This research addresses problems in machine perception and robotics. The work is focused in two areas: recognizing curved objects in images, and mobile robot navigation. Recognizing complex curved 3D objects, whose image features depend strongly on viewpoint, is one of the fundamental problems of computer vision. Objects are modelled by collections of algebraic surfaces and their intersection curves, and the geometric constraints involved in predicting and interpreting the images of these models are represented by sets of polynomial constraints. Techniques from algebraic geometry and robust numerical methods can be used to solve these constraints. Viewpoint dependent features are predicted from an object model and represented as an aspect graph which enumerates all topologically distinct views. Elimination theory is used to relate image measurements to objects, and optimization techniques can be applied to estimate an object's pose; objects are then recognized from a library of models. Problems to be addressed include automatic generation of object models, new object representations, prediction for sensors with limited resolution, computational efficiency, and indexing large data bases. Mobile robots provide a dynamic test-bed for robust computer vision algorithms in an unstructured world. In addition to developing new sensors, research focuses on obtaining the necessary information to perform a task. While some activities are readily achieved through visual serving, others require developing a 3D representation of the environment. Stereo and structure-from-motion provide 3D information from image measurements which can be incorporated into a relational map. This map forms the basis for motion planning; paths revisit previously seen places and strategies for exploring new areas can be determined. Additionally, robot tasks and cultural constraints are described more naturally when objects are recognized within this map.
