Search results for "Euclidean Distance"

Central catadioptric image processing with geodesic metric

2011

International audience; Because of the distortions produced by the insertion of a mirror, catadioptric images cannot be processed similarly to classical perspective images. Now, although the equivalence between such images and spherical images is well known, the use of spherical harmonic analysis often leads to image processing methods which are more difficult to implement. In this paper, we propose to define catadioptric image processing from the geodesic metric on the unitary sphere. We show that this definition allows to adapt very simply classical image processing methods. We focus more particularly on image gradient estimation, interest point detection, and matching. More generally, th…

A finite element-based machine learning approach for modeling the mechanical behavior of the breast tissues under compression in real-time

2017

[EN] This work presents a data-driven method to simulate, in real-time, the biomechanical behavior of the breast tissues in some image-guided interventions such as biopsies or radiotherapy dose delivery as well as to speed up multimodal registration algorithms. Ten real breasts were used for this work. Their deformation due to the displacement of two compression plates was simulated off-line using the finite element (FE) method. Three machine learning models were trained with the data from those simulations. Then, they were used to predict in real-time the deformation of the breast tissues during the compression. The models were a decision tree and two tree-based ensemble methods (extremely…

Cartoon filter via adaptive abstraction

2016

We propose a non-parametric methodology to realize abstraction images.The redundant wavelet "a trous" algorithm is applied for details detection.An multi-scale circular median filter is used as a smoothing filter.The proposed algorithm is simple and fast on low-cost entry-level hardware. Abstraction in computer graphics defines a procedure that discriminates the essential information that is worth keeping. Usually details, that correspond to higher frequency components, allow to distinguish otherwise similar images. Vice versa, low frequencies are related to the main information, which are larger structures. Contours themselves may also be identified by high frequencies and separate each pi…

Distance Functions, Clustering Algorithms and Microarray Data Analysis

2010

Distance functions are a fundamental ingredient of classification and clustering procedures, and this holds true also in the particular case of microarray data. In the general data mining and classification literature, functions such as Euclidean distance or Pearson correlation have gained their status of de facto standards thanks to a considerable amount of experimental validation. For microarray data, the issue of which distance function works best has been investigated, but no final conclusion has been reached. The aim of this extended abstract is to shed further light on that issue. Indeed, we present an experimental study, involving several distances, assessing (a) their intrinsic sepa…

Covering and differentiation

1995

A methodology to assess the intrinsic discriminative ability of a distance function and its interplay with clustering algorithms for microarray data …

2013

Abstract Background Clustering is one of the most well known activities in scientific investigation and the object of research in many disciplines, ranging from statistics to computer science. Following Handl et al., it can be summarized as a three step process: (1) choice of a distance function; (2) choice of a clustering algorithm; (3) choice of a validation method. Although such a purist approach to clustering is hardly seen in many areas of science, genomic data require that level of attention, if inferences made from cluster analysis have to be of some relevance to biomedical research. Results A procedure is proposed for the assessment of the discriminative ability of a distance functi…

On the points realizing the distance to a definable set

2011

Abstract We prove a definable/subanalytic version of a useful lemma, presumably due to John Nash, concerning the points realizing the Euclidean distance to an analytic submanifold of R n . We present a parameter version of the main result and we discuss the properties of the multifunction obtained.

Finite linear spaces in which any n-gon is euclidean

1986

Abstract An n-gon of a linear space is a set S of n points no three of which are collinear. By a diagonal point of S we mean a point p off S with the property that at least two lines through p intersect S in two points. The number of diagonal points is called the type of S. For example, a 4-gon has at most three diagonal points. We call an n-gon euclidean if (roughly speaking) it contains the maximal possible number of 4-gons of type 3. In this paper, we characterize all finite linear spaces in which, for a fixed number n ⩾ 5, any n-gon is euclidean. It turns out that these structures are essentially projective spaces or punctured projective spaces.

Scalable Ellipsoidal Classification for Bipartite Quantum States

2008

The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as s…

Vector representation of non-standard spellings using dynamic time warping and a denoising autoencoder

2017

The presence of non-standard spellings in Twitter causes challenges for many natural language processing tasks. Traditional approaches mainly regard the problem as a translation, spell checking, or speech recognition problem. This paper proposes a method that represents the stochastic relationship between words and their non-standard versions in real vectors. The method uses dynamic time warping to preprocess the non-standard spellings and autoencoder to derive the vector representation. The derived vectors encode word patterns and the Euclidean distance between the vectors represents a distance in the word space that challenges the prevailing edit distance. After training the autoencoder o…