We have developed a technique to study how good computers can be at diagnosing gastrointestinal lesions from regular (white light and narrow banded) colonoscopic videos compared to two levels of clinical knowledge (expert and beginner). Our technique includes a novel tissue classification approach which may save clinician's time by avoiding chromoendoscopy, a time-consuming staining procedure using indigo carmine. Our technique also discriminates the severity of individual lesions in patients with many polyps, so that the gastroenterologist can directly focus on those requiring polypectomy. Technically, we have designed and developed a framework combining machine learning and computer vision algorithms, which performs a virtual biopsy of hyperplastic lesions, serrated adenomas and adenomas. Serrated adenomas are very difficult to classify due to their mixed/hybrid nature and recent studies indicate that they can lead to colorectal cancer through the alternate serrated pathway. Our approach is the first step to avoid systematic biopsy for suspected hyperplastic tissues. We also propose a database of colonoscopic videos showing gastrointestinal lesions with ground truth collected from both expert image inspection and histology. We not only compare our system with the expert predictions, but we also study if the use of 3D shape features improves classification accuracy, and compare our technique's performance with three competitor methods.