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A new set of variable dimensional local shape descriptors for 3D registration is proposed and applied to 3D model building from range images. The descriptors are based on a large set of properties represented as high dimensional histograms. The novelty of the method is two fold: first, it offers a generalized platform for a large class of local shape descriptors; second, unlike previously devised descriptors that are of low dimensionality and compact size, these descriptors are high dimensional and highly discriminating. The new approach suggests investing more into descriptor generation and comparison and in return gaining a higher percentage of inliers in the set of hypothesized point matches across the images being registered. This in turn drastically reduces the required number of RANSAC iterations for finding the alignment between two images, as is confirmed by experimentation in a 3D model building application. It is also shown that the correct choice of properties can increase the effectiveness of feature correspondences, thereby increasing the possible acquisition angle between overlapping images.