On Pencils of Tangent Planes and the Recognition of Smooth 3D Shapes from Silhouettes

This paper presents a geometric approach to recognizing smooth objects from their outlines. We define a signature function that associates feature vectors with objects and baselines connecting pairs of possible viewpoints. Feature vectors, which can be projective, affine, or Euclidean, are computed using the planes that pass through a fixed baseline and are also tangent to the object's surface. In the proposed framework, matching a test outline to a set of training outlines is equivalent to finding intersections in feature space between the images of the training and the test signature functions. The paper presents experimental results for the case of internally calibrated perspective cameras, where the feature vectors are angles between epipolar tangent planes.