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Rotation invariance has been studied in the computer vision community primarily in the context of small in-plane rotations. This is usually achieved by building invariant image features. However, the problem of achieving invariance for…
This study introduces a pore morphology algorithm that emphasizes the central role of topology in multiphase flow through porous media. Analysis of drainage in lattice-based pore networks identifies two key quantities, the percolation…
Many edge and contour detection algorithms give a soft-value as an output and the final binary map is commonly obtained by applying an optimal threshold. In this paper, we propose a novel method to detect image contours from the extracted…
Depth information provides valuable insights into the 3D structure especially the outline of objects, which can be utilized to improve the semantic segmentation tasks. However, a naive fusion of depth information can disrupt feature and…
Photographs are characterized by different compositional attributes like the Rule of Thirds, depth of field, vanishing-lines etc. The presence or absence of one or more of these attributes contributes to the overall artistic value of an…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
Image inpainting has earned substantial progress, owing to the encoder-and-decoder pipeline, which is benefited from the Convolutional Neural Networks (CNNs) with convolutional downsampling to inpaint the masked regions semantically from…
Humans are able to recognize objects based on both local texture cues and the configuration of object parts, yet contemporary vision models primarily harvest local texture cues, yielding brittle, non-compositional features. Work on…
Typically, a salient object detection (SOD) model faces opposite requirements in processing object interiors and boundaries. The features of interiors should be invariant to strong appearance change so as to pop-out the salient object as a…
Salient object detection plays an important part in a vision system to detect important regions. Convolutional neural network (CNN) based methods directly train their models with large-scale datasets, but what is the crucial feature for…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Preliminary results of extensive numerical experiments on a simple model specified by the smooth canonical strongly chaotic 2D-map with global virtual invariant curves (VICs) are presented and discussed. We focus on the statistics of the…
We establish cross-ratio invariants for surfaces in 4-space in an analogous way to Uribe-Vargas's work for surfaces in 3-space. We study the geometric locii of local and multi-local singularities of ortogonal projections of the surface. The…
We present a novel approach to object classification and detection which requires minimal supervision and which combines visual texture cues and shape information learned from freely available unlabeled web search results. The explosion of…
We study the structure of representations, defined as approximations of minimal sufficient statistics that are maximal invariants to nuisance factors, for visual data subject to scaling and occlusion of line-of-sight. We derive analytical…
We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…
It is known that $C^r$ Morse-Smale vector fields form an open dense subset in the space of vector fields on orientable closed surfaces and are structurally stable for any $r \in \mathbb{Z}_{>0}$. In particular, $C^r$ Morse vector fields…
Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet…
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under M\"{o}bius transformations.…
We compute the critical surface for the existence of invariant tori of a family of Hamiltonian systems with two and three degrees of freedom. We use and compare two methods to compute the critical surfaces: renormalization-group…