Related papers: Robust Shape Regularity Criteria for Superpixel Ev…

The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…

The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…

Shape metrics for objects in high dimensions remain sparse. Those that do exist, such as hyper-volume, remain limited to objects that are better understood such as Platonic solids and $n$-Cubes. Further, understanding objects of ill-defined…

An accurate method for warping images is presented. Differently from most commonly used techniques, this method guarantees the conservation of the intensity of the transformed image, evaluated as the sum of its pixel values over the whole…

The loss function of an unsupervised multimodal image registration framework has two terms, i.e., a metric for similarity measure and regularization. In the deep learning era, researchers proposed many approaches to automatically learn the…

We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any orbit (finite or infinite) in the phase space with a set of…

A supersymmetric (SUSY) model of radius stabilization is constructed for the S^1/Z_2 warped compactifications with a hypermultiplet in five dimensions. Requiring the continuity of scalar field across the boundaries, we obtain radius…

The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…

Camera calibration using planar targets has been widely favored, and two types of control points have been mainly considered as measurements: the corners of the checkerboard and the centroid of circles. Since a centroid is derived from…

Finding correspondences between structural entities decomposing images is of high interest for computer vision applications. In particular, we analyze how to accurately track superpixels - visual primitives generated by aggregating adjacent…

Visual Object tracking research has undergone significant improvement in the past few years. The emergence of tracking by detection approach in tracking paradigm has been quite successful in many ways. Recently, deep convolutional neural…

The rules in a shape grammar apply in terms of embedding to take advantage of the parts that emerge visually in the appearance of shapes. While the shapes are kept unanalyzed as a computation moves forward, part-structures for shapes can be…

We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust…

In this paper, we establish robustness to noise perturbations of polyhedral regularization of linear inverse problems. We provide a sufficient condition that ensures that the polyhedral face associated to the true vector is equal to that of…

Structural quantities such as order parameters and correlation functions are often employed to gain insight into the physical behavior and properties of condensed matter systems. While standard quantities for characterizing structure exist,…

Introducing accelerated reconstruction algorithms into clinical settings requires measures of uncertainty quantification that accurately assess the relevant uncertainty introduced by the reconstruction algorithm. Many currently deployed…

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…

Manifold regularization is a commonly used technique in semi-supervised learning. It enforces the classification rule to be smooth with respect to the data-manifold. Here, we derive sample complexity bounds based on pseudo-dimension for…

Deep learning requires regularization mechanisms to reduce overfitting and improve generalization. We address this problem by a new regularization method based on distributional robust optimization. The key idea is to modify the…

We focus on the analysis of planar shapes and solid objects having thin features and propose a new mathematical model to characterize them. Based on our model, that we call an epsilon-shape, we show how thin parts can be effectively and…