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We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of approximation by adaptive finite elements, when no constraint…
We formulate and discuss the affine-invariant matrix midrange problem on the cone of $n\times n$ positive definite Hermitian matrices $\mathbb{P}(n)$, which is based on the Thompson metric. A particular computationally efficient midpoint of…
Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The…
We propose a robust classification algorithm for curves in 2D and 3D, under the special and full groups of affine transformations. To each plane or spatial curve we assign a plane signature curve. Curves, equivalent under an affine…
The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.
This paper presents premier and innovative time-domain multi-scale method for shape identification in electro-sensing using pulse-type signals. The method is based on transform-invariant shape descriptors computed from filtered polarization…
The logarithmic model offers new tools for image processing. An efficient method for image enhancement is to use an affine transformation with the logarithmic operations: addition and scalar multiplication. We define some criteria for…
Moment invariants are well-established and effective shape descriptors for image classification. In this report, we introduce a package for R-language, named IM, that implements the calculation of moments for images and allows the…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
Here, we propose a new modified quantum mechanics and its new algorithms of atomic fine-structure,asymmetric variational method based on hydrogen-like atom orbit. In addition, as we all know, the ab initio calculation of atomic…
In this paper, a novel image moments based model for shape estimation and tracking of an object moving with a complex trajectory is presented. The camera is assumed to be stationary looking at a moving object. Point features inside the…
This paper focuses on the equidimensional decomposition of affine varieties defined by sparse polynomial systems. For generic systems with fixed supports, we give combinatorial conditions for the existence of positive dimensional components…
The technique requires the epipolar geometry to be pre-estimated between each image pair. It exploits the constraints which the camera movement implies, in order to apply a closed-form correction to the parameters of the input affinities.…
We develop a natural variant of Dikin's affine-scaling method, first for semidefinite programming and then for hyperbolic programming in general. We match the best complexity bounds known for interior-point methods. All previous…
We propose a novel method to accurately reconstruct a set of images representing a single scene from few linear multi-view measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background…
An image fusion method based on salient features is proposed in this paper. In this work, we have concentrated on salient features of the image for fusion in order to preserve all relevant information contained in the input images and tried…