Discrete Minimum Distortion Correspondence Problems for Non-rigid Shape Matching

Abstract

Abstract. Similarity and correspondence are two fundamental archetype problems in shape analysis, encountered in numerous application in computer vision and pattern recognition. Many methods for shape similarity and correspondence boil down to the minimum-distortion correspondence problem, in which two shapes are endowed with certain structure, and one attempts to find the matching with smallest structure distortion between them. Defining structures invariant to some class of shape transformations results in an invariant minimum-distortion correspondence or similarity. In this paper, we model shapes using local and global structures, formulate the invariant correspondence problem as binary graph labeling, and show how different choice of structure results in invariance under various classes of deformations.

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

“…e.g. (Bronstein et al, 2011;Funkhouser and Shilane, 2006;Gelfand et al, 2005;Lipman and Funkhouser, 2009;Wang et al, 2010;Windheuser et al, 2011;Zeng et al, 2010;Zhang et al, 2008), the only fully-automatic non-rigid approaches to intra-operative registration of range data in abdominal procedures have been applied in open surgery (dos and do not provide real-time performance. To avoid the computational demands of repeating the registration process over time, an alternative registration approach involves continuously updating an initially performed registration via tissue tracking using the endoscopic image information acquired during surgery.…”

From Low-Cost Depth Sensors to CAD: Cross-Domain 3D Shape Retrieval via Regression Tree Fields

“…To this end, various local features have been developed to describe the local geometry of 3D models, including MeshHoG as a 3D extension of the SIFT feature [7], Heat Kernel Signature [8] [11], and Intrinsic Shape Context [9]. Realizing the sensitivity to model noise for those local descriptors [15], researchers also proposed to use high-level topological features [19][20], or aggregate low-level features to mid-level representations such as the extended Bag-of-Words model [10][21] and graph correspondences [22].…”

Hierarchical Matching of Non-rigid Shapes

“…Wang et al . [36] used a similar problem formulation, casted as a graph labeling problem, and experimented with different surface descriptors and metrics.…”

“…Each point x ∈ X is now matched to a point c(x) ∈ Y by the mapping c. We denote y = c(x) if C(x, y) = 1. In each iteration we search for the best correspondence between x and c(x) neighborhood, instead of all points y ∈ Y , in a manner similar to [36]. Between iterations we add points x ∈ X and y ∈ Y using the 2-optimal Farthest Point Sampling (FPS) strategy [15], evaluate the neighborhood in Y of the new points, reevaluate the neighborhood of the old points, and continue until convergence.…”