Computerized Detection of Colonic Polyps at CT Colonography on the Basis of Volumetric Features: Pilot Study1

1 From the Departments of Radiology (H.Y., Y.M., P.M., A.H.D.) and Medicine (D.T.R.), University of Chicago, 5841 S Maryland Ave, MC2026, Chicago, IL 60637. Received February 22, 2001; revision requested March 21; revision received June 26; accepted July 27. Supported in part by a grant from the University of Chicago Cancer Research Center.

	ABSTRACT

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PURPOSE: To develop a computer-aided diagnosis (CAD) scheme for automated detection of colonic polyps on the basis of volumetric features and to assess its accuracy on the basis of colonoscopy, the standard.

MATERIALS AND METHODS: Computed tomographic (CT) colonography was performed in patients with use of standard bowel cleansing, air insufflation, and helical scanning in supine and prone positions. The colon was extracted from volumetric data sets generated from transverse CT sections. Volumetric features characterizing polyps were computed at each point in the extracted colon. Polyps were detected by means of hysteresis thresholding and fuzzy clustering followed by a rule-based test on the basis of feature values. Locations of the detected polyps were compared with those detected at conventional colonoscopy.

RESULTS: Forty-one cases were analyzed: nine cases with polyps and 32 without polyps. Each case with polyps had one polyp of clinically important size (six were 5–9 mm; three, 10 mm). Thus, there were 82 volumetric data sets, 18 included polyps. Eighty-nine percent (16 of 18) of the polyps were detected. Each of the two false-negative findings was detected in the other position; thus, 100% of polyp cases were detected, with 2.5 false-positive findings per patient. The false-positive findings were similar to those due to common perceptual errors. Most of the false-positive findings were easily distinguishable from true polyps by experienced radiologists.

CONCLUSION: The CAD scheme has the potential to depict polyps with high sensitivity and an acceptable false-positive rate.

　

Index terms: Colon, CT, 75.12115, 75.12117, 75.12119 • Colon neoplasms, 75.311 • Computers, diagnostic aid • Images, analysis, 75.12115, 75.12117, 75.12119

	INTRODUCTION

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Colon cancer is the second leading cause of cancer deaths in the United States (1,2). Individuals older than 50 years have a 5% probability of developing colon cancer and a 2.5% probability of dying of it (3,4). Early detection and removal of polyps can reduce the risk of colon cancer and thus result in a decrease in the mortality rate from colorectal cancer (5–12). Computed tomographic (CT) colonography is a technique for detecting colorectal neoplasms by using volumetric CT data and has been advocated as a screening technique for colorectal cancer (13).

A typical CT colonographic examination produces 150–300 transverse CT images each for imaging data sets obtained in patients in the supine and prone positions. Multi-detector row CT scanners may yield an even larger number of images. Therefore, the time required for a diagnostic interpretation of an entire CT colonographic examination remains an important issue in translating CT colonography from the research area to routine clinical implementation (14,15). The visibility and conspicuity of polyps, and thus the accuracy of detecting polyps, may depend primarily on the image acquisition parameters (16–18) and display methods, both of which are still under investigation. For CT colonography to be a clinically practical means of evaluating the colon for polyps and masses, the technique must be feasible for interpreting a large number of images in a time-effective fashion and for detecting polyps with high accuracy.

Computer-aided detection is attractive because it has the potential to reduce radiologists’ interpretation time, as well as increase the diagnostic accuracy in the detection of polyps. Computer-aided diagnosis (CAD) schemes for automated detection of polyps at CT colonography have been reported (19–22). However, these studies were either based on simulated polyps (19,20), reported a large number of false-positive findings (21), or yielded a low sensitivity (22).

The purpose of this study was to develop a CAD scheme for automated detection of colonic polyps on the basis of volumetric features and to assess its accuracy on the basis of colonoscopic findings, the standard.

	MATERIALS AND METHODS

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Database of CT Colonographic Data and Patient Selection
Our study was approved by our institutional review board; informed consent was obtained. We retrospectively collected CT colonographic cases that were acquired during 1998 and 1999. All patients underwent CT colonography after the standard precolonoscopic cleansing followed by colonoscopy, which was performed on the same day as CT. All colonoscopies were performed by experienced endoscopists. Two experienced radiologists (A.H.D. and P.M.) examined these cases visually and independently and scored the adequacy of preparation and distention by using a 0–100-point scale. Cases with scores of 50 or less (nondiagnostic quality) were excluded. If a case was scored higher than 50 by one radiologist but lower than 50 by the other radiologist, the two radiologists reached a consensus decision regarding the final score. Cases in which there were feces, fluid, poorly distended colons, and motion artifacts were included if they were scored at more than 50. Cases of colitis were excluded.

Helical CT (GE 9800 CTi; GE Medical Systems, Milwaukee, Wis) with 5-mm collimation and reconstruction intervals of 1.5–2.5 mm was performed in patients in both supine and prone positions after rectal insufflation with room air. The matrix size of the resulting transverse images was 512 x 512, with a spatial resolution of 0.5–0.7 mm/pixel. A 180° linear interpolation and standard reconstruction algorithm were used. For minimizing radiation exposure, a reduced current of 100 mA with 120 kVp was used.

The location of polyps was determined at CT colonography by the two radiologists by means of visual confirmation with reference to colonoscopic and pathologic reports, as well as in consultation with an endoscopist (D.T.R.). Each radiologist determined the location and size of the polyps independently. If their determinations differed, they made a consensus decision. The size of polyps was determined primarily on the basis of the pathologic report. If only fragments of a polyp were provided for pathologic examination, the size reported at colonoscopy was used. In this study, we defined the clinically important size of polyps as being at least 5 mm, which is the lower limit of the size range of the polyps that are considered to be clinically important (13). We chose this lower limit as a conservative criterion, because the measured size of polyps varies depending on their conspicuity.

As a result, CT colonographic studies in 41 patients (15 men, 26 women; age range, 32–84 years; mean age, 57 years) were collected from a total of 50 CT colonographic examinations. This cohort of patients included nine patients with polyps and 32 patients without polyps. Each of the nine patients had a polyp that was confirmed at colonoscopy to be larger than or equal to the clinically important size of 5 mm. Seven of the polyps were located in the sigmoid colon and two were located in the descending colon. Of the nine polyps, six measured between 5 and 10 mm; one, 12 mm; one, 25 mm; and one, 30 mm.

Overall Detection Scheme
Polyps were detected with a CAD scheme (Fig 1) developed in our laboratory. First, transverse CT sections obtained at CT colonography were interpolated along the transverse direction with a linear interpolation to yield an isotropic volume data set for the elimination of the differences in the reconstruction intervals among data sets. Then the colon was segmented by removing noncolonic structures from the isotropic volume data sets on the basis of a priori knowledge of the abdominal anatomy (23). At each voxel of the segmented colon, several volumetric features characterizing polyps, folds, and colonic walls were computed. Possible polyps were segmented by means of hysteresis thresholding (24) with use of some of these volumetric features. Polyps were then detected by means of fuzzy clustering (25) in a feature space generated by the feature values, followed by a rule-based linear discriminant analysis in the feature space. All of these processes were performed automatically without human intervention. Details of these steps are described in the following sections.

fig.ommitted Figure 1. Diagram of the CAD scheme for detection of polyps at CT colonography.

 
Segmentation of the Colon
Prior to the detection process, colons were extracted from the isotropic volume data sets so that the search regions for polyps in the data sets were restricted. Extraction was performed automatically with a recently developed segmentation method (23) that consists of the following five steps: (a) An isotropic volume is smoothed by means of a three-dimensional Gaussian filter. (b) The volume outside the body is segmented on the basis of thresholding of CT values, followed by a three-dimensional connectivity test. This volume is dilated inward so that the resulting volume includes the skin. The resulting volume is called an air mask. (c) Bone structures that correspond to the spine, pelvis, and parts of the ribs in the original volume are segmented in the same manner, and the segmented bone structures are dilated outward to include completely the boundary of the spine, pelvis, and ribs. The resulting volume is called a bone mask. (d) The three-dimensional gradient of the CT value is calculated at each voxel that does not belong to the volumes defined by the union of the two masks. Those voxels that have gradient and CT values greater than the predefined threshold values are retained. (e) Finally, the remaining voxels are labeled by means of the connectivity test, and the connected component that has the largest number of voxels is identified as the extracted colon (Fig 2).

fig.ommitted Figure 2. A, Coronal image of an isotropic volume data set generated from CT colonographic images in a 70-year-old woman. B, Image of the segmented colon obtained with an application of a segmentation algorithm to the isotropic volume in A. Our segmentation algorithm segments a thick region that contains the entire colon and not only the surface of the colonic wall. A portion of the small intestine (arrow) contiguous to the colon was extracted with the entire colon. Volumetric features used for the detection of polyps were calculated from individual voxels in this thick region.

 
It should be noted that the computer software extracts a thick contiguous region that encompasses the entire colon and not the surface of the colonic wall. Therefore, with our extraction method, we do not have the problem of failing to acquire voxels that are part of the colon because of inaccurate extraction of the colonic wall; such loss is often observed when only the surface of the colonic wall is extracted.

Extraction of Volumetric Features Characterizing Polyps, Folds, and Colonic Walls
After the colons were extracted, two features, the volumetric shape index and the curvedness values (26–28), were calculated at each voxel in the segmented thick colon region. The shape index (26) characterizes the topologic shape of the volume in the vicinity of a voxel. This index determines to which of the following five topologic shapes a voxel belongs: cup, rut, saddle, ridge, or cap. The shape index is normalized between 0 and 1. Voxels that belong to the cup shape have values around 0; rut, around 0.25; saddle, around 0.5; ridge, around 0.75; and cap, around 1.0; although the transition from one topologic shape to another occurs continuously (Fig 3). The curvedness of a voxel represents the magnitude of the effective curvature at the voxel, which is defined as the square root of the sum of the squared minimum and maximum curvatures at the voxel (28). Generally, points on a large spherelike object have small curvedness values.

fig.ommitted Figure 3. Illustration of the relationship between the values of the shape index and the shapes.

 
On the three-dimensional volumetric data, polyps generally appear as bulbous caplike structures adhering to the colonic wall with small to medium curvedness values, whereas folds appear as elongated ridgelike structures having large curvedness values. The colonic walls appear as nearly flat cuplike structures and have small curvedness values. Therefore, combinations of these two features are expected to differentiate effectively among polyps, folds, and colonic walls.

Figure 4, A–C, shows transverse, coronal, and sagittal sections, respectively, of a volume of interest that was extracted from an isotropic volume data set. A 9-mm polyp is indicated with an arrow. Figure 4, D–F, shows transverse, coronal, and sagittal sections, respectively, of the same volume of interest as in A–C but in which only the segmented colon regions are shown. Voxels with shape index values that correspond to cap shape are green; saddle or ridge, pink; and rut or cup, brown. As expected, most portions of the polyp are green, whereas folds and colonic walls are pink and brown, respectively.

fig.ommitted   Figure 4. CT images obtained from multiplanar reformatting of a volume of interest containing a 9-mm polyp (arrow). A-C, Transverse, coronal, and sagittal sections, respectively, of a volume of interest extracted from an isotropic volume set. D-F, Transverse, coronal, and sagittal sections, respectively, of the segmented colon obtained in the same volume of interest as in A-C. Voxels that have shape index values corresponding to the cap, saddle or ridge, and rut or cup shapes are green, pink, and brown, respectively. As expected, a substantial portion of the polyp is green, whereas folds and colonic walls are pink and brown, respectively.

 
Figure 5, A, shows an endoscopic view of another polyp depicted with conventional volume rendering (29). The polyp is indicated by an arrow. Although the polyp appears as a bumpy structure in this image, it is inconspicuous with this representation. Figure 5, B, represents the same endoscopic view of the polyp obtained with the same volume-rendering method as that in part A. However, in this figure, voxels were colored according to their shape index values in the same manner as in Figure 4, D–F. With this coloring scheme, polyps, folds, and the colonic wall are clearly separated, and the polyp is easily distinguishable from other structures. Figures 4 and 5 demonstrate the potential of the shape index to help differentiate polyps from other structures in a colon.

fig.ommitted   Figure 5. Three-dimensional endoscopic views of the polyp obtained with conventional volume rendering. Although the polyp is depicted as a bumpy structure (arrow in A), it is difficult to identify it with this representation. In B, the voxels are colored according to their shape index values with the same color scheme as in Figure 4. The polyp (arrow) is clearly depicted and differentiated from folds and the colonic wall. A and B demonstrate the effectiveness of the shape index in differentiating polyps from other normal structures in the colon.

 
Detection of Polyps
On the basis of the characteristic values of the shape index and the curvedness of the polyps, we extracted possible polyps from a volumetric data set by using the following steps. First, voxels that had shape index and curvedness values between predefined minimum and maximum values were extracted and used as seed points in the succeeding process. The minimum and maximum threshold values for the shape index were set at 0.9 and 1.0, respectively, to select structures that belong to the cap shape (Fig 3). The minimum and maximum threshold values for curvedness were set at 0.08 and 0.20 mm^-1, respectively, to correspond to effective polyp sizes of 12.5 and 5.0 mm, respectively. It should be noted that a polyp may not always have a perfect cap structure and only a part of it may exhibit a caplike structure, as illustrated in Figures 4 and 5. We used strict threshold values for the shape index and curvedness to help identify small regions on polyps that had nearly complete cap structures, as well as regions with curvedness values that were completely within the range of targeted polyps.

Starting with seed points, hysteresis thresholding (24) on the basis of the shape index and curvedness value was applied to the thick region that encompassed the entire colon (Fig 2). Hysteresis thresholding extracts a set of spatially connected voxels to the seed points that have the shape index and curvedness values within the predefined minimum and maximum values. This process was used for extracting a large connected component that corresponds to the major portion of a polyp. For this purpose, we used relaxed minimum and maximum threshold values compared with those used in the earlier seed point extraction process. Because the peripheral region of a polyp does not always show a perfect cap shape, the minimum threshold value for the shape index was relaxed to 0.8 for the inclusion of "skirts" of the polyps connected to the colonic walls or folds, which might have a shape close to a domelike structure that is a transient shape from a ridge to a cap. The maximum threshold was kept as 1.0, because this was the maximum possible value of the shape index.

Similarly, the peripheral region of a polyp may have curvedness value that is smaller or larger than that of the center region of a polyp. Therefore, the minimum and maximum threshold values for curvedness were relaxed to 0.05 and 0.25 mm^-1, respectively, to correspond to effective polyp sizes of 20 and 4 mm, respectively, for the identification of clinically important polyps (5 mm). As a result of hysteresis thresholding, approximately 40 connected components per data set were obtained. These connected components consisted of multiple detections of the same polyps at different locations. Therefore, we merged the components that were located close (<10 mm) to each other to generate a reduced set of connected components.

We observed that owing to noise, the resulting connected components included a large number of small bumpy structures. To differentiate these components from polyps, we used a fuzzy c-means clustering (25), with the locations of the connected components as the seed points for the clustering process. Fuzzy c-means clustering helps grouping of connected components with similar feature values to make a cluster. The similarity measure is defined as a Euclidian distance between the values of features at each voxel. The features consist of the CT value, the gradient of the CT value, the shape index, the curvedness value, and the spatial coordinates of the voxel. This fuzzy clustering process is effective in identifying the major region of a polyp as a large cluster because the voxels within a single polyp are expected to have similar feature values and to be spatially located close together. On the other hand, the clustering process keeps the connected components owing to noise as a small isolated cluster, because they tend to contain voxels that have feature values distinctly different from those of their surrounding voxels.

At the end of the clustering process, a value that indicates the degree of a fuzzy membership function of the voxel in a cluster was assigned to each voxel. The higher the value of the membership function, the more likely it was that the voxel belonged to the cluster (minimum is 0 and maximum is 1). Voxels with values greater than 0.9 were kept, and separate clusters were obtained. Because small clusters are likely to be generated due to noise, thresholding with a minimum volume of 35 mm³ was applied to individual clusters to yield possible polyps. This minimum volume is equivalent to the volume of a 4-mm polyp, which is small enough to retain clinically important polyps that are larger than 5 mm. Approximately 12 possible polyps per data set were obtained as a result of fuzzy clustering.

Figure 6a and 6b shows the distributions of the shape index and the curvedness values for the possible polyps that were obtained before and after, respectively, the fuzzy clustering process. True-positive findings are depicted by squares, whereas false-positive findings are depicted by dots. The number of false-positive findings is much smaller in Figure 6b than in Figure 6a. On both images, true-positive findings tend to have higher shape index values and lower curvedness values than do false-positive findings. However, some of the true-positive findings in Figure 6b have higher shape index values and lower curvedness values than do those for the corresponding true-positive findings in Figure 6a. Therefore, to eliminate the false-positive findings, a rule-based linear discriminant analysis was performed on the mean shape index and the curvedness values of these possible polyps. In this analysis, the dividing line in Figure 6b could eliminate a large number of false-positive findings when the possible polyps in the upper left region above the line were regarded as false-positive findings.

fig.ommitted Figure 6a. (a, b) Scatterplots depict the distribution of the shape index and curvedness values for possible polyps before (a) and after (b) the fuzzy clustering process (Fig 1). Gray dots depict true-positive findings and black squares depict false-positive findings. The number of false-positive findings in b is much smaller than that in a because of the effect of fuzzy clustering. As expected, polyps have higher shape index values and lower curvedness values than do a majority of the false-positive findings. The solid line in b was used in the CAD scheme to help discriminate true- from false-positive findings. A substantial number of false-positive findings can be eliminated by disregarding the possible polyps in the upper left region above the line. (c, d) Scatterplots depict the distribution of CT and gradient values (Hounsfield units) for possible polyps before (c) and after (d) fuzzy clustering. Black squares depict true-positive findings and gray dots depict false-positive findings. The number of false-positive findings in d is much smaller than that in c because of the effect of fuzzy clustering. However, a substantial overlap remains between the true- and false-positive findings in d. Although the minimum and maximum threshold values for CT and gradient values (dashed lines) were used to reduce false-positive findings in the CAD scheme, thresholding was effective only for the elimination of outliers located outside the central rectangular region.

 

fig.ommitted Figure 6b. (a, b) Scatterplots depict the distribution of the shape index and curvedness values for possible polyps before (a) and after (b) the fuzzy clustering process (Fig 1). Gray dots depict true-positive findings and black squares depict false-positive findings. The number of false-positive findings in b is much smaller than that in a because of the effect of fuzzy clustering. As expected, polyps have higher shape index values and lower curvedness values than do a majority of the false-positive findings. The solid line in b was used in the CAD scheme to help discriminate true- from false-positive findings. A substantial number of false-positive findings can be eliminated by disregarding the possible polyps in the upper left region above the line. (c, d) Scatterplots depict the distribution of CT and gradient values (Hounsfield units) for possible polyps before (c) and after (d) fuzzy clustering. Black squares depict true-positive findings and gray dots depict false-positive findings. The number of false-positive findings in d is much smaller than that in c because of the effect of fuzzy clustering. However, a substantial overlap remains between the true- and false-positive findings in d. Although the minimum and maximum threshold values for CT and gradient values (dashed lines) were used to reduce false-positive findings in the CAD scheme, thresholding was effective only for the elimination of outliers located outside the central rectangular region.

 

fig.ommitted Figure 6c. (a, b) Scatterplots depict the distribution of the shape index and curvedness values for possible polyps before (a) and after (b) the fuzzy clustering process (Fig 1). Gray dots depict true-positive findings and black squares depict false-positive findings. The number of false-positive findings in b is much smaller than that in a because of the effect of fuzzy clustering. As expected, polyps have higher shape index values and lower curvedness values than do a majority of the false-positive findings. The solid line in b was used in the CAD scheme to help discriminate true- from false-positive findings. A substantial number of false-positive findings can be eliminated by disregarding the possible polyps in the upper left region above the line. (c, d) Scatterplots depict the distribution of CT and gradient values (Hounsfield units) for possible polyps before (c) and after (d) fuzzy clustering. Black squares depict true-positive findings and gray dots depict false-positive findings. The number of false-positive findings in d is much smaller than that in c because of the effect of fuzzy clustering. However, a substantial overlap remains between the true- and false-positive findings in d. Although the minimum and maximum threshold values for CT and gradient values (dashed lines) were used to reduce false-positive findings in the CAD scheme, thresholding was effective only for the elimination of outliers located outside the central rectangular region.

 

fig.ommitted Figure 6d. (a, b) Scatterplots depict the distribution of the shape index and curvedness values for possible polyps before (a) and after (b) the fuzzy clustering process (Fig 1). Gray dots depict true-positive findings and black squares depict false-positive findings. The number of false-positive findings in b is much smaller than that in a because of the effect of fuzzy clustering. As expected, polyps have higher shape index values and lower curvedness values than do a majority of the false-positive findings. The solid line in b was used in the CAD scheme to help discriminate true- from false-positive findings. A substantial number of false-positive findings can be eliminated by disregarding the possible polyps in the upper left region above the line. (c, d) Scatterplots depict the distribution of CT and gradient values (Hounsfield units) for possible polyps before (c) and after (d) fuzzy clustering. Black squares depict true-positive findings and gray dots depict false-positive findings. The number of false-positive findings in d is much smaller than that in c because of the effect of fuzzy clustering. However, a substantial overlap remains between the true- and false-positive findings in d. Although the minimum and maximum threshold values for CT and gradient values (dashed lines) were used to reduce false-positive findings in the CAD scheme, thresholding was effective only for the elimination of outliers located outside the central rectangular region.

 
Figure 6c and 6d shows the distributions of CT values and gradient values for the same set of possible polyps. True-positive findings are more concentrated in 6d than in 6c. However, no substantial differences between the distributions of true-positive and false-positive findings are observed in this figure. Therefore, thresholding of CT values and gradients of CT values was effective only to eliminate outliers. As shown in this figure, we applied simple thresholding with minimum and maximum values for the mean CT values (minimum, -550 HU; maximum, -150 HU) and the mean gradient of CT values (minimum, 145 HU; maximum, 300 HU) of individual possible polyps.

Final polyps detected with the CAD scheme were obtained by regarding the possible polyps in the lower right region of the solid line in Figure 6b and those within the upper and lower threshold values in Figure 6d as detected polyps.

Evaluation of CAD Results
The overall performance of this detection scheme was evaluated by means of a free-response receiver operating characteristic (ROC) analysis on the basis of true- and false-positive findings; this is a generalization of ROC analysis (30). ROC analysis is restricted to situations in which two decision alternatives (normal vs abnormal) are available for each case as a whole. In contrast, free-response ROC analysis can be used when a lesion may be present at more than one position in each case and a CAD algorithm helps in the detection of these lesions. Therefore, free-response ROC analysis allows one to study the detectability of a lesion not only on a case-by-case basis but also on a lesion-by-lesion basis when more than one lesion is present in a given case (30). A free-response ROC curve plots the sensitivity as a function of the average number of false-positive findings (false-positive rate).

The locations of polyps detected with CAD were compared with the true locations of polyps. Detected polyps that were within 5 mm from the true locations were identified as true-positive findings and the others as false-positive findings. In this study, two methods were used to calculate the sensitivity and the average number of false-positive findings: (a) evaluation based on volumetric data sets (by-data-set evaluation) and (b) evaluation based on patients or cases (by-patient evaluation). With both methods, the CAD scheme processed the supine and prone volumetric data sets independently to yield possible polyps. With the first method, supine and prone views of a patient were considered as different data sets, and the sensitivity per data set and the average number of false-positive findings per data set were calculated. With the second method, a polyp was regarded as detected if it was detected on either the supine or the prone view of a patient, and the average number of false-positive findings per patient was calculated. With both methods, free-response ROC curves were generated by moving the dividing line in Figure 6b while keeping its slope constant and by scoring the possible polyps in the lower right region of this dividing line as detected polyps.

For the analysis of false-positive findings, locations of the detected polyps were marked on the muliplanar reformatted views of volume data sets, and each of the experienced radiologists visually and independently inspected the cause of these false-positive findings by using multiplanar reformatted views, with reference to colonoscopic reports. Both the prone and supine views were used as needed during the interpretation. If the two radiologists’ conclusions differed, they made a consensus decision regarding the cause of the false-positive findings.

	RESULTS

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Detection Performance
In the evaluation of the CAD scheme by means of volume data sets, a total of 82 volumetric data sets (18 data sets with one polyp each, and 64 data sets without polyps) were used. In this by-patient evaluation, 89% (16 of 18) of true polyps were detected, with a false-positive rate of 2.0 per data set.

One of the two false-negative findings at colonoscopy was a polyp that was 7 mm on the supine view of the sigmoid colon. As shown in Figure 7a, this polyp appeared much smaller than expected from the physical size because of the partial volume effect, although the same polyp appeared larger on the prone view (Fig 7b). In addition, the polyp appears to be flat on the supine view, whereas it appears more rounded on the prone view. Consequently, the polyp on the supine view did not contain a sufficient number of voxels with low curvedness values and high shape index values; therefore, the polyp was eliminated with thresholding operations of the volume in the detection process. The other false-negative polyp was in a different data set and was also false-negative at CT colonography, because the polyp was located in a completely collapsed segment of the colon. If the colon is not well prepared, the current CAD scheme is limited, and adequate detection may not be possible.

fig.ommitted Figure 7. CT colonographic images of the supine view of a false-negative polyp (arrow in A) in the sigmoid colon. Although the polyp was 7 mm, it appears smaller than expected from the size, which was due mainly to the partial volume effect, and it also appears to be flat. On this view, the polyp did not contain adequate voxels with low curvedness values and high shape index to be detected. B, Prone view of the same polyp (arrow) as in A. The polyp appears rounder and larger than its supine counterpart; thus, it was depicted with the CAD scheme.

 
Of the two false-negative findings, the first occurred on a supine view in one patient, and the second occurred on the prone view in a different patient. Each of the polyps was detected on the other view in the same patient (ie, on the prone view in the first false-negative finding and on the supine view in the second false-negative finding). Consequently, the CAD scheme depicted 100% of the polyps in the by-patient evaluation.

In Figure 8, the dashed free-response ROC curve represents the performance of the CAD scheme on the basis of data sets. The solid free-response ROC curve in Figure 8 shows the performance of the scheme based on patients, which was generated in the same manner as the dashed free-response ROC curve. The solid free-response ROC curve indicates that the scheme yielded 100% sensitivity, with 2.5 false-positive findings per patient.

fig.ommitted Figure 8. Free-response ROC curves show the performance of the CAD scheme for clinically important (5 mm) polyps. The curves were generated by moving the dividing line in Figure 6b from the lower right corner to the upper right corner while maintaining the slope of the line and regarding the possible polyps above and below the line as false- and true-positive, respectively. The solid curve represents the performance of the scheme on the basis of results of CT colonography in 41 patients. A polyp was regarded as detected if it was detected on either the supine or the prone view. The dashed curve represents the performance of the scheme on the basis of 82 CT colonographic volumetric data sets. Polyps and false-positive findings on supine and prone views were counted independently.

 
Four patients with polyps had polyps that were less than 5 mm in size at colonoscopy: one 3-mm polyp in the rectum, five 3-mm polyps in the ascending colon, one 3-mm polyp in the transverse colon, and one diminutive polyp in the cecum. The exact locations of these small polyps were not identified in the colonoscopic reports. We were not able to confirm the locations of these polyps at CT colonography because of their small size; therefore, we could not establish their true locations. However, visual inspection of all the detected polyps by the two experienced radiologists with reference to the colonoscopic report indicated that none of these four diminutive polyps were detected with our scheme.

Analysis of False-Positive Findings
A total of 145 false-positive findings were detected when the scheme was set at 89% sensitivity and 2.0 false-positive findings per data set. Visual inspection of these false-positive findings indicated that they were classified as the nine types shown in the Table. The types of false-positive findings that were included in our computer output were similar to those due to common perceptual errors of radiologists (31). All had high shape index and low curvedness values and thus exhibited polyplike structures. However, most of these false-positive findings could be easily distinguished from true polyps by the experienced radiologists.

fig.ommitted Types of False-positive Findings Generated with CAD

 
False-positive findings caused by folds other than flexures composed about 30% of all the false-positive findings in our scheme. They consisted of sharp folds at the sigmoid, folds prominent on the colon wall, two converging folds, ends of folds in the tortuous colon, and folds in a colon that was not well distended.

Small intestines and the stomach were sometimes contiguous with the colon; thus, they were segmented in the scheme with the colon (Fig 2). Therefore, residual materials inside these organs caused about 20% of all false-positive findings. The false-positive findings were differentiated from polyps once these normal extracolonic organs were identified by radiologists when they examined the polyps depicted with the CAD scheme. False-positive findings caused by ileocecal valves consisted of approximately 14% of all false-positive findings depicted with the CAD scheme. However, differentiating false-positive findings due to the ileocecal valve from polyps was not difficult for the radiologists because of the characteristic location and appearance of the valve.

Retained stool is often a major source of error for radiologists. However, with our CAD scheme, this made up a relatively small portion (approximately 14%) of the false-positive findings because of the exclusion of cases with inadequately prepared colons. Moreover, some of the fecal materials have low average CT values and high gradient values because of the heterogeneity caused by the air in the stool; thus, they were eliminated by means of thresholding operations on the basis of these two features. The two radiologists found that most of these false-positive findings were distinguishable from polyps if both prone and supine views were provided.

Rectal tubes and anorectal junctions were false-positive findings of the CAD scheme (Fig 9). Nine percent of false-positive findings were caused by a rectal tube inserted in the anus for air insufflation during CT colonographic examinations. The tips of the rectal tubes were often sufficiently separated from the rectal wall, and part of the catheter tip simulated a caplike structure, which was identified by the computer as a polyp. Partial volume averaging at anorectal junctions caused about 3% of false-positive findings, which were caused by elevation of the anorectal junctions by the rectal tube. We observed that the partial volume effect enhanced the effect of anorectal junctions that mimicked polyps. They were all easily distinguished by the radiologist on all images.

fig.ommitted Figure 9. CT colonographic images of (A) a false-positive finding (arrow) due to a rectal tube and (B) a false-positive finding (arrow) due to the anorectal junction.

 
Although flexural pseudotumors (masslike projections of the colon wall on the inside of an acute curve) presented common pitfalls on transverse and endoluminal images for the radiologists, they consisted of only about 6% of the false-positive findings. The characteristic location of flexural pseudotumors made it possible to differentiate these false-positive findings from polyps.

Some of the CT colonographic data sets in our database contained motion artifacts. However, such artifacts yielded only 3.5% of the false-positive findings. In these cases, motion artifacts created artificial bumps on normal structures that were similar to polyps (Fig 10). Although the number of false-positive findings that were caused solely by motion artifacts was small, motion artifacts affected the appearance of other false-positive findings, in particular those due to folds, so that they appeared polyplike. Only 3% of false-positive findings were caused by extrinsic compression. This can be attributed to the fact that most of the extrinsic compressions appear to be flattened bumps and do not exhibit sharp caps.

fig.ommitted Figure 10. CT colonographic image of a false-positive finding (arrow) due to motion artifact.

 
Diverticula caused no false-positive findings. This can be attributed to the fact that our method is designed to depict only caplike structures and not cup-like structures, whereas diverticula appear as depressed structures rather than raised structures. When a diverticulum is impacted with fecal materials, it may appear as a raised lesion and mimic a polyp. Such cases were not observed in our database; however, this can be a potential problem when the database is expanded.

	DISCUSSION

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In the past several years, various techniques for the visualization of CT colonographic scans, such as three-dimensional volume rendering (17,32), straightening of colons (33,34), cylindric map projections (35), and "virtual pathology" examinations (36) were reported to be useful for improving the diagnosis of colonic polyps with CT colonography. These methods are used primarily for increasing the conspicuity of polyps for human observers. Summers et al (19) and Paik et al (20) proposed CAD schemes that were potentially useful for automated detection of polyps. However, the accuracy of their schemes in the detection of polyps at colonographic examination in patients with known polyps is uncertain because their studies were performed on the basis of simulated polyps. Vining et al (21) evaluated their CAD scheme on the basis of 10 patients with 15 polyps confirmed at colonoscopy. However, they reported a large number of false-positive findings (approximately 50 per case) and a sensitivity of approximately 73%. Summers et al (22) evaluated their CAD scheme on the basis of 20 patients. Although they achieved an acceptable false-positive rate, they reported a relatively low sensitivity. The high sensitivity and the low false-positive rate in our preliminary results with our CAD scheme show promise of a computerized detection method as a potential aid for interpreting CT colonographic examinations.

Multiobjective Optimization
The free-response ROC curve in Figure 8 may provide only a suboptimal estimation of the possible maximum performance of our CAD scheme in the sense that the curve may not indicate the best possible sensitivity at a given false-positive rate. This is generally true when a free-response ROC curve is generated by a change in the threshold value for a single decision variable, which is in our case the distance between each candidate and the dividing line (Fig 6b). A multiobjective optimization method has been proposed (37) for the generation of an optimal free-response ROC curve that is greater than or equal to any possible free-response ROC curve for the given data and for a CAD scheme. With this method, multiple objectives (eg, sensitivity and false-positive rate) are optimized simultaneously by using a multiobjective genetic algorithm. This method, however, is computationally very expensive, because the multiobjective genetic algorithm is a population-based optimization method and is computationally intractable for a complex scheme such as our CAD scheme. Generation of the optimal free-response ROC curve requires a simplification of the scheme or selection of a small subset of parameters to be adjusted during the optimization process; future studies are needed on this subject.

Free-Response ROC Analysis
In addition to the limitations, free-response ROC analysis has a disadvantage that neither formal curve-fitting procedures nor a statistical test for the evaluation of the statistical difference between two free-response ROC curves was available. Although a method called alternative free-response ROC analysis (38) has been proposed, the validity and reliability of the alternative free-response ROC analysis are not yet fully established (30). The purpose of this study was to determine whether our CAD scheme had the potential to depict polyps at CT colonography with high diagnostic performance. This potential has been shown even though the free-response ROC curves in Figure 8 have these disadvantages and may provide a suboptimal estimation of the performance of our CAD scheme.

Size of the CT Colonographic Database
We were able to collect only a small number of polyps for this pilot study; thus, we are limited in making generalizations about the detection accuracy of our CAD scheme. Evaluation of a larger number of cases of polyps are desirable so that we can obtain a statistically solid performance measurement. It should be noted that, as indicated in Figure 6b, the volumetric features obtained from the true polyps were concentrated in a small region in the feature space. This indicates that the volumetric features used for the detection task characterize the true polyps well. Furthermore, we found that the types of false-positive findings generated with our scheme were similar among different cases, which indicates that our detection results have the potential to be applicable to a larger number of CT colonographic cases. Although our method appears promising, extension to a larger database, retrospectively and prospectively, will be needed to confirm the usefulness of the method.

Need for Observer Studies
Two radiologists examined all of the findings with our CAD scheme for the analysis of false-positive findings. When their interpretations differed, they made a consensus decision regarding the type of false-positive finding. We performed this analysis to understand the types of false-positive findings generated with the CAD scheme and not to estimate the benefit of the CAD scheme. To evaluate the benefit of our CAD scheme in the improvement of radiologists’ reading time and detection performance, we need to conduct an observer study on the basis of an ROC analysis (39), as has been conducted for other types of CAD schemes (40).

Clinical Relevance
If the results of our study, 100% sensitivity with 2.5 false-positive findings per patient, are translated to a larger screening population, radiologists will need to interpret only few regions that are indicated with the CAD scheme in a CT colonographic examination. Moreover, radiologists will be able to closely examine the area of false-positive findings to differentiate false-positive findings from true polyps. Thus, the number of false-positive detections will be substantially reduced at CT colonography when radiologists are aided by CAD. Currently, the cost-effectiveness of CT colonography in screening colon cancer is not known, because the lower limit of the detectable size of lesions at CT colonography is not completely known, which affects the frequency of follow-up. With the aid of a CAD scheme with high diagnostic performance, it is reasonable to expect a substantial reduction in the interpretation time, while the accuracy will be maintained or increased. Such a CAD scheme has the potential to bring CT colonography one step closer to a cost-effective clinical practice and especially to the screening setting. Future studies that estimate improvement in radiologists’ reading times and detection accuracies with CAD are expected to show the benefit of this detection scheme in a clinical setting.

	STATISTICAL CONSULTANT COMMENTARY

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In this article, the authors applied linear discriminant analysis to determine the dividing line for possible polyps by using both shape index and curvedness (Fig 6b). Discriminant analysis is the statistical method for determining the linear or curvilinear boundaries that separate two or more groups by using a number of variables. To be precise, let x and y be the two variables, and we wish to use the variables to discriminate or separate patients into two well-defined and discrete groups. It could happen that the use of x and y separately may be futile or not very effective, but the discriminant analysis in which both x and y are used together could be very effective.

This analysis can yield the optimal boundaries on the basis of a combination of the variables and is at least as efficient but practically always superior to that based on the boundary determined by means of separate analysis for each variable. Thus, in Figure 6b, for example, analysis of the two variables separately would result in the boundary defined by the shape index to be greater than 0.87 and the curvedness of less than 0.14 for possible polyps. The boundary that is based on the presented line, which was derived from discriminant analysis based on both factors, is better because it minimizes the sum of false-positive and false-negative findings. Although the effectiveness of discriminant analysis for the presented data may not be so obvious, the result of the analysis can be extremely effective in some situations.

In conclusion, investigators are advised to consider using discriminant analysis if they wish to determine the boundaries to separate two or more different groups of subjects by using two or more variables. Several widely available statistical packages can be used to perform the discriminant analysis.

	ACKNOWLEDGMENTS

 
The authors thank the members of the Kurt Rossmann Laboratories in the Department of Radiology at the University of Chicago for helpful discussions and Elisabeth F. Lanzl for improving the manuscript for this article.

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