The ability to automatically match two-dimensional (2D) scans of three-dimensional (3D) objects is a basic problem in 3D modeling. Mian, Bennamoun, and Owens describe a novel method for matching surface features, using third-order tensors that characterize each surface segment. Matched tensors in each image are used to generate correspondences between each image. With sufficient different views, the entire object can be modeled, including areas hidden in some of the views.

The goal is to have an automated process that does not require user intervention. The procedure begins with finding coarse features by essentially connecting the dots from a point cloud generated in acquiring the view. The number of points used and the number of triangular segments describing the surface of the object are determined by proximity tests, and tests on the norms of each segment, so that proper tensors describing each surface patch can be generated. Based on the coarse surface representation of the object, corresponding features among views can be registered. Then, a finer mesh is generated, and a complete 3D model can be produced using the matched views.

This is a fairly long paper, at 22 pages, but it is thorough. It begins with an introduction that is a review of the literature. The next section describes the tensor representation of the surface elements. The tensors need to be stable with respect to local axis systems, so that they can be matched (section 3). Matching the tensors pairwise in an automatic process is discussed in the fourth section. Generating the 3D model is covered in a short fifth section. The sixth section starts the presentation of results using the tensor technique. Section 7 presents a quantitative analysis of the accuracy, robustness, and efficiency of the automatic registration algorithm. The eighth section presents data demonstrating the superior performance of the authors’ tensor method compared to using spin images. The tensor approach is fast, reliable, and robust. Its novelty is the basis of an Australian software patent application.