Dror Sholomon

Daniel Rika, Dror Sholomon, Eli David et al.

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.

Daniel Rika, Dror Sholomon, Eli David et al.

Pairwise compatibility measure (CM) is a key component in solving the jigsaw puzzle problem (JPP) and many of its recently proposed variants. With the rapid rise of deep neural networks (DNNs), a trade-off between performance (i.e., accuracy) and computational efficiency has become a very significant issue. Whereas an end-to-end DNN-based CM model exhibits high performance, it becomes virtually infeasible on very large puzzles, due to its highly intensive computation. On the other hand, exploiting the concept of embeddings to alleviate significantly the computational efficiency, has resulted in degraded performance, according to recent studies. This paper derives an advanced CM model (based on modified embeddings and a new loss function, called hard batch triplet loss) for closing the above gap between speed and accuracy; namely a CM model that achieves SOTA results in terms of performance and efficiency combined. We evaluated our newly derived CM on three commonly used datasets, and obtained a reconstruction improvement of 5.8% and 19.5% for so-called Type-1 and Type-2 problem variants, respectively, compared to best known results due to previous CMs.

Daniel Rika, Dror Sholomon, Eli David et al.

This paper presents a versatile hybrid framework for addressing 2D real-world reconstruction tasks formulated as jigsaw puzzle problems (JPPs) with square, non-overlapping pieces. Our approach integrates a deep learning (DL)-based compatibility measure (CM) model that evaluates pairs of puzzle pieces holistically, rather than focusing solely on their adjacent edges as traditionally done. This DL-based CM is paired with an optimized genetic algorithm (GA)-based solver, which iteratively searches for a global optimal arrangement using the pairwise CM scores of the puzzle pieces. Extensive experimental results highlight the framework's adaptability and robustness across multiple real-world domains. Notably, our unique hybrid methodology achieves state-of-the-art (SOTA) results in reconstructing Portuguese tile panels and large degraded puzzles with eroded boundaries.

Dror Sholomon, Eli David, Nathan S. Netanyahu

In this paper we propose the first effective automated, genetic algorithm (GA)-based jigsaw puzzle solver. We introduce a novel procedure of merging two "parent" solutions to an improved "child" solution by detecting, extracting, and combining correctly assembled puzzle segments. The solver proposed exhibits state-of-the-art performance solving previously attempted puzzles faster and far more accurately, and also puzzles of size never before attempted. Other contributions include the creation of a benchmark of large images, previously unavailable. We share the data sets and all of our results for future testing and comparative evaluation of jigsaw puzzle solvers.

Dror Sholomon, Eli David, Nathan S. Netanyahu

In this paper we introduce new types of square-piece jigsaw puzzles, where in addition to the unknown location and orientation of each piece, a piece might also need to be flipped. These puzzles, which are associated with a number of real world problems, are considerably harder, from a computational standpoint. Specifically, we present a novel generalized genetic algorithm (GA)-based solver that can handle puzzle pieces of unknown location and orientation (Type 2 puzzles) and (two-sided) puzzle pieces of unknown location, orientation, and face (Type 4 puzzles). To the best of our knowledge, our solver provides a new state-of-the-art, solving previously attempted puzzles faster and far more accurately, handling puzzle sizes that have never been attempted before, and assembling the newly introduced two-sided puzzles automatically and effectively. This paper also presents, among other results, the most extensive set of experimental results, compiled as of yet, on Type 2 puzzles.

Dror Sholomon, Eli David, Nathan S. Netanyahu

In this paper we propose the first effective genetic algorithm (GA)-based jigsaw puzzle solver. We introduce a novel crossover procedure that merges two "parent" solutions to an improved "child" configuration by detecting, extracting, and combining correctly assembled puzzle segments. The solver proposed exhibits state-of-the-art performance, as far as handling previously attempted puzzles more accurately and efficiently, as well puzzle sizes that have not been attempted before. The extended experimental results provided in this paper include, among others, a thorough inspection of up to 30,745-piece puzzles (compared to previous attempts on 22,755-piece puzzles), using a considerably faster concurrent implementation of the algorithm. Furthermore, we explore the impact of different phases of the novel crossover operator by experimenting with several variants of the GA. Finally, we compare different fitness functions and their effect on the overall results of the GA-based solver.

Dror Sholomon, Eli David, Nathan S. Netanyahu

In this paper we propose the first genetic algorithm (GA)-based solver for jigsaw puzzles of unknown puzzle dimensions and unknown piece location and orientation. Our solver uses a novel crossover technique, and sets a new state-of-the-art in terms of the puzzle sizes solved and the accuracy obtained. The results are significantly improved, even when compared to previous solvers assuming known puzzle dimensions. Moreover, the solver successfully contends with a mixed bag of multiple puzzle pieces, assembling simultaneously all puzzles.