83,224 research outputs found
A Global Approach for Solving Edge-Matching Puzzles
We consider apictorial edge-matching puzzles, in which the goal is to arrange
a collection of puzzle pieces with colored edges so that the colors match along
the edges of adjacent pieces. We devise an algebraic representation for this
problem and provide conditions under which it exactly characterizes a puzzle.
Using the new representation, we recast the combinatorial, discrete problem of
solving puzzles as a global, polynomial system of equations with continuous
variables. We further propose new algorithms for generating approximate
solutions to the continuous problem by solving a sequence of convex
relaxations
Reflections After Seattle
The WTO cannot operate in isolation from the concerns of the world in which it exists. Our ability to advance trade, build a stronger system, and move forward in a new round will hinge on our ability to make simultaneous progression on these issues. How do we do this? First, we must move toward a more collective leadership, one that reflects the reality of a multipolar world and especially the emergence of developing-country powers. Second, we need to look at the policy challenges we face as pieces of an interconnected puzzle. Third, we need a new forum for the management of these complex issues, one that is truly representative of the new global realities and that brings world leaders together to tackle an expanded policy agenda and the new challenges of globalization. Fourth, there is a need for a clear mandate from leaders to promote a common global strategy and common global actions
Multi-Phase Relaxation Labeling for Square Jigsaw Puzzle Solving
We present a novel method for solving square jigsaw puzzles based on global
optimization. The method is fully automatic, assumes no prior information, and
can handle puzzles with known or unknown piece orientation. At the core of the
optimization process is nonlinear relaxation labeling, a well-founded approach
for deducing global solutions from local constraints, but unlike the classical
scheme here we propose a multi-phase approach that guarantees convergence to
feasible puzzle solutions. Next to the algorithmic novelty, we also present a
new compatibility function for the quantification of the affinity between
adjacent puzzle pieces. Competitive results and the advantage of the
multi-phase approach are demonstrated on standard datasets.Comment: 10 pages, 7 figures. Published in Proceedings of the 18th
International Joint Conference on Computer Vision, Imaging and Computer
Graphics Theory and Applications - Volume 4 VISAPP: VISAPP, 785-795, 202
Interlocking structure design and assembly
Many objects in our life are not manufactured as whole rigid pieces. Instead, smaller components are made to be later assembled into larger structures. Chairs are assembled from wooden pieces, cabins are made of logs, and buildings are constructed from bricks. These components are commonly designed by many iterations of human thinking. In this report, we will look at a few problems related to interlocking components design and assembly. Given an atomic object, how can we design a package that holds the object firmly without a gap in-between? How many pieces should the package be partitioned into? How can we assemble/extract each piece? We will attack this problem by first looking at the lower bound on the number of pieces, then at the upper bound. Afterwards, we will propose a practical algorithm for designing these packages. We also explore a special kind of interlocking structure which has only one or a small number of movable pieces. For example, a burr puzzle. We will design a few blocks with joints whose combination can be assembled into almost any voxelized 3D model. Our blocks require very simple motions to be assembled, enabling robotic assembly. As proof of concept, we also develop a robot system to assemble the blocks. In some extreme conditions where construction components are small, controlling each component individually is impossible. We will discuss an option using global controls. These global controls can be from gravity or magnetic fields. We show that in some special cases where the small units form a rectangular matrix, rearrangement can be done in a small space following a technique similar to bubble sort algorithm
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
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
Optimization for automated assembly of puzzles
The puzzle assembly problem has many application areas such as restoration and reconstruction of archeological findings, repairing of broken objects, solving jigsaw type puzzles, molecular docking problem, etc. The puzzle pieces usually include not only geometrical shape information but also visual information such as texture, color, and continuity of lines. This paper presents a new approach to the puzzle assembly problem that is based on using textural features and geometrical constraints. The texture of a band outside the border of pieces is predicted by inpainting and texture synthesis methods. Feature values are derived from these original and predicted images of pieces. An affinity measure of corresponding pieces is defined and alignment of the puzzle pieces is formulated as an optimization problem where the optimum assembly of the pieces is achieved by maximizing the total affinity measure. An fft based image registration technique is used to speed up the alignment of the pieces. Experimental results are presented on real and artificial data sets
A texture based approach to reconstruction of archaeological finds
Reconstruction of archaeological finds from fragments, is a tedious task requiring many hours of work from the archaeologists and restoration personnel. In this paper we present a framework for the full reconstruction of the original objects using texture and surface design information on the sherd. The texture of a band outside the border of pieces is predicted by inpainting and texture synthesis methods. The confidence of this process is also defined. Feature values are derived from these original and predicted images of pieces. A combination of the feature and confidence values is used to generate an affinity measure of corresponding pieces. The optimization of total affinity gives the best assembly of the piece. Experimental results are presented on real and artificial data
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