Shape measurements form powerful features for recognizing objects, and many imaging modalities produce three-dimensional shape information. Stereo-photogrammetric techniques have been extensively developed, and many researchers have looked at related techniques such as shape from motion, shape from accommodation, and shape from shading. Recently, considerable attention has focused on laser radar systems for imaging distant objects, such as automobiles from an airborne platform, and on laser-based active stereo imaging for close-range objects, such as part scanners for automated inspection. Each use of these laser imagers generally results in a range image, an array of distance measurements as a function of direction. For multi-look data or data fused from multiple sensors, we may more generally treat the data as a 3D point-cloud, an unordered collection of 3D points measured from the surface of the scene. This paper presents a general approach to object recognition in the presence of significant clutter, that is suitable for application to a wide range of 3D imaging systems. The approach relies on a probabilistic framework relating 3D point-cloud data and the objects from which they are measured. Through this framework a minimum probability of error recognition algorithm is derived that accounts for both obscuring and nonobscuring clutter, and that accommodates arbitrary (range and cross-range) measurement errors. The algorithm is applied to a problem of target recognition from actual 3D point-cloud data measured in the laboratory from scale models of civilian automobiles. Noisy 3D measurements are used to train models of the automobiles, and these models are used to classify the automobiles when present in a scene containing natural and man-made clutter.