Automatic polyp detection is an increasingly important task in medical imaging with virtual colonoscopy [15] being widely used. In this paper, we present a 3D object detection algorithm and show its application on polyp detection from CT images. We make the following contributions: (1) The system adopts Probabilistic Boosting Tree (PBT) to probabilistically detect polyps. Integral volume and 3D Haar filters are introduced to achieve fast feature computation. (2) We give an explicit convergence rate analysis for the AdaBoost algorithm [2] and prove that the error at each step \in t+1. is tightly bounded by the previous error \in t. (3) For a 3D polyp template, a generative model is defined. Given the bound and convergence analysis, we analyze the role of "sample alignment" in the template design and devise a robust and efficient algorithm for polyp detection. The overall system has been tested on 150 volumes and the results obtained are very encouraging.