Efficient Recognition of Partially Visible Objects Using a Logarithmic Complexity Matching Technique

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Abstract
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 algo rithms are considerably less efficient than they might be, typ ically being O(IN) or worse, where I is the number offeatures in the image and N is the number of features in the model set. This is invariably due to the feature-matching portion of the algorithm. In this paper we discuss an algorithm that significantly improves the efficiency offeature matching. In addition, we show experimentally that our recognition algo rithm is accurate and robust. Our algorithm uses the local shape of contour segments near critical points, represented in slope angle-arclength space (θ-s space), as fundamental fea ture vectors. These feature vectors are further processed by projecting them onto a subspace in θ-s space that is obtained by applying the Karhunen-Loève expansion to all such fea tures in the set of models, yielding the final feature vectors. This allows the data needed to store the features to be re duced, while retaining nearly all information important for recognition. The heart of the algorithm is a technique for performing matching between the observed image features and the precomputed model features, which reduces the runtime complexity from O(IN) to O(I log I + I log N), where I and N are as above. The matching is performed using a tree data structure, called a kD tree, which enables multidi mensional searches to be performed in O(log) time.

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