Search results for "Affine"
showing 10 items of 183 documents
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…
Approximation of W1, Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
2018
Abstract Let Ω ⊂ R n , n ≥ 4 , be a domain and 1 ≤ p [ n / 2 ] , where [ a ] stands for the integer part of a. We construct a homeomorphism f ∈ W 1 , p ( ( − 1 , 1 ) n , R n ) such that J f = det D f > 0 on a set of positive measure and J f 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) f k such that f k → f in W 1 , p .
The asymptotic covariance matrix of the Oja median
2003
The Oja median, based on a sample of multivariate data, is an affine equivariant estimate of the centre of the distribution. It reduces to the sample median in one dimension and has several nice robustness and efficiency properties. We develop different representations of its asymptotic variance and discuss ways to estimate this quantity. We consider symmetric multivariate models and also the more narrow elliptical models. A small simulation study is included to compare finite sample results to the asymptotic formulas.
The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies
2003
We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform …
Inference based on the affine invariant multivariate Mann–Whitney–Wilcoxon statistic
2003
A new affine invariant multivariate analogue of the two-sample Mann–Whitney–Wilcoxon test based on the Oja criterion function is introduced. The associated affine equivariant estimate of shift, the multivariate Hodges-Lehmann estimate, is also considered. Asymptotic theory is developed to provide approximations for null distribution as well as for a sequence of contiguous alternatives to consider limiting efficiencies of the test and estimate. The theory is illustrated by an example. Hettmansperger et al. [9] considered alternative slightly different affine invariant extensions also based on the Oja criterion. The methods proposed in this paper are computationally more intensive, but surpri…
Sign test of independence between two random vectors
2003
A new affine invariant extension of the quadrant test statistic Blomqvist (Ann. Math. Statist. 21 (1950) 593) based on spatial signs is proposed for testing the hypothesis of independence. In the elliptic case, the new test statistic is asymptotically equivalent to the interdirection test by Gieser and Randles (J. Amer. Statist. Assoc. 92 (1997) 561) but is easier to compute in practice. Limiting Pitman efficiencies and simulations are used to compare the test to the classical Wilks’ test. peerReviewed
k-Step shape estimators based on spatial signs and ranks
2010
In this paper, the shape matrix estimators based on spatial sign and rank vectors are considered. The estimators considered here are slight modifications of the estimators introduced in Dümbgen (1998) and Oja and Randles (2004) and further studied for example in Sirkiä et al. (2009). The shape estimators are computed using pairwise differences of the observed data, therefore there is no need to estimate the location center of the data. When the estimator is based on signs, the use of differences also implies that the estimators have the so called independence property if the estimator, that is used as an initial estimator, has it. The influence functions and limiting distributions of the es…
Tests of multinormality based on location vectors and scatter matrices
2007
Classical univariate measures of asymmetry such as Pearson’s (mean-median)/σ or (mean-mode)/σ often measure the standardized distance between two separate location parameters and have been widely used in assessing univariate normality. Similarly, measures of univariate kurtosis are often just ratios of two scale measures. The classical standardized fourth moment and the ratio of the mean deviation to the standard deviation serve as examples. In this paper we consider tests of multinormality which are based on the Mahalanobis distance between two multivariate location vector estimates or on the (matrix) distance between two scatter matrix estimates, respectively. Asymptotic theory is develop…