Related papers: Vertex characterization via second-order topologic…

The purpose of this paper is to introduce an algorithm that can detect the most unusual part of a digital image in probabilistic setting. The most unusual part of a given shape is defined as a part of the image that has the maximal distance…

We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…

We study random 2-dimensional complexes in the Linial - Meshulam model and find torsion in their fundamental groups at various regimes. We find a simple algorithmically testable criterion for a subcomplex of a random 2-complex to be…

We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering…

Contour detection has been a fundamental component in many image segmentation and object detection systems. Most previous work utilizes low-level features such as texture or saliency to detect contours and then use them as cues for a…

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

The texture is defined as spatial structure of the intensities of the pixels in an image that is repeated periodically in the whole image or regions, and makes the concept of the image. Texture, color and shape are three main components…

Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…

Visual Recognition is one of the fundamental challenges in AI, where the goal is to understand the semantics of visual data. Employing mid-level representation, in particular, shifted the paradigm in visual recognition. The mid-level…

Textures often show multiscale properties and hence multiscale techniques are considered useful for texture analysis. Scale-space theory as a biologically motivated approach may be used to construct multiscale textures. In this paper…

A new method based on complex networks is proposed for color-texture analysis. The proposal consists on modeling the image as a multilayer complex network where each color channel is a layer, and each pixel (in each color channel) is…

Estimating a depth map from multiple views of a scene is a fundamental task in computer vision. As soon as more than two viewpoints are available, one faces the very basic question how to measure similarity across >2 image patches.…

The problem of 3D object recognition is of immense practical importance, with the last decade witnessing a number of breakthroughs in the state of the art. Most of the previous work has focused on the matching of textured objects using…

Throughout this work, the vertex decomposability and shellability of graphs formed from other graphs by various operations are investigated. Also among the other things, by using some graph operations, new classes of Cohen-Macaulay graphs…

In this work, we develop intuitive controls for editing the style of 3D objects. Our framework, Text2Mesh, stylizes a 3D mesh by predicting color and local geometric details which conform to a target text prompt. We consider a disentangled…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

Finding correspondences is a fundamental and extensively researched problem in computer vision and graphics. In this work, we examine the underexplored task of estimating segmentation-to-segmentation correspondence between images in the…

Topological features - global properties not discernible locally - emerge in systems from liquid crystals to magnets to fractional quantum Hall systems. Deeper understanding of the role of topology in physics has led to a new class of…

The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…