquired using the same scanning protocol.
directions. The intensities of those 23 voxels in a local volumeform a twenty–three dimensional (23-D) local intensity vector.
The goal of the low-level processing is to classify the body C. Vector Quantization Algorithm voxels based on their local intensity vectors.
For the low-level classification, the K–L transformation was Each dataset consists of millions of body voxels, where each first applied to the local vector series. In the K–L domain, the voxel has a 23-D local intensity vector. This requires inten- feature vectors were formed by the first five principal com- sive computational effort to manipulate such a large quantity ponents from the transformed vector series. Then, the feature of vectors. To reduce the computing burden, a feature anal- vectors were classified into several classes. There are several ysis of the local vector series is necessary The principal approaches to classify the vectors In general, an automated

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 12, DECEMBER 2000 THE GREATEST MAGNITUDES OF THE DIFFERENCE BETWEEN THE SUBJECTS= CDF AND THE SOURCE CDF algorithm is desired, i.e., an unsupervised self-adaptive vectorquantization (VQ) algorithm is a candidate. A self-adaptiveon-line VQ algorithm was developed and is presented below.
Let , be the feature vector series, where is the number of feature vectors; denote the maximum number of classes; and be a threshold for vector similarity.
The VQ algorithm generates a representative vector be the number of feature vectors in the th class An example showing the intensity value change gradually from tissue A to tissue B. The overlap area represents the partial volume region.
The algorithm is outlined as follows.
The algorithm is similar to an unsupervised clustering algo- rithm. The number of classes and the representative vectors are updated continuously when more vectors are included in the 2) Obtain the class number calculation. From this point, the algorithm can be regarded as a learning procedure. It depends only on two parameters: the upper bound of possible classes and larity threshold. In abdominal CT images, there are roughly four classes that can be perceived based on their intensity features:1) air, 2) soft tissue, 3) muscle, and 4) bone or the enhanced residual materials. The intensity values of these four classes in- crease from the lowest to the highest. Due to partial volume ef- Update the representative vector of fect, there exists an intensity slope between two spatially con- tiguous tissue areas (see Fig. 2). The voxels in this slope-area are called partial volume voxels. To mitigate the under or overestimation of tissue boundary, it is reasonable to find the tissue Generate a new class boundary within the slope-area rather than on the edge of the slope-area. In other words, the partial volume area should be di-vided into two subareas. The left partial volume class is calledpartial volume from and the right one is called partial 3) Label each feature vector to a class . The partial volume area from according to the nearest neighbor rule labeled as tissue and the partial volume area from labeled as tissue in this study. In the CT images, there are two kinds of voxels within the colon lumen: 1) air and 2) enhanced materials. Each kind has a partial volume overlap to area of softtissue/muscle. Assigning two partial volume classes to each of the overlap areas results in four partial volume classes in total.
Therefore, the maximum class number for the classification algorithm was set to eight in this study.
is more crucial to the classification than . If it is too large, only one class could be is the Euclidean distance between obtained. If it is too small, redundant classes may occur. Ac- gives the integer which realizes the min- cording to our numerical experiments, was set to the square root of the maximum component variance of the feature vector The class number and the representative vector for each class series. This allows the VQ algorithm to achieve the minimum can be obtained in a single scan on all feature vectors. This re- class number with the maximum variance. Since T is estimated duces greatly the computing time as compared to iterative VQ from the data, the algorithm is self-adaptive.
algorithms, e.g., the LBG algorithm The representativevector of each class is an estimation of the mean vector of that D. Extraction of the Colon Lumen class. From the central limit theorem the larger the number The results of the low-level classification were represented in a class is, the more accurate the representative vector esti- as a labeled image with integer values. The colon lumen con- mates the mean vector of that class. For a colon dataset, there sisted of four kinds of labeled voxels: 1) air, 2) partial volume are millions of body voxels. Hence, the representative vector is from air to soft tissue/muscle, 3) enhanced materials, and 4) a good estimation to the mean of that class partial volume from enhanced materials to soft tissue/muscle.

CHEN et al.: A NOVEL APPROACH TO EXTRACT COLON LUMEN FROM CT IMAGES FOR VIRTUAL COLONOSCOPY ray from an air voxel and examining whether the ray reaches anenhanced voxel within 2 mm.
E. Evaluation Method Optical colonoscopy is currently utilized as the gold stan- dard for validating virtual colonoscopy methods for detectingcolonic polyps of 5 mm or larger in diameter. For the electroniccleansing without physical bowel washing, the gold standard isnot applicable. Instead, we acquired both supine and prone scansfor each subject and furthermore repeated the scans on the nextday for the volunteers, aiming to measure the reproducibility,repeatability and robustness on partial volume effect of the pre-sented electronic cleansing technique. The results were subjec-tively judged by an experienced radiologist. Four objective pa-rameters were calculated from the results to indirectly measurethe performance. The first two were used to measure the seg-mentation error created by partial volume effect. The other twowere used to demonstrate reproducibility (by the same dataset) A CT slice image and the delineated contour of colon lumen.
and repeatability (by both supine and prone scans of the samesubject) of the method. All these four parameters were calcu-lated from the extracted colon lumen.
1) Average thickness of the partial volume layer (ATPV): These four classes were denoted by 1, 2, 3, and 4, respectively.
This is the average thickness in 3-D space of the partial By applying the inverse K–L transformation to the class repre- volume layer from both air and enhanced materials to soft sentative vectors, the intensities in the original image space for tissue/muscle. If this parameter is larger than 5 mm, then each class were obtained. Classes 1 and 3 were easily segmented polyps of 5 mm in diameter may not be accurately de- since their intensities were the lowest and the highest, respec- tively. Since class 1 includes voxels of lung and class 3 includes 2) Partial volume percentage (PVP): PVP voxels of bone and these voxels are not physically associated of the volume of partial volume layer from air to soft with the colon lumen, we can use region-growing strategies to tissue/muscle and the volume of partial volume layer from remove the non colon-lumen voxels from classes 1 and 3. This enhanced materials to soft tissue/muscle)/(the volume of is the high-level processing.
entire extracted colon lumen).
We removed lung voxels first. The regions of lungs are two The volume was counted by the number of voxels in the contiguous 3-D volume on the left and right sides of the chest. If region. This parameter estimates the ratio of the partial FOV covers the entire colon, air voxels in the top slice must be volume voxels to the entire colon lumen.
lung voxels. Two air voxels for both left and right lungs were 3) Mean intensities of the air lumen (AL) and the enhanced determined as seeds for growing out the entire lung volume materials (ERM) voxels. The intensity is in HU.
by using a region-growing algorithm. After removing the lung volume, the remained voxels in class 1 were inside the colon of the parameter defined previously for the supine dataset lumen. Given the air lumen, the partial volume voxels of class is one corresponding to the prone dataset acquired 2 from air to soft tissue/muscle were then determined because from the same subject on the same day. The definition they were contiguous to the air lumen in both geometry space applies to the two-day scans. A smaller value and intensity feature.
reflects a better reproducibility or repeatability.
Assuming that bone is separated from colon lumen, the voxels of enhanced materials were then determined from class 3 by a III. RESULTS AND DISCUSSION seed in the lumen with the region-growing algorithm. If a voxelbelonged to class 3 and there existed at least one voxel of air For subjects 3, 4, and 6, only supine scan was acquired (Table in the lumen which was 2.5 mm or less away from the given I). For subjects 1, 2, 5, and 7, both supine and prone scans were voxel, it was a seed for growing out the volume of the enhanced acquired on two consecutive days. Subject 8 was scanned in the materials. The partial volume voxels of class 4 from enhanced supine position on two consecutive days. There was a total of materials to the soft tissue/muscle were determined by finding 21 datasets, 13 in supine position and eight in prone position.
the class closest to the material class in both geometry space and The 15 datasets in the training samples were used to determine intensity feature. Given the four classes of voxels representing the size of the feature vectors and the general K–L matrix. It the colon lumen, the last task was to label the boundary voxels took nearly 6 hours to generate the K–L matrix. This matrix between air and enhanced materials in the image space. The en- was then applied to segment all the 21 datasets. Fig. 3 shows a hanced material forms a basin-like volume with a flat surface CT slice image and the extracted lumen contour within the CT due to the gravitation This surface was the boundary be- image. Fig. 4 depicts the removed enhanced materials in 3-D.
tween air and enhanced material, and was found by sending a Fig. 5(a) displays the outside view of the entire extracted colon

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 12, DECEMBER 2000 Demonstration of removal of enhanced material (arrows).
The overview of the entire colon lumen (a) and the inside view of a segment of colon lumen (b).
lumen and Fig. 5(b) shows the inside view of a colon segment.
remained on the wall surface near the boundary between These figures were generated from subject 8. The segmentation air and enhanced material, these were smaller than 5 mm of the colon lumen took less than 9 minutes on a SGI/Octane and were not clinically significant. In one subject, at some desktop workstation with dual CPU's of R10000, 250 MHz, and locations, the small bowel adjacent to the colon, appeared 890 MB RAM. No parallel implementation was utilized. Since "attached" to the colon lumen. For example, subject 1 did we did not utilize seeded region-growing technique to grow out not follow the diet instruction, eating a big breakfast on the the lumen, our method was able to delineate all segments of the first day prior to CT scan, which resulted in the stomach and entire colon lumen when collapses presented.
small bowel filled with enhanced materials. The extractedlumen included part of the stomach and several small bowelsegments. (In the second day after correcting the error, thecolon lumen was successfully extracted). For subject 7, A. Subjective Evaluation due to a 5-mm thickness collimation, some boundary areas The radiologist examined the segmentation results and between the lungs and colon were not resolved, resulted in was satisfied. The entire lumens from 13 datasets of subjects connection of lungs and colon lumen. The algorithm could 2, 3, 4, 5, 6, and 8 were successfully delineated, where four still remove the enhanced materials and extracted the lumen datasets showed colon collapses. The enhanced materials including part of the lungs. (A smaller slice collimation were removed satisfactorily. Although some small artifacts in data acquisition is recommended). Excluding the two CHEN et al.: A NOVEL APPROACH TO EXTRACT COLON LUMEN FROM CT IMAGES FOR VIRTUAL COLONOSCOPY PARTIAL VOLUME ERROR ESTIMATION REPEATABILITY TEST datasets of subject 1 and four datasets of subject 7 from the resolution. This may be achieved by a multidetector ring CT total 21 datasets, 15 lumens were successfully delineated and were inspected using our developed virtual colonoscopy In our algorithm, the colon lumen is delineated by removing system The attached areas between colon and small the volume which is not associated with the colon lumen, rather bowel, as well as between colon and lungs, were deleted than finding some seeds of the colon lumen to grow out the manually before navigating through the colon lumens. The entire lumen. This ensures that the entire colon lumen could be navigations through both supine and prone scans, as well as delineated even if there are collapsed segments. This is a very the second day scans of each subject agreed each other, i.e., attractive advantage considering that the colon collapse happens they agreed with the assumed gold standard that the young volunteers have no polyps.
The partial volume effect was considered in our algorithm.
The average partial volume layer shown in Table III is 2.57 mm B. Objective Evaluation or less in thickness. This ensures that polyps of 5 mm or larger indiameter cannot be affected by the partial volume effect within The supine and prone datasets acquired on the same day from the extracted colon lumen. However, some of the flat polyps subjects 1, 2, and 8, respectively, were used to compute the pa- could be missed.
rameters for repeatability test and partial volume effect mea- All the parameter differences in Table IV are less than 8.3% surement. The results are listed in Tables III and IV, where S# and most of them are less than 6.5%, demonstrating good re- means subject #. The reproducibility test from the same dataset peatability of our method. This statement concurs with the sub- was excellent, because of the fully automated process.
jective evaluation.
C. Discussion D. Conclusion If the bowel preparation instruction was followed, as most Our two-stage segmentation method designed for the bowel subjects did, the segmentation results were satisfactory. The en- preparation using a low-residue diet with ingested colonic hanced colonic materials were removed successfully except for contrast solutions was computational efficiency and showed some small artifacts near the area where air, colon wall, and en- satisfactory performance. Since the training samples include hanced material connected. These artifacts form a small artifi- patient datasets, the segmentation method is applicable to both cial horizontal ring on the colon wall surface that can be easily cases with and without additional physical bowel cleansing.
distinguished from the colonic folds. Nevertheless, if a polyp Most importantly, the electronic colon cleansing technique smaller than 5 mm is located on the ring, it could potentially demonstrated the feasibility of performing virtual colonoscopy be missed in the virtual colonoscopy examination. Further re- without the need for pre-procedure physical bowel cleansing.
search is needed to minimize these artifacts for detecting smallerpolyps. If a segment of small bowel touches the colon and is filled with the enhanced materials, this segment may be delin- The authors greatly appreciate the valuable comments on K–S eated with a higher probability as the colon lumen. This can be test from Dr. S. Li.
avoided by not eating any food/drink in the morning prior to CTscan. Another possible solution is to use an interactive display tool to manually correct the touched segment. The attachment [1] C. Chatfield and A. J. Collins, Introduction to Multivariate Anal- of the lungs to colon lumen can be avoided with a higher axial London, U.K.: Chapman & Hall, 1980.
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 19, NO. 12, DECEMBER 2000 [2] W. Feller, An Introduction to Probability Theory and its Applications, [12] T. N. Papps, "An adaptive clustering algorithm for image segmentation," New York: Wiley, 1968.
IEEE Trans. Signal Processing, vol. 40, pp. 901–914, 1992.
[3] K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd [13] T. Parkins, "Computer lets doctors fly through the virtual colon," JNCI, New York: Academic, 1990.
vol. 86, pp. 1046–1047, 1994.
[4] A. Gersho and R. M. Gray, Vector Quantization and Signal Compres- [14] G. Rubin, C. Beaulieu, V. Argiro, H. Ringl, A. Norbash, J. Feller, M.
Boston, MA: Kluwer, 1992.
Dake, R. Jeffrey, and S. Napel, "Perspective volume rendering of CT [5] S. Geman and D. Geman, "Stochastic relaxiation, Gibbs distributions, and MR images: Applications for endoscopic imaging," Radiology, vol.
and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Ma- 199, pp. 321–330, 1996.
chine Intell., vol. 6, pp. 721–741, 1984.
[15] B. Simons, A. Morrison, R. Lev, and W. Verhoek-Oftendahl, "Relation- [6] A. Hara, C. Johnson, J. Reed, D. Ahlquist, H. Nelson, R. Ehman, C. Mc- ship of polyps to cancer of the large intestine," J. National Cancer Inst., Collough, and D. Ilstrup, "Detection of Colorectal Polyps by CT Colog- vol. 84, pp. 962–966, 1992.
raphy: Feasibility of a novel technique," Gastroenterology, vol. 110, pp.
[16] N. V. Smirnov, "On the estimation of discrepancy between empirical 284–290, 1996.
curves of distribution for two independent samples" (in Russian), Bull. [7] L. Hong, A. Kaufman, Y.-C. Wei, A. Viswambharan, M. Wax, and Z.
Moscow Univ., vol. 2, pp. 3–16, 1939.
Liang, "3-D virtual colonoscopy," in Proc. Biomedical Visualization, M.
Loew and N. Gershon, Eds., Atlanta, GA, 1995, pp. 26–33.
London, U.K.: Chapman & Hall, 1993.
[8] L. Hong, Z. Liang, A. Viswambharan, A. Kaufman, and M. Wax, "Re- [18] D. J. Vining, D. Gelfand, R. Bechtold, E. Scharling, E. F. Grishaw, and construction and visualization of 3-D models of colonic surface," IEEE R. Shifirin, "Technical feasibility of colon imaging with helical CT and Trans. Nucl. Sci., vol. 44, pp. 1297–1302, 1997.
virtual reality," in 1994 Ann. Meeting Amer. Roentgen Ray. Soc., New [9] Z. Liang, F. Yang, M. Wax, J. Li, J. You, A. Kaufman, L. Hong, H. Li, and Orleans, p. 104.
A. Viswambharan, "Inclusion of a priori information in segmentation of [19] J. Zhang, J. W. Modestino, and D. A. Langan, "Maximum-likelihood pa- colon lumen for 3-D virtual colonoscapy," in Conf. Rec. IEEE NSS-MIC, rameter estimation for unsupervised stochastic model-based image seg- Albuquerque, NM, Nov. 1997.
mentation," IEEE Trans. Image Processing, vol. 3, pp. 404–420, 1994.
[10] Y. Linde, A. Buzo, and R. M. Gray, "An algorithm for vector quantizer [20] "Cancer facts and figures," Amer. Cancer Soc., Atlanta, GA, pt. 2, 1998.
designed," IEEE Trans. Commun., vol. 28, pp. 84–95, 1980.
[11] E. McFarland, J. Brink, J. Loh, G. Wang, V. Argiro, D. Balfe, J. Heiken, and M. Vannier, "Visualization of colorectal polyps with spiral CTcolography: Evaluation of processing parameters with perspectivevolume rendering," Radiology, vol. 205, pp. 701–707, 1997.

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