The Iterative Closest Point (ICP)
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.
Figure 1: The Gaussian kd-tree accelerates a broad class of non-linear filters, including the bilateral (left), non-local means (middle), and a novel non-local means for geometry (right). AbstractWe propose a method for accelerating a broad class of non-linear filters that includes the bilateral, non-local means, and other related filters. These filters can all be expressed in a similar way: First, assign each value to be filtered a position in some vector space. Then, replace every value with a weighted linear combination of all values, with weights determined by a Gaussian function of distance between the positions. If the values are pixel colors and the positions are (x, y) coordinates, this describes a Gaussian blur. If the positions are instead (x, y, r, g, b) coordinates in a five-dimensional space-color volume, this describes a bilateral filter. If we instead set the positions to local patches of color around the associated pixel, this describes non-local means. We describe a Monte-Carlo kdtree sampling algorithm that efficiently computes any filter that can be expressed in this way, along with a GPU implementation of this technique. We use this algorithm to implement an accelerated bilateral filter that respects full 3D color distance; accelerated non-local means on single images, volumes, and unaligned bursts of images for denoising; and a fast adaptation of non-local means to geometry. If we have n values to filter, and each is assigned a position in a d-dimensional space, then our space complexity is O(dn) and our time complexity is O(dn log n), whereas existing methods are typically either exponential in d or quadratic in n.
We propose a framework for pairwise registration of shapes represented by point cloud data (PCD)
We propose a method for segmentation of 3D scanned shapes into simple geometric parts. Given an input point cloud, our method computes a set of components which possess one or more slippable motions: rigid motions which, when applied to a shape, slide the transformed version against the stationary version without forming any gaps. Slippable shapes include rotationally and translationally symmetrical shapes such as planes, spheres, and cylinders, which are often found as components of scanned mechanical parts. We show how to determine the slippable motions of a given shape by computing eigenvalues of a certain symmetric matrix derived from the points and normals of the shape. Our algorithm then discovers slippable components in the input data by computing local slippage signatures at a set of points of the input and iteratively aggregating regions with matching slippable motions. We demonstrate the performance of our algorithm for reverse engineering surfaces of mechanical parts.
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