Related papers: Physical Knot Classification Beyond Accuracy: A Be…
Recent studies classify the topology of proteins by analysing the distribution of their projections using knotoids. The approximation of this distribution depends on the number of projection directions that are sampled. Here we investigate…
Computational topology is a vibrant contemporary subfield and this article integrates knot theory and mathematical visualization. Previous work on computer graphics developed a sequence of smooth knots that were shown to converge point wise…
Our goal is to one day take a photo of a knot and have a phone automatically recognize it. In this expository work, we explain a strategy to approximate this goal, using a mixture of modern machine learning methods (in particular…
Knots in wood are critical to both aesthetics and structural integrity, making their detection and pairing essential in timber processing. However, traditional manual annotation was labor-intensive and inefficient, necessitating automation.…
Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the…
A {\it stuck knot} is a knot diagram containing designated crossings, called {\it stuck crossings}, whose incident strands are required to remain locally non-separable. These rigidity constraints restrict the allowable ambient isotopies and…
Knits and crochets are mechanical metamaterials with a long history and can typically be produced from a single yarn. Despite the simplicity of the manufacturing process, they exhibit a wide range of structural configurations with diverse…
Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically…
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by…
3D object classification is a crucial problem due to its significant practical relevance in many fields, including computer vision, robotics, and autonomous driving. Although deep learning methods applied to point clouds sampled on CAD…
The goal of this paper is to discuss the possibility of finding an algorithm that can give all distinct knots up to a desired complexity. Two such algorithms are presented, one based on projections on a plane, the other on closed…
The fingerprint classification problem is to sort fingerprints into pre-determined groups, such as arch, loop, and whorl. It was asserted in the literature that minutiae points, which are commonly used for fingerprint matching, are not…
Fine-grained visual classification aims to recognize images belonging to multiple sub-categories within a same category. It is a challenging task due to the inherently subtle variations among highly-confused categories. Most existing…
Topological consistency plays a crucial role in the task of boundary segmentation for reticular images, such as cell membrane segmentation in neuron electron microscopic images, grain boundary segmentation in material microscopic images and…
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
Recently, human pose estimation mainly focuses on how to design a more effective and better deep network structure as human features extractor, and most designed feature extraction networks only introduce the position of each anatomical…
Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently…
Image classifiers are information-discarding machines, by design. Yet, how these models discard information remains mysterious. We hypothesize that one way for image classifiers to reach high accuracy is to first zoom to the most…
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or…
In the industry, the value of wood-logs strongly depends on their internal structure and more specifically on the knots' distribution inside the trees. As of today, CT-scanners are the prevalent tool to acquire accurate images of the trees…