Non-Rigid Puzzles

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non-rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non-rigid multi-part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non-rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario

Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the problem is strongly NP-complete even if the pieces are all polyominos. On the positive side, we show that the problem can be solved in polynomial time if the number of pieces is a fixed constant

JigsawNet: Shredded Image Reassembly using Convolutional Neural Network and Loop-based Composition

This paper proposes a novel algorithm to reassemble an arbitrarily shredded image to its original status. Existing reassembly pipelines commonly consist of a local matching stage and a global compositions stage. In the local stage, a key challenge in fragment reassembly is to reliably compute and identify correct pairwise matching, for which most existing algorithms use handcrafted features, and hence, cannot reliably handle complicated puzzles. We build a deep convolutional neural network to detect the compatibility of a pairwise stitching, and use it to prune computed pairwise matches. To improve the network efficiency and accuracy, we transfer the calculation of CNN to the stitching region and apply a boost training strategy. In the global composition stage, we modify the commonly adopted greedy edge selection strategies to two new loop closure based searching algorithms. Extensive experiments show that our algorithm significantly outperforms existing methods on solving various puzzles, especially those challenging ones with many fragment pieces

Solving Jigsaw Puzzles By the Graph Connection Laplacian

We propose a novel mathematical framework to address the problem of automatically solving large jigsaw puzzles. This problem assumes a large image, which is cut into equal square pieces that are arbitrarily rotated and shuffled, and asks to recover the original image given the transformed pieces. The main contribution of this work is a method for recovering the rotations of the pieces when both shuffles and rotations are unknown. A major challenge of this procedure is estimating the graph connection Laplacian without the knowledge of shuffles. We guarantee some robustness of the latter estimate to measurement errors. A careful combination of our proposed method for estimating rotations with any existing method for estimating shuffles results in a practical solution for the jigsaw puzzle problem. Numerical experiments demonstrate the competitive accuracy of this solution, its robustness to corruption and its computational advantage for large puzzles

Puzzling the 120-cell

We introduce Quintessence: a family of burr puzzles based on the geometry and combinatorics of the 120-cell. We discuss the regular polytopes, their symmetries, the dodecahedron as an important special case, the three-sphere, and the quaternions. We then construct the 120-cell, giving an illustrated survey of its geometry and combinatorics. This done, we describe the pieces out of which Quintessence is made. The design of our puzzle pieces uses a drawing technique of Leonardo da Vinci; the paper ends with a catalogue of new puzzles.Comment: 25 pages, many figures. Exposition and figures improved throughout. This is the long version of the shorter published versio