TEN: Twin Embedding Networks for the Jigsaw Puzzle Problem with Eroded Boundaries

TL;DR

This paper presents TEN, a CNN-based encoder that improves jigsaw puzzle reconstruction accuracy with eroded boundaries by using latent boundary representations, achieving faster speeds and better accuracy than classical and neural network methods.

Contribution

Introduction of Twin Embedding Network (TEN), a novel CNN encoder for boundary-based puzzle piece representation, enhancing accuracy and speed in degraded puzzle scenarios.

Findings

Up to 8.5% and 16.8% accuracy improvements for different puzzle types.

TEN is significantly faster than typical neural network models.

TEN bridges the gap between classical methods and neural networks for real-world puzzles.

Abstract

This paper introduces the novel CNN-based encoder Twin Embedding Network (TEN), for the jigsaw puzzle problem (JPP), which represents a puzzle piece with respect to its boundary in a latent embedding space. Combining this latent representation with a simple distance measure, we demonstrate improved accuracy levels of our newly proposed pairwise compatibility measure (CM), compared to that of various classical methods, for degraded puzzles with eroded tile boundaries. We focus on this problem instance for our case study, as it serves as an appropriate testbed for real-world scenarios. Specifically, we demonstrated an improvement of up to 8.5% and 16.8% in reconstruction accuracy, for so-called Type-1 and Type-2 problem variants, respectively. Furthermore, we also demonstrated that TEN is faster by a few orders of magnitude, on average, than a typical deep neural network (NN) model, i.e., it is as fast as the classical methods. In this regard, the paper makes a significant first attempt at bridging the gap between the relatively low accuracy (of classical methods and the intensive computational complexity (of NN models), for practical, real-world puzzle-like problems.