In recent years there has been a tremendous increase in computer vision research using range images (or depth maps) as sensor input data. The most attractive feature of range images is the explicitness of the surface information. Many industrial and navigational robotic tasks will be more easily accomplished if such explicit depth information can be efficiently obtained and interpreted. Intensity image understanding research has shown that the early processing of sensor data should be data-driven. The goal of early processing is to generate a rich description for later processing. Classical differential geometry provides a complete local description of smooth surfaces. The first and second fundamental forms of surfaces provide a set of differential-geometric shape descriptors that capture domain-independent surface information. Mean curvature and Gaussian curvature are the fundamental second-order surface characteristics that possess desirable invariance properties and represent extrinsic and intrinsic surface geometry respectively. The signs of these surface curvatures are used to classify range image regions into one of eight basic viewpoint-independent surface types. Experimental results for real and synthetic range images show the properties, usefulness, and importance of differential-geometric surface characteristics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26326/1/0000413.pd
