Adenomatous polyps in the colon are believed to be the precursor to colorectal carcinoma, the second leading cause of cancer deaths in United States. In this paper, we propose a new method for computer-aided detection of polyps in computed tomography (CT) colonography (virtual colonoscopy), a technique in which polyps are imaged along the wall of the air-inflated, cleansed colon with X-ray CT. Initial work with computer aided detection has shown high sensitivity, but at a cost of too many false positives. We present a statistical approach that uses support vector machines to distinguish the differentiating characteristics of polyps and healthy tissue, and uses this information for the classification of the new cases. One of the main contributions of the paper is the new three-dimensional pattern processing approach, called random orthogonal shape sections method, which combines the information from many random images to generate reliable signatures of shape. The input to the proposed system is a collection of volume data from candidate polyps obtained by a high-sensitivity, low-specificity system that we developed previously. The results of our ten-fold cross-validation experiments show that, on the average, the system increases the specificity from 0.19 (0.35) to 0.69 (0.74) at a sensitivity level of 1.0 (0.95).