相关论文: Geometric primitive feature extraction - concepts,…

We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that…

Estimates of image gradients play a ubiquitous role in image segmentation and classification problems since gradients directly relate to the boundaries or the edges of a scene. This paper proposes an unified approach to gradient estimation…

Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…

The need for fast, effective and accurate surveys have become increasingly necessary. A major part of the research is supported by photographic surveys which are used for capturing expansive natural surfaces using a wide range of sensors --…

As supported by abundant experimental evidence, neural networks are state-of-the-art for many approximation tasks in high-dimensional spaces. Still, there is a lack of a rigorous theoretical understanding of what they can approximate, at…

This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…

We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

Image segmentation is a crucial step in a wide range of method image processing systems. It is useful in visualization of the different objects present in the image. In spite of the several methods available in the literature, image…

Partial differential equations (PDEs) with multiple scales or those defined over sufficiently large domains arise in various areas of science and engineering and often present problems when approximating the solutions numerically. Machine…

A fundamental question for edge detection in noisy images is how faint can an edge be and still be detected. In this paper we offer a formalism to study this question and subsequently introduce computationally efficient multiscale edge…

Edge detection is an important field in image processing. Edges characterize object boundaries and are therefore useful for segmentation, registration, feature extraction, and identification of objects in a scene. In this paper, an approach…

Full 3D estimation of human pose from a single image remains a challenging task despite many recent advances. In this paper, we explore the hypothesis that strong prior information about scene geometry can be used to improve pose estimation…

Given a set of astrometric observations of the same object, the problem of orbit determination is to compute the orbit and to assess its uncertainty and reliability. For the next generation surveys, with much larger number density of…

A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…

Describing a scene in terms of primitives -- geometrically simple shapes that offer a parsimonious but accurate abstraction of structure -- is an established and difficult fitting problem. Different scenes require different numbers of…

A fundamental challenge in diagnostic imaging is the phenomenon of topological equivalence, where benign and malignant structures share global topology but differ in critical geometric detail, leading to diagnostic errors in both…

Image registration is a classic problem of computer vision with several applications across areas like defence, remote sensing, medicine etc. Feature based image registration methods traditionally used hand-crafted feature extraction…

Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…