Related papers: Vertex characterization via second-order topologic…
In this paper, we design linear time algorithms to recognize and determine topological invariants such as the genus and homology groups in 3D. These properties can be used to identify patterns in 3D image recognition. This has tremendous…
Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been…
Corner detection is widely used in various computer vision tasks, such as image matching and 3D reconstruction. Our research indicates that there are theoretical flaws in Zhang et al.'s use of a simple corner model to obtain a series of…
Spatially embedded networks are important in several disciplines. The prototypical spatial net- work we assume is the Random Geometric Graph of which many properties are known. Here we present new results for the two-point degree…
In a recent work (ECCC, TR18-171, 2018), we introduced models of testing graph properties in which, in addition to answers to the usual graph-queries, the tester obtains {\em random vertices drawn according to an arbitrary distribution…
Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks.…
Previous literature suggests that perceptual similarity is an emergent property shared across deep visual representations. Experiments conducted on a dataset of human-judged image distortions have proven that deep features outperform…
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…
Accurately localizing and identifying vertebrae from CT images is crucial for various clinical applications. However, most existing efforts are performed on 3D with cropping patch operation, suffering from the large computation costs and…
A vector topology on a vector space over a topological field is a (not necessarily Hausdorff) topology by which the addition and scalar multiplication are continuous. We prove that, if an isomorphism between the lattice of topologies of two…
Vascular networks play a crucial role in understanding brain functionalities. Brain integrity and function, neuronal activity and plasticity, which are crucial for learning, are actively modulated by their local environments, specifically…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
We propose a novel optimization-based paradigm for 3D human model fitting on images and scans. In contrast to existing approaches that directly regress the parameters of a low-dimensional statistical body model (e.g. SMPL) from input…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
Understanding body part geometry is crucial for precise medical diagnostics. Curves effectively describe anatomical structures and are widely used in medical imaging applications related to cardiovascular, respiratory, and skeletal…
It is shown that the tail in the two-level spectral correlation function R(s) for particles on 2D closed disordered surfaces is determined entirely by surface topology: $R(s)=-\chi/(6\pi^2\beta s^2)$, where $\beta$ = 1,2 or 4 for the…
This work proposes a new method for place recognition based on the scene architecture. From depth video, we compute the 3D model and we derive and describe geometrically the 2D map from which the scene descriptor is deduced to constitute…
We develop a linear algebraic framework for the shape-from-shading problem, because tensors arise when scalar (e.g. image) and vector (e.g. surface normal) fields are differentiated multiple times. The work is in two parts. In this first…
Chirality information (i.e. information that allows distinguishing left from right) is ubiquitous for various data modes in computer vision, including images, videos, point clouds, and meshes. While chirality has been extensively studied in…
The topological vertex is a universal series which can be regarded as an object in combinatorics, representation theory, geometry, or physics. It encodes the combinatorics of 3D partitions, the action of vertex operators on Fock space, the…