Two-dimensional partially visible object recognition using efficient multidimensional range queries

An important task in computer vision is the recognition of partially visible two-dimensional objects in a gray scale image. Recent works addressing this problem have attempted to match spatially local features from the image to features generated by models of the objects. However, many algorithms are less efficient than is possible. This is due primarily to insufficient attention being paid to the issues of reducing the data in features and feature matching. In this paper we discuss an algorithm that addresses both of these problems. Our algorithm uses the local shape of contour segments near critical points, represented in slope angle-arclength space (θ-s space), as the fundamental feature vectors. These fundamental feature vectors are further processed by projecting them onto a subspace of θ-s space that is obtained by applying the Karhunen-Loève expansion to all critical points in the model set to obtain the final feature vectors. This allows the data needed to store the features to be reduced, while retaining nearly all their recognitive information. The resultant set of feature vectors from the image are matched to the model set using multidimensional range queries to a database of model feature vectors. The database is implemented using an efficient data-structure called a k-d tree. The entire recognition procedure for one image has complexity O(IlogI + IlogN), where I is the number of features in the image, and N is the number of model features. Experimental results showing our algorithm's performance on a number of test images are presented.