Image processing and pattern recognition can be performed efficiently on a pyramid computer. In this paper, pyramid computer algorithms are presented that operate on an arbitrary digitized picture existing in the nxn base of the pyramid. Algorithms are presented that solve the component labeling and nearest neighbor problems in theta (n**1**/**2) time. An algorithm that identifies the extreme points of the convex hull for an arbitrary figure in theta (log**2n) time is presented, as is an algorithm to compute the external diameter of a figure in theta (n**1**/**3log n) time. These results are not only superior to existing results, but they also have the advantage of not posing restrictions on the digitized picture.