Robust and flexible puzzle solving with corner-based cycle consistent correspondences

Solving jigsaw puzzles is a classic problem in computer vision with various applications. Over the past decades, many useful approaches have been introduced. Most existing works use edge-wise similarity measures for assembling puzzles with square pieces of the same size, and recent work innovates to use the loop constraint to improve efficiency and accuracy. We observe that most existing techniques cannot be easily extended to puzzles with rectangular pieces of arbitrary sizes, and no existing loop constraints can be used to model such challenging scenarios. In this paper, we propose a new corner-wise matching approach, modelled using the MatchLift framework to solve square puzzles with cycle consistency. We further show one exciting example illustrating how puzzles with rectangular pieces of arbitrary sizes would be solved by our techniqu

Image Processing Applications in Real Life: 2D Fragmented Image and Document Reassembly and Frequency Division Multiplexed Imaging

In this era of modern technology, image processing is one the most studied disciplines of signal processing and its applications can be found in every aspect of our daily life. In this work three main applications for image processing has been studied. In chapter 1, frequency division multiplexed imaging (FDMI), a novel idea in the field of computational photography, has been introduced. Using FDMI, multiple images are captured simultaneously in a single shot and can later be extracted from the multiplexed image. This is achieved by spatially modulating the images so that they are placed at different locations in the Fourier domain. Finally, a Texas Instruments digital micromirror device (DMD) based implementation of FDMI is presented and results are shown. Chapter 2 discusses the problem of image reassembly which is to restore an image back to its original form from its pieces after it has been fragmented due to different destructive reasons. We propose an efficient algorithm for 2D image fragment reassembly problem based on solving a variation of Longest Common Subsequence (LCS) problem. Our processing pipeline has three steps. First, the boundary of each fragment is extracted automatically; second, a novel boundary matching is performed by solving LCS to identify the best possible adjacency relationship among image fragment pairs; finally, a multi-piece global alignment is used to filter out incorrect pairwise matches and compose the final image. We perform experiments on complicated image fragment datasets and compare our results with existing methods to show the improved efficiency and robustness of our method. The problem of reassembling a hand-torn or machine-shredded document back to its original form is another useful version of the image reassembly problem. Reassembling a shredded document is different from reassembling an ordinary image because the geometric shape of fragments do not carry a lot of valuable information if the document has been machine-shredded rather than hand-torn. On the other hand, matching words and context can be used as an additional tool to help improve the task of reassembly. In the final chapter, document reassembly problem has been addressed through solving a graph optimization problem