相关论文: Application of integral invariants to apictorial j…

Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…

Automatic assembly of apictorial jigsaw puzzles presents a classic curve matching problem, fundamentally challenged by discrete and noisy contour data obtained from digitization. Conventional smoothing methods, which are required to process…

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…

This paper introduces a new shape-matching methodology, combinative matching, to combine interlocking parts for geometric shape assembly. Previous methods for geometric assembly typically rely on aligning parts by finding identical surfaces…

Pairwise compatibility calculation is at the core of most fragments-reconstruction algorithms, in particular those designed to solve different types of the jigsaw puzzle problem. However, most existing approaches fail, or aren't designed to…

This paper proposes a novel algorithm to reassemble an arbitrarily shredded image to its original status. Existing reassembly pipelines commonly consist of a local matching stage and a global compositions stage. In the local stage, a key…

The automatic assembly problem has attracted increasing interest due to its complex challenges that involve 3D representation. This paper introduces Jigsaw++, a novel generative method designed to tackle the multifaceted challenges of…

In this paper, we introduce the following problem in the theory of algorithmic self-assembly: given an input shape as the seed of a tile-based self-assembly system, design a finite tile set that can, in some sense, uniquely identify whether…

Image composition aims to blend multiple objects to form a harmonized image. Existing approaches often assume precisely segmented and intact objects. Such assumptions, however, are hard to satisfy in unconstrained scenarios. We present…

Automated assembly of 3D fractures is essential in orthopedics, archaeology, and our daily life. This paper presents Jigsaw, a novel framework for assembling physically broken 3D objects from multiple pieces. Our approach leverages…

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…

In the abstract Tile Assembly Model, self-assembling systems consisting of tiles of different colors can form structures on which colored patterns are ``painted.'' We explore the complexity, in terms of the numbers of unique tile types…

Jigsaw puzzle solving requires the rearrangement of unordered pieces into their original pose in order to reconstruct a coherent whole, often an image, and is known to be an intractable problem. While the possible impact of automatic puzzle…

We propose a general framework for solving inverse self-assembly problems, i.e. designing interactions between elementary units such that they assemble spontaneously into a predetermined structure. Our approach uses patchy particles as…

One emerging approach for the fabrication of complex architectures on the nanoscale is to utilize particles customized to intrinsically self-assemble into a desired structure. Inverse methods of statistical mechanics have proven…

The goal of inverse self-assembly is to design inter-particle interactions capable of assembling the units into a desired target structure. The effective assembly of complex structures often requires the use of multiple components, each new…

Image inpainting refers to the restoration of an image with missing regions in a way that is not detectable by the observer. The inpainting regions can be of any size and shape. This is an ill-posed inverse problem that does not have a…

By suitable examples we illustrate an algorithm for composition of inverse problems.

We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn…

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…