161 research outputs found
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
Domain Generalization by Solving Jigsaw Puzzles
Human adaptability relies crucially on the ability to learn and merge
knowledge both from supervised and unsupervised learning: the parents point out
few important concepts, but then the children fill in the gaps on their own.
This is particularly effective, because supervised learning can never be
exhaustive and thus learning autonomously allows to discover invariances and
regularities that help to generalize. In this paper we propose to apply a
similar approach to the task of object recognition across domains: our model
learns the semantic labels in a supervised fashion, and broadens its
understanding of the data by learning from self-supervised signals how to solve
a jigsaw puzzle on the same images. This secondary task helps the network to
learn the concepts of spatial correlation while acting as a regularizer for the
classification task. Multiple experiments on the PACS, VLCS, Office-Home and
digits datasets confirm our intuition and show that this simple method
outperforms previous domain generalization and adaptation solutions. An
ablation study further illustrates the inner workings of our approach.Comment: Accepted at CVPR 2019 (oral
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
Image Reconstruction from Bag-of-Visual-Words
The objective of this work is to reconstruct an original image from
Bag-of-Visual-Words (BoVW). Image reconstruction from features can be a means
of identifying the characteristics of features. Additionally, it enables us to
generate novel images via features. Although BoVW is the de facto standard
feature for image recognition and retrieval, successful image reconstruction
from BoVW has not been reported yet. What complicates this task is that BoVW
lacks the spatial information for including visual words. As described in this
paper, to estimate an original arrangement, we propose an evaluation function
that incorporates the naturalness of local adjacency and the global position,
with a method to obtain related parameters using an external image database. To
evaluate the performance of our method, we reconstruct images of objects of 101
kinds. Additionally, we apply our method to analyze object classifiers and to
generate novel images via BoVW
- …