In a recent paper [10], M.E. Kahoui and M. Ouali have proved that over an algebraically closed field k of characteristic zero, residual coordinates in k[X][Z1,…,Zn] are one-stable coordinates. this we extend their result to the case arbitrary characteristic. fact, show holds when k[X] is replaced by any one-dimensional seminormal domain R which affine k. For our proof, S. Maubach [11] giving cr...

Learning and synthesizing stabilizing controllers for unknown nonlinear control systems is a challenging problem real-world industrial applications. Koopman operator theory allows one to analyze through the lens of linear bilinear systems. The key idea these methods lies in transformation coordinates system into observables, which are that allow representation original (control system) as highe...

In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to curves. The extension makes it possible to reconstruct 3D-curves up to projective transformations, from a number of their 2Dprojections. We also extend the bundle adjustment technique from point features to curves. The first step of the curve reconstruction algorithm is based on affine shape, is ...

Simple geometric objects and transformations appear in representations and algorithms of geometric facilities in computer applications such as modelling, robotics, or graphics. Usually, these applications only support objects and transformations fully describable by rational parameters, and a computer display of points of the objects at least implicitly requires points with rational coordinates...

Binary image registration has been addressed by many authors recently however most of the proposed approaches are restricted to affine transformations. In this paper a novel approach is proposed to estimate the parameters of a general projective transformation (also called homography) that aligns two shapes. Recovering such projective transformations is a fundamental problem in computer vision ...

Convex-concave sets and Arnold hypothesis. The notion of convexity is usually defined for subsets of affine spaces, but it can be generalized for subsets of projective spaces. Namely, a subset of a projective space RP is called convex if it doesn’t intersect some hyperplane L ⊂ RP and is convex in the affine space RP \L. In the very definition of the convex subset of a projective space appears ...

The size of 3D data stored around the web has become bigger. Therefore the development of recognition applications and retrieval systems of 3D models is important. This paper deals with invariants for 3D models recognition. Thus under general affine transform we propose in a first time determinants of three points to realize invariance under affinity. To solve starting point problem we needs Fo...

We extend a method for color weak compensation based on the criterion of preservation of subjective color differences between color normal and color weak observers presented in [2]. We introduce a new algorithm for color weak compensation using local affine maps between color spaces of color normal and color weak observers. We show how to estimate the local affine map and how to determine corre...

Culik 11, K . and S . Dube, Rational and affine expressions for image description, Discrete Applied Mathematics 41 (1993) 85-120 . In this paper, the representation, generation and inference of images using automata-theoretic techniques is investigated . It is shown that highly complex images, including "fractal" (self-similar) images, can be manipulated by the application of these techniques ....

We report on relative performance numbers for affine and projective pairings on a dual-core Cortex A9 ARM processor. Using a fast inversion in the base field and doing inversion in extension fields by using the norm map to reduce to inversions in smaller fields, we find a very low ratio of inversion-to-multiplication costs. In our implementation, this favors using affine coordinates, even for t...