Efficient Pose Clustering Using a Randomized Algorithm

Pose clustering is a method to perform object recognition by determining hypothetical object poses and finding clusters of the poses in the space of legal object positions. An object that appears in an image will yield a large cluster of such poses close to the correct position of the object. If there are m model features and n image features, then there are O(m3n3) hypothetical poses that can be determined from minimal information for the case of recognition of three-dimensional objects from feature points in two-dimensional images. Rather than clustering all of these poses, we show that pose clustering can have equivalent performance for this case when examining only O(mn) poses, due to correlation between the poses, if we are given two correct matches between model features and image features. Since we do not usually know two correct matches in advance, this property is used with randomization to decompose the pose clustering problem into O(n2) problems, each of which clusters O(mn) poses, for a total complexity of O(mn3) . Further speedup can be achieved through the use of grouping techniques. This method also requires little memory and makes the use of accurate clustering algorithms less costly. We use recursive histograming techniques to perform clustering in time and space that is guaranteed to be linear in the number of poses. Finally, we present results demonstrating the recognition of objects in the presence of noise, clutter, and occlusion.