Search results for "Function"
showing 10 items of 14432 documents
An evaluation framework and a benchmark for multi/hyperspectral image compression
2011
International audience; This paper benchmarks three multi/hyperspectral image compression approaches: the classic Multi-2D compression approach and two different implementations of 3D approach (Full 3D and Hybrid). All approaches are combined with a spectral PCA decorrelation stage to optimize performance. These three compression approaches are compared within a larger comparison framework than the conventionally used PSNR, which includes eight metrics divided into three families. The comparison is carried out with regard to variations in bitrates, spatial, and spectral dimensions variations of images. The time and memory consumption difference between the three approaches is also discussed…
Spatial correction in dynamic photon emission by affine transformation matrix estimation
2014
International audience; Photon emission microscopy and Time Resolved Imaging have proved their efficiency for defect localization on VLSI. A common process to find defect candidate locations is to draw a comparison between acquisitions on a normally working device and a faulty one. In order to be accurate and meaningful, this method requires that the acquisition scene remains the same between the two parts. In practice, it can be difficult to set. In this paper, a method to correct position by affine matrix transformation is suggested. It is based on image features detection, description and matching and affine transformation estimation.
An optimized algorithm of image stitching in the case of a multi-modal probe for monitoring the evolution of scars
2013
International audience; We propose a new system that makes possible to monitor the evolution of scars after the excision of a tumorous dermatosis. The hardware part of this system is composed of a new optical innovative probe with which two types of images can be acquired simultaneously: an anatomic image acquired under a white light and a functional one based on autofluorescence from the protoporphyrin within the cancer cells. For technical reasons related to the maximum size of the area covered by the probe, acquired images are too small to cover the whole scar. That is why a sequence of overlapping images is taken in order to cover the required area. The main goal of this paper is to des…
Kolmogorov Superposition Theorem and Wavelet Decomposition for Image Compression
2009
International audience; Kolmogorov Superposition Theorem stands that any multivariate function can be decomposed into two types of monovariate functions that are called inner and external functions: each inner function is associated to one dimension and linearly combined to construct a hash-function that associates every point of a multidimensional space to a value of the real interval $[0,1]$. These intermediate values are then associated by external functions to the corresponding value of the multidimensional function. Thanks to the decomposition into monovariate functions, our goal is to apply this decomposition to images and obtain image compression. We propose a new algorithm to decomp…
Kolmogorov Superposition Theorem and Its Application to Multivariate Function Decompositions and Image Representation
2008
International audience; In this paper, we present the problem of multivariate function decompositions into sums and compositions of monovariate functions. We recall that such a decomposition exists in the Kolmogorov's superposition theorem, and we present two of the most recent constructive algorithms of these monovariate functions. We first present the algorithm proposed by Sprecher, then the algorithm proposed by Igelnik, and we present several results of decomposition for gray level images. Our goal is to adapt and apply the superposition theorem to image processing, i.e. to decompose an image into simpler functions using Kolmogorov superpositions. We synthetise our observations, before …
Sobolev and bounded variation functions on metric measure spaces
2014
International audience
Computational approach to compact Riemann surfaces
2017
International audience; A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on…
Characterizations of convex approximate subdifferential calculus in Banach spaces
2016
International audience; We establish subdifferential calculus rules for the sum of convex functions defined on normed spaces. This is achieved by means of a condition relying on the continuity behaviour of the inf-convolution of their corresponding conjugates, with respect to any given topology intermediate between the norm and the weak* topologies on the dual space. Such a condition turns out to also be necessary in Banach spaces. These results extend both the classical formulas by Hiriart-Urruty and Phelps and by Thibault.
Surfaces of minimal degree of tame representation type and mutations of Cohen–Macaulay modules
2017
We provide two examples of smooth projective surfaces of tame CM type, by showing that any parameter space of isomorphism classes of indecomposable ACM bundles with fixed rank and determinant on a rational quartic scroll in projective 5-space is either a single point or a projective line. For surfaces of minimal degree and wild CM type, we classify rigid Ulrich bundles as Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a complete classification of rigid ACM bundles is given in terms of the action of the braid group in three strands.
Categorical action of the extended braid group of affine type $A$
2017
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.