Matching Tensors for Automatic Correspondence and Registration

Abstract

Abstract.Complete 3-D modeling of a free-form object requires acquisition from multiple view-points. These views are then required to be registered in a common coordinate system by establishing correspondence between them in their regions of overlap. In this paper, we present an automatic correspondence technique for pair-wise registration of different views of a free-form object. The technique is based upon a novel robust representation scheme reported in this paper. Our representation scheme defines local 3-D grids over the object's surface and represents the surface inside each grid by a fourth order tensor. Multiple tensors are built for the views which are then matched, using a correlation and verification technique to establish correspondence between a model and a scene tensor. This correspondence is then used to derive a rigid transformation that aligns the two views. The transformation is verified and refined using a variant of ICP. Our correspondence technique is fully automatic and does not assume any knowledge of the viewpoints or regions of overlap of the data sets. Our results show that our technique is accurate, robust, efficient and independent of the resolution of the views.

Geometry and Convergence Analysis of Algorithms for Registration of 3D Shapes

“…Robust point set registration using a statistical rather than geometric approach has been proposed by Tsin and Kanade (2004). For an overview of further recent literature on registration we also refer to (Eggert et al (1998); Gelfand et al (2003); Ikemoto et al (2003); Mian et al (2004); Rodrigues et al (2002) and the references therein.…”

3D Recognition and Segmentation of Objects in Cluttered Scenes

“…1 shows the high resolution models and their corresponding low resolution models which are obtained by applying a mesh simplification algorithm [10] to the high resolution models. The high resolution models were built with our automatic 3D modeling algorithm [20][21] (range data courtesy of the University of Stuttgart [12]). Only the low resolution models were stored in our model library.…”

“…Briefly our algorithm proceeds as follows. During an offline phase a 3D model library of objects is built along with their tensor representations [20]. A 4D hash table (variant of [17]) is also constructed from the model tensors for quick indexing.…”

From unordered range images to 3D models: a fully automatic multiview correspondence algorithm

“…During an offline representation phase, tensors are built for all the range images [15]. First all the range images, in the form of point clouds, are converted into triangular meshes Å (where ½ AE ).…”

“…In this paper we propose a fully automatic and efficient multiview correspondence algorithm based on our previous work [15] [16]. Our algorithm efficiently builds tensors for all range images and indexes them through a table for fast reference (Section 2).…”