Colorectal cancer is the third most common type of cancer worldwide. However, this disease can be prevented by detection and removal of precursor adenomatous polyps during optical colonoscopy (OC). During OC, the endoscopist looks for colon polyps. While hyperplastic polyps are benign lesions, adenomatous polyps are likely to become cancerous. Hence, it is a common practice to remove all identified polyps and send them to subsequent histological analysis. But removal of hyperplastic polyps poses unnecessary risk to patients and incurs unnecessary costs for histological analysis. In this paper, we develop the first part of a novel optical biopsy application based on narrow-band imaging (NBI). A barrier to an automatic system is that polyp classification algorithms require manual segmentations of the polyps, so we automatically segment polyps in colonoscopic NBI data. We propose an algorithm, Shape-UCM, which is an extension of the gPb-OWT-UCM algorithm, a state-of-the-art algorithm for boundary detection and segmentation. Shape-UCM solves the intrinsic scale selection problem of gPb-OWT-UCM by including prior knowledge about the shape of the polyps. Shape-UCM outperforms previous methods with a specificity of 92%, a sensitivity of 71%, and an accuracy of 88% for automatic segmentation of a test set of 87 images.