Reassembling fractured objects by geometric matching

Abstract

We present a system for automatic reassembly of broken 3D solids. Given as input 3D digital models of the broken fragments, we analyze the geometry of the fracture surfaces to find a globally consistent reconstruction of the original object. Our reconstruction pipeline consists of a graph-cuts based segmentation algorithm for identifying potential fracture surfaces, feature-based robust global registration for pairwise matching of fragments, and simultaneous constrained local registration of multiple fragments. We develop several new techniques in the area of geometry processing, including the novel integral invariants for computing multi-scale surface characteristics, registration based on forward search techniques and surface consistency, and a non-penetrating iterated closest point algorithm. We illustrate the performance of our algorithms on a number of real-world examples.

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

“…The pairwise registration was then generated by the Iterative Closest Point (ICP) algorithm. The algorithm iteratively revised the transformation (combination of translation and rotation) needed to minimize the distance from the source to the reference point cloud [62]. The proposed approach for optimization is based on the concept of difference surface and the introduction of signed distance.…”

Multiscale 3D Feature Extraction and Matching

“…4) Registration. For each keypoint k on A find its correspondence on B by finding the keypoint on B whose feature vector has the smallest L 2 distance from the feature vector of k. Finally, use a branch and bound approach similar to [3] to eliminate incorrect point-point correspondences and register B with A.…”

“…The main applications of shape matching are 3D shape registration, recognition, retrieval, and classification. These applications, in turn, are used in higher-level processing tasks, such as 3D search engines [2] and automatic 3D model generation from physical objects [3].…”

“…In this case, the similarity is measured between partial regions of input objects, where the relative position, orientation, scale, and the extent of overlap may be unknown. Although various algorithms exist in the literature for 3D partial shape matching [3], [4], they do not handle shapes of arbitrary scale. We address this problem by introducing a new 3D surface matching approach based on the scale-space theory of signals.…”

Pairwise region-based scan alignment

“…Examples of such descriptors include curvature-based quantities [9], [18], [5], shape index [4], integral volume descriptor [7], [11]. These descriptors are computed around a small neighborhood.…”