13 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
Solving Jigsaw Puzzles with Eroded Boundaries
Jigsaw puzzle solving is an intriguing problem which has been explored in
computer vision for decades. This paper focuses on a specific variant of the
problem - solving puzzles with eroded boundaries. Such erosion makes the
problem extremely difficult, since most existing solvers utilize solely the
information at the boundaries. Nevertheless, this variant is important since
erosion and missing data often occur at the boundaries. The key idea of our
proposed approach is to inpaint the eroded boundaries between puzzle pieces and
later leverage the quality of the inpainted area to classify a pair of pieces
as 'neighbors or not'. An interesting feature of our architecture is that the
same GAN discriminator is used for both inpainting and classification; Training
of the second task is simply a continuation of the training of the first,
beginning from the point it left off. We show that our approach outperforms
other SOTA methodsComment: 8 page
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
A Novel Hybrid Scheme Using Genetic Algorithms and Deep Learning for the Reconstruction of Portuguese Tile Panels
This paper presents a novel scheme, based on a unique combination of genetic
algorithms (GAs) and deep learning (DL), for the automatic reconstruction of
Portuguese tile panels, a challenging real-world variant of the jigsaw puzzle
problem (JPP) with important national heritage implications. Specifically, we
introduce an enhanced GA-based puzzle solver, whose integration with a novel
DL-based compatibility measure (DLCM) yields state-of-the-art performance,
regarding the above application. Current compatibility measures consider
typically (the chromatic information of) edge pixels (between adjacent tiles),
and help achieve high accuracy for the synthetic JPP variant. However, such
measures exhibit rather poor performance when applied to the Portuguese tile
panels, which are susceptible to various real-world effects, e.g.,
monochromatic panels, non-squared tiles, edge degradation, etc. To overcome
such difficulties, we have developed a novel DLCM to extract high-level
texture/color statistics from the entire tile information.
Integrating this measure with our enhanced GA-based puzzle solver, we have
demonstrated, for the first time, how to deal most effectively with large-scale
real-world problems, such as the Portuguese tile problem. Specifically, we have
achieved 82% accuracy for the reconstruction of Portuguese tile panels with
unknown piece rotation and puzzle dimension (compared to merely 3.5% average
accuracy achieved by the best method known for solving this problem variant).
The proposed method outperforms even human experts in several cases, correcting
their mistakes in the manual tile assembly
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