Author

# Weixin Kong

Bio: Weixin Kong is an academic researcher from Brown University. The author has an hindex of 3, co-authored 3 publications receiving 281 citations.

##### Papers

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Brown University

^{1}TL;DR: R ridges of 3D fragments scanned using a laser range finder are detected using a dynamic programming method and a pair of ridges are matched using a generalization of the 2D curve matching approach to space curves by using an energy solution involving curvature and torsion.

Abstract: We approach the problem of 2D and 3D puzzle solving by matching the geometric features of puzzle pieces three at a time. First, we define an affinity measure for a pair of pieces in two stages, one based on a coarse-scale representation of curves and one based on a fine-scale elastic curve matching method. This re-examination of the top coarse-scale matches at the fine scale results in an optimal relative pose as well as a matching cost which is used as the affinity measure for a pair of pieces. Pairings with overlapping boundaries are impossible and are removed from further consideration, resulting in a set of top valid candidate pairs. Second, triples arising from generic junctions are formed from this rank-ordered list of pairs. The puzzle is solved by a recursive grouping of triples using a best-first search strategy, with backtracking in the case of overlapping pieces. We also generalize aspects of this approach to matching of 3D pieces. Specifically, ridges of 3D fragments scanned using a laser range finder are detected using a dynamic programming method. A pair of ridges are matched using a generalization of the 2D curve matching approach to space curves by using an energy solution involving curvature and torsion, which are computed using a novel robust numerical method. The reconstruction of map fragments and broken tiles using this method is illustrated.

175 citations

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Brown University

^{1}TL;DR: The overall approach to the automatic estimation of mathematical models of such pots from 3D measurements of sherds is presented, which is a representation suitable for comparisons, geometric feature extraction, visualization and digital archiving.

Abstract: A heretofore unsolved problem of great archaeological importance is the automatic assembly of pots made on a wheel from the hundreds (or thousands) of sherds found at an excavation site. An approach is presented to the automatic estimation of mathematical models of such pots from 3D measurements of sherds. The overall approach is formulated and described and some detail is provided on the elements of the procedure. The end result is a representation suitable for comparisons, geometric feature extraction, visualization and digital archiving. Matching of fragments and aligning them geometrically is based on matching break-curves (curves on a pot surface separating fragments), estimated axes and profile curves for individual fragments and groups of matched fragments, and a number of features of groups of break-curves. Pot assembly is a bottom-up maximum likelihood performance-based search. In our case, associated with subassemblies of fragments is a loglikelihood which is a sum of energy functions. Experiments are illustrated on pots which were broken for the purpose, and on sherds from an archaeological dig located in Petra, Jordan. The addressed problem and solution can be considered as problems in "geometric learning" and in "perceptual grouping," where subgroups of pot fragments at a site location are to be assembled into individual virtual pots and other fragments are to be discarded as clutter.

65 citations

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Brown University

^{1}TL;DR: An approach is presented to the automatic estimation of mathematical models of such pots from 3D measurements of sherds, using a Bayesian approach beginning with a description of the complete set of geometric parameters that determine the distribution of the sherd measurement data.

Abstract: A heretofore unsolved problem of great archaeological importance is the automatic assembly of pots made on a wheel from the hundreds (or thousands) of sherds found at an excavation site. An approach is presented to the automatic estimation of mathematical models of such pots from 3D measurements of sherds. A Bayesian approach is formulated beginning with a description of the complete set of geometric parameters that determine the distribution of the sherd measurement data. Matching of fragments and aligning them geometrically into configurations is based on matching break-curves (curves on a pot surface separating fragments), estimated axis and profile curve pairs for individual fragments and configurations of fragments, and a number of features of groups of break-curves. Pot assembly is a bottom-up maximum likelihood performance-based search. Experiments are illustrated on pots which were broken for the purpose, and on sherds from an archaeological dig located in Petra, Jordan. The performance measure can also be an aposteriori probability, and many other types of information can be included, e.g., pot wall thickness, surface color, patterns on the surface, etc. This can also be viewed as the problem of learning a geometric object from an unorganized set of free-form fragments of the object and of clutter, or as a problem of perceptual grouping.

46 citations

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01 Jul 2006

TL;DR: This work develops 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.

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.

318 citations

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Vassar College

^{1}TL;DR: It is shown that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete.

Abstract: We show that jigsaw puzzles, edge-matching puzzles, and polyomino packing puzzles are all NP-complete. Furthermore, we show direct equivalences between these three types of puzzles: any puzzle of one type can be converted into an equivalent puzzle of any other type.

241 citations

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13 Jun 2010TL;DR: In this article, the problem of reconstructing an image from a bag of square, non-overlapping image patches, the jigsaw puzzle problem, is considered and a graphical model is developed to solve it.

Abstract: We explore the problem of reconstructing an image from a bag of square, non-overlapping image patches, the jigsaw puzzle problem. Completing jigsaw puzzles is challenging and requires expertise even for humans, and is known to be NP-complete. We depart from previous methods that treat the problem as a constraint satisfaction problem and develop a graphical model to solve it. Each patch location is a node and each patch is a label at nodes in the graph. A graphical model requires a pairwise compatibility term, which measures an affinity between two neighboring patches, and a local evidence term, which we lack. This paper discusses ways to obtain these terms for the jigsaw puzzle problem. We evaluate several patch compatibility metrics, including the natural image statistics measure, and experimentally show that the dissimilarity-based compatibility – measuring the sum-of-squared color difference along the abutting boundary – gives the best results. We compare two forms of local evidence for the graphical model: a sparse-and-accurate evidence and a dense-and-noisy evidence. We show that the sparse-and-accurate evidence, fixing as few as 4 – 6 patches at their correct locations, is enough to reconstruct images consisting of over 400 patches. To the best of our knowledge, this is the largest puzzle solved in the literature. We also show that one can coarsely estimate the low resolution image from a bag of patches, suggesting that a bag of image patches encodes some geometric information about the original image.

181 citations

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01 Aug 2008TL;DR: This work presents an inexpensive system for acquiring all three types of information, and associated metadata, for small objects such as fragments of wall paintings, and presents a novel 3-D matching algorithm that efficiently searches for matching fragments using the scanned geometry.

Abstract: Although mature technologies exist for acquiring images, geometry, and normals of small objects, they remain cumbersome and time-consuming for non-experts to employ on a large scale. In an archaeological setting, a practical acquisition system for routine use on every artifact and fragment would open new possibilities for archiving, analysis, and dissemination. We present an inexpensive system for acquiring all three types of information, and associated metadata, for small objects such as fragments of wall paintings. The acquisition system requires minimal supervision, so that a single, non-expert user can scan at least 10 fragments per hour. To achieve this performance, we introduce new algorithms to robustly and automatically align range scans, register 2-D scans to 3-D geometry, and compute normals from 2-D scans. As an illustrative application, we present a novel 3-D matching algorithm that efficiently searches for matching fragments using the scanned geometry.

161 citations

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05 Jun 2002TL;DR: The overall strategy follows that of previous algorithms but applies a number of new ideas, such as robust fiducial points, "highest- confidence-first" search, and frequent global reoptimization of partial solutions.

Abstract: We present a new algorithm for automatically solving jigsaw puzzles by shape alone. The algorithm can solve more difficult puzzles than could be solved before, without the use of backtracking or branch-and-bound. The algorithm can handle puzzles in which pieces border more than four neighbors, and puzzles with as many as 200 pieces. Our overall strategy follows that of previous algorithms but applies a number of new ideas, such as robust fiducial points, "highest- confidence-first" search, and frequent global reoptimization of partial solutions.

151 citations