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result(s) for
"Jigsaw puzzles."
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Where Oliver fits
Oliver--a puzzle piece--has always dreamed about where he'll fit. Will he be in the mane of a unicorn? The tentacle of a pirate squid? The helmet of an astronaut? When he finally goes in search of his perfect place, he finds that trying to fit in is a lot harder than he thought.
Book
Pictorial and Apictorial Polygonal Jigsaw Puzzles from Arbitrary Number of Crossing Cuts
Jigsaw puzzle solving, the problem of constructing a coherent whole from a set of non-overlapping unordered visual fragments, is fundamental to numerous applications, and yet most of the literature of the last two decades has focused thus far on less realistic puzzles whose pieces are identical squares. Here we formalize a new type of jigsaw puzzle where the pieces are general convex polygons generated by cutting through a global polygonal shape/image with an arbitrary number of straight cuts, a generation model inspired by the celebrated Lazy caterer’s sequence. We analyze the theoretical properties of such puzzles, including the inherent challenges in solving them once pieces are contaminated with geometrical noise. To cope with such difficulties and obtain tractable solutions, we abstract the problem as a multi-body spring-mass dynamical system endowed with hierarchical loop constraints and a layered reconstruction process. We define evaluation metrics and present experimental results on both apictorial and pictorial puzzles to show that they are solvable completely automatically.
Journal Article
The puzzler : one man's quest to solve the most baffling puzzles ever, from crosswords to jigsaws to the meaning of life
\"The New York Times bestselling author of The Year of Living Biblically goes on a journey to understand the enduring power of puzzles: why we love them, what they do to our brains, and how they can improve our world\"-- Provided by publisher.
BOOK
Genetic-based square jigsaw puzzle solver using the combined color+texture compatibility criterion
When reconstructing jigsaw puzzles, the state-of-the-art algorithms struggle to distinguish between identically colored pieces that belong to different objects. This limitation significantly impacts the accuracy of puzzle solvers, especially in complex images with repetitive colors or textures. To address this issue, we propose a new GA-based square jigsaw puzzle solver. A combined color and texture discriminator is incorporated into the proposed solver to prevent pieces that have the same color but come from distinct objects from being joined together incorrectly. Color and texture features are extracted separately using the sum of square distances and Gabor filter. To evaluate the performance of the proposed solver, we used a dataset consisting 66 images: 20 puzzles with 432 pieces from the MIT collection, 20 puzzles with 540 pieces, and 20 puzzles with 805 pieces from the McGill collection, and 3 puzzles with 2360 pieces, and 3 puzzles with 3300 pieces from the Pomeranz collection. For the direct, neighbor, and largest component comparisons, the proposed method's accuracy is 92.91%, 96.66%, and 90.83%, respectively. The proposed method demonstrates an improvement of 11.9%, and 3.65% in accuracy based on direct and neighbor comparison criteria, on the database images when compared to current state-of-the-art GA-based square jigsaw puzzle solver.
Journal Article
A Jigsaw Puzzle Solver-Based Attack on Image Encryption Using Vision Transformer for Privacy-Preserving DNNs
In this paper, we propose a novel attack on image encryption for privacy-preserving deep neural networks (DNNs). Although several encryption schemes have been proposed for privacy-preserving DNNs, existing cipher-text-only attacks (COAs) have succeeded in restoring visual information from encrypted images. Image encryption using the Vision Transformer (ViT) is known to be robust against existing COAs due to the operations of block scrambling and pixel shuffling, which permute divided blocks and pixels in an encrypted image. However, the correlation between blocks in the encrypted image can still be exploited for reconstruction. Therefore, in this paper, a novel jigsaw puzzle solver-based attack that utilizes block correlation is proposed to restore visual information from encrypted images. In the experiments, we evaluated the security of image encryption for privacy-preserving deep neural networks using both conventional and proposed COAs. The experimental results demonstrate that the proposed attack is able to restore almost all visual information from images encrypted for being applied to ViTs.
Journal Article
Hand-drawn cadastral map parsing, stitching and assembly via jigsaw puzzles
We present a robust method for parsing the content of hand-drawn cadastral maps in order to obtain high-resolution, digitized assemblies of larger regions from individual maps. The parsing phase involves solving a challenging background grid detection plem. We exploit the geometry of detected grids for stitching overlapping map images. A novel method for computing geometric compatibilities between non-overlapping map pieces is also introduced. It is shown to be important since existing chromatic compatibility measures are not as useful for hand-drawn maps. Assembly of maps involves solving an arbitrary-boundary jigsaw puzzle problem with non-overlapping pieces of the same rectangular shape. It corresponds to finding a maximum spanning graph within a multigraph whose edge weights are the piece compatibilities. Since the problem is NP-hard, we develop a polynomial time approximation algorithm that involves two distinct greedy decisions at each iteration. In contrast to existing evaluation metrics for fixed-boundary jigsaw puzzles, we present an
F
1
-score based evaluation scheme for the arbitrary-boundary jigsaw problem that evaluates relative placements of pieces instead of absolute locations. On a testing set of 218 images of 109 cadastral maps comprising 15 different map assembly problems, we achieve a high average
F
1
-score of 0.88. Results validate our compatibility measure as well as the two-stage greedy nature of our method. An ablation study isolates the importance of individual modules of the developed pipeline.
Journal Article
Jigsaw puzzle difficulty assessment and analysis of influencing factors based on deep learning method
Jigsaw puzzle is a casual game that can be used for leisure and stress relief. This paper presents a novel algorithm for quantifying and estimating the time required for users to complete jigsaw puzzle games and providing game difficulty reference for game designers. Firstly, a difficulty quantification model is proposed. Then, based on observation and hypothesis, it is believed that jigsaw puzzle difficulty is related to elements such as texture in the puzzle. Finally, experimental validation demonstrates that jigsaw puzzle difficulty is related to the texture and number of repeated elements in the puzzle. The algorithm is tested on a large amount of jigsaw puzzle game datasets, subsequently verifying its effectiveness and accuracy. The main contribution of this algorithm is to provide a new quantitative evaluation method for jigsaw puzzle game difficulty, which can assist game designers in optimizing game difficulty and enhancing user experience. Our data, code, and model are available at CunHua-YYT/JigsawSort (github.com).
Journal Article
JPSSL: SAR Terrain Classification Based on Jigsaw Puzzles and FC-CRF
Effective features play an important role in synthetic aperture radar (SAR) image interpretation. However, since SAR images contain a variety of terrain types, it is not easy to extract effective features of different terrains from SAR images. Deep learning methods require a large amount of labeled data, but the difficulty of SAR image annotation limits the performance of deep learning models. SAR images have inevitable geometric distortion and coherence speckle noise, which makes it difficult to extract effective features from SAR images. If effective semantic context features cannot be learned for SAR images, the extracted features struggle to distinguish different terrain categories. Some existing terrain classification methods are very limited and can only be applied to some specified SAR images. To solve these problems, a jigsaw puzzle self-supervised learning (JPSSL) framework is proposed. The framework comprises a jigsaw puzzle pretext task and a terrain classification downstream task. In the pretext task, the information in the SAR image is learned by completing the SAR image jigsaw puzzle to extract effective features. The terrain classification downstream task is trained using only a small number of labeled data. Finally, fully connected conditional random field processing is performed to eliminate noise points and obtain a high-quality terrain classification result. Experimental results on three large-scene high-resolution SAR images confirm the effectiveness and generalization of our method. Compared with the supervised methods, the features learned in JPSSL are highly discriminative, and the JPSSL achieves good classification accuracy when using only a small amount of labeled data.
Journal Article
Application of Integral Invariants to Apictorial Jigsaw Puzzle Assembly
We present a method for the automatic assembly of apictorial jigsaw puzzles. This method relies on integral area invariants for shape matching and an optimization process to aggregate shape matches into a final puzzle assembly. Assumptions about individual piece shape or arrangement are not necessary. We illustrate our method by solving example puzzles of various shapes and sizes.
Journal Article
A jigsaw puzzle inspired algorithm for solving large-scale no-wait flow shop scheduling problems
The no-wait flow shop scheduling problem (NWFSP), as a typical NP-hard problem, has important ramifications in the modern industry. In this paper, a jigsaw puzzle inspired heuristic (JPA) is proposed for solving NWFSP with the objective of minimizing makespan. The core idea behind JPA is to find the best match for each job until all the jobs are scheduled in the set of process. In JPA, a waiting time matrix is constructed to measure the gap between two jobs. Then, a matching matrix based on the waiting time matrix is obtained. Finally, the optimal scheduling sequence is built by using the matching matrix. Experimental results on large-scale benchmark instances show that JPA is superior to the state-of-the-art heuristics.
Journal Article