相关论文: Critical Contours: An Invariant Linking Image Flow…

A fundamental problem in computer vision is that of inferring the intrinsic, 3D structure of the world from flat, 2D images of that world. Traditional methods for recovering scene properties such as shape, reflectance, or illumination rely…

Convolutional Neural Network (CNN) features have been successfully employed in recent works as an image descriptor for various vision tasks. But the inability of the deep CNN features to exhibit invariance to geometric transformations and…

Exterior contour and interior structure are both vital features for classifying objects. However, most of the existing methods consider exterior contour feature and internal structure feature separately, and thus fail to function when…

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…

The U-shape structure has shown its advantage in salient object detection for efficiently combining multi-scale features. However, most existing U-shape based methods focused on improving the bottom-up and top-down pathways while ignoring…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

For particles confined to two dimensions, any curvature of the surface affects the structural, kinetic and thermodynamic properties of the system. If the curvature is non-uniform, an even richer range of behaviours can emerge. Using a…

Piecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their common origin in smooth Morse theory, various notions of critical…

Computed tomography (CT) can capture volumes large enough to measure a statistically meaningful number of micron-sized particles with a sufficiently good resolution to allow for the analysis of individual particles. However, the development…

The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of this kind of vector field: Connectedness of critical points…

We investigate discrete spin transformations, a geometric framework to manipulate surface meshes by controlling mean curvature. Applications include surface fairing -- flowing a mesh onto say, a reference sphere -- and mesh extrusion --…

The analysis of contours of scalar fields plays an important role in visualization. For example the contour tree and contour statistics can be used as a means for interaction and filtering or as signatures. In the context of tensor field…

Context is essential for semantic segmentation. Due to the diverse shapes of objects and their complex layout in various scene images, the spatial scales and shapes of contexts for different objects have very large variation. It is thus…

Humans are able to precisely communicate diverse concepts by employing sketches, a highly reduced and abstract shape based representation of visual content. We propose, for the first time, a fully convolutional end-to-end architecture that…

In this paper, we present a robust method for scene recognition, which leverages Convolutional Neural Networks (CNNs) features and Sparse Coding setting by creating a new representation of indoor scenes. Although CNNs highly benefited the…

This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…

Despite the importance of image representations such as histograms of oriented gradients and deep Convolutional Neural Networks (CNN), our theoretical understanding of them remains limited. Aiming at filling this gap, we investigate three…

In this paper, we study the prescribed $Q$-curvature problem on closed four-dimensional Riemannian manifolds when the total integral of the $Q$-curvature is a positive integer multiple of the one of the four-dimensional round sphere. This…

We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles…

Scene graphs provide structured abstractions for scene understanding, yet they often overfit to spurious correlations, severely hindering out-of-distribution generalization. To address this limitation, we propose CURVE, a causality-inspired…