Robust Algorithms for Object Localization

Model-based localization, the task of estimating an object's pose from sensed and corresponding model features, is a fundamental task in machine vision. Exact constant time localization algorithms have been developed for the case where the sensed features and the model features are the same type. Still, it is not uncommon for the sensed features and the model features to be of different types, i.e., sensed data points may correspond to model faces or edges. Previous localization approaches have handled different model and sensed features of different types via sampling and synthesizing virtual features to reduce the problem of matching features of dissimilar types to the problem of matching features of similar types. Unfortunately, these approaches may be suboptimal because they introduce artificial errors. Other localization approaches have reformulated object localization as a nonlinear least squares problem where the error is between the sensed data and model features in image coordinates (the Euclidean image error metric). Unfortunately, all of the previous approaches which minimized the Euclidean image error metric relied on gradient descent methods to find the global minima, and gradient descent methods may suffer from problems of local minima. In this paper, we describe an exact, efficient solution to the nonlinear least squares minimization problem based upon resultants, linear algebra, and numerical techniques. On a SPARC 20, our localization algorithm runs in a few microseconds for rectilinear polygonal models, a few milliseconds for generic polygonal models, and one second for generalized polygonal models (models composed of linear edges and circular arcs).