Search results for "Affine transformation"
showing 10 items of 99 documents
Affine Algebraic Varieties
2000
Algebraic geometers study zero loci of polynomials. More accurately, they study geometric objects, called algebraic varieties, that can be described locally as zero loci of polynomials. For example, every high school mathematics student has studied a bit of algebraic geometry, in learning the basic properties of conic sections such as parabolas and hyperbolas.
Anomalous Anosov flows revisited
2017
This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In the second part, we give a new surgery type construction of Anosov flows, which yields non-transitive Anosov flows in all odd dimensions.
Illustrating the classification of real cubic surfaces
2006
Knorrer and Miller classified the real projective cubic surfaces in P(R) with respect to their topological type. For each of their 45 types containing only rational double points we give an affine equation, s.t. none of the singularities and none of the lines are at infinity. These equations were found using classical methods together with our new visualization tool surfex. This tool also enables us to give one image for each of the topological types showing all the singularities and lines.
Invariant Feature Matching for Image Registration Application Based on New Dissimilarity of Spatial Features
2016
An invariant feature matching method is proposed as a spatially invariant feature matching approach. Deformation effects, such as affine and homography, change the local information within the image and can result in ambiguous local information pertaining to image points. New method based on dissimilarity values, which measures the dissimilarity of the features through the path based on Eigenvector properties, is proposed. Evidence shows that existing matching techniques using similarity metrics--such as normalized cross-correlation, squared sum of intensity differences and correlation coefficient--are insufficient for achieving adequate results under different image deformations. Thus, new…
Bifurcations of Reachable Sets Near an Abnormal Direction and Consequences
2007
We describe precisely, under generic conditions, the contact and the bifurcations of the reachable set at time T along an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer γ into two sectors, bordered by the first Pontryagin’s cone along γ, called the L ∞-sector and the L 2-sector. Moreover we find again necessary and sufficient conditions of optimality of an abnormal trajectory for such systems, for any optimization problem.
Composition of SIFT features for robust image representation
2010
In this paper we propose a novel feature based on SIFT (Scale Invariant Feature Transform) algorithm1 for the robust representation of local visual contents. SIFT features have raised much interest for their power of description of visual content characterizing punctual information against variation of luminance and change of viewpoint and they are very useful to capture local information. For a single image hundreds of keypoints are found and they are particularly suitable for tasks dealing with image registration or image matching. In this work we stretched the spatial coverage of descriptors creating a novel feature as composition of keypoints present in an image region while maintaining…
Multi-modal Medical Image Registration by Local Affine Transformations
2018
Image registration is the process of finding the geometric transformation that, applied to the floating image, gives the registered image with the highest similarity to the reference image. Registering a pair of images involves the definition of a similarity function in terms of the parameters of the geometric transformation that allows the registration. This paper proposes to register a pair of images by iteratively maximizing the empirical mutual information through coordinate gradient descent. Hence, the registered image is obtained by applying a sequence of local affine transformations. Rather than adopting a uniformly spaced grid to select image blocks to locally register, as done by s…
An Evolution of the Non-Parameter Harris Affine Corner Detector: A Distributed Approach
2009
A parallel version of a new automatic Harris-based corner detector is presented. A scheduler to dynamically and homogeneously distribute high computational workload on heterogeneous parallel architectures such as Grid systems has been implemented to speedup the whole procedure. Experimental results show the robustness of the underlying scheduler, which can be easily exploited in various automatic image analysis systems.
Fuzzy Smoothed Composition of Local Mapping Transformations for Non-rigid Image Registration
2009
This paper presents a novel method for medical image regis- tration. The global transformation is obtained by composing affine trans- formations, which are recovered locally from given landmarks. Transfor- mations of adjacent regions are smoothed to avoid blocking artifacts, so that a unique continuous and differentiable global function is obtained. Such composition is operated using a technique derived from fuzzy C- means clustering. The method was successfully tested on several datasets; results, both qualitative and quantitative, are shown. Comparisons with other methods are reported. Final considerations on the efficiency of the technique are explained.
Computing the Arrangement of Circles on a Sphere, with Applications in Structural Biology
2009
International audience; Balls and spheres are the simplest modeling primitives after affine ones, which accounts for their ubiquitousness in Computer Science and Applied Mathematics. Amongst the many applications, we may cite their prevalence when it comes to modeling our ambient 3D space, or to handle molecular shapes using Van der Waals models. If most of the applications developed so far are based upon simple geometric tests between balls, in particular the intersection test, a number of applications would obviously benefit from finer pieces of information. Consider a sphere $S_0$ and a list of circles on it, each such circle stemming from the intersection between $S_0$ and another spher…