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Discrete-Time Wavelet Extrema Representation - Design and Consistent Reconstruction
Concepts associés (26)
Espace d'échelle
La théorie de lEspace d'échelle () est un cadre pour la représentation du signal développé par les communautés de la vision artificielle, du , et du traitement du signal. C'est une théorie formelle pour manipuler les structures de l'image à différentes échelles, en représentant une image comme une famille d'images lissées à un paramètre, la représentation d'espace échelle, paramétrée par la taille d'un noyau lissant utilisé pour supprimer les structures dans les petites échelles. Soit un signal.
Scale space implementation
In the areas of computer vision, and signal processing, the notion of scale-space representation is used for processing measurement data at multiple scales, and specifically enhance or suppress image features over different ranges of scale (see the article on scale space). A special type of scale-space representation is provided by the Gaussian scale space, where the image data in N dimensions is subjected to smoothing by Gaussian convolution.
Multi-scale approaches
The scale space representation of a signal obtained by Gaussian smoothing satisfies a number of special properties, scale-space axioms, which make it into a special form of multi-scale representation. There are, however, also other types of "multi-scale approaches" in the areas of computer vision, and signal processing, in particular the notion of wavelets. The purpose of this article is to describe a few of these approaches: For one-dimensional signals, there exists quite a well-developed theory for continuous and discrete kernels that guarantee that new local extrema or zero-crossings cannot be created by a convolution operation.
Wavelet transform
In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform. A function is called an orthonormal wavelet if it can be used to define a Hilbert basis, that is a complete orthonormal system, for the Hilbert space of square integrable functions.
Discrete wavelet transform
In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time). Haar wavelet The first DWT was invented by Hungarian mathematician Alfréd Haar. For an input represented by a list of numbers, the Haar wavelet transform may be considered to pair up input values, storing the difference and passing the sum.
Blob detection
In computer vision, blob detection methods are aimed at detecting regions in a that differ in properties, such as brightness or color, compared to surrounding regions. Informally, a blob is a region of an image in which some properties are constant or approximately constant; all the points in a blob can be considered in some sense to be similar to each other. The most common method for blob detection is convolution.
Filter bank
In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal.
Scale-invariant feature transform
[[Fichier:Matching of two images using the SIFT method.jpg|thumb|right|alt=Exemple de mise en correspondance de deux images par la méthode SIFT : des lignes vertes relient entre eux les descripteurs communs à un tableau et une photo de ce même tableau, de moindre qualité, ayant subi des transformations. |Exemple de résultat de la comparaison de deux images par la méthode SIFT (Fantasia ou Jeu de la poudre, devant la porte d’entrée de la ville de Méquinez, par Eugène Delacroix, 1832).
Ondelette
thumb|Ondelette de Daubechies d'ordre 2. Une ondelette est une fonction à la base de la décomposition en ondelettes, décomposition similaire à la transformée de Fourier à court terme, utilisée dans le traitement du signal. Elle correspond à l'idée intuitive d'une fonction correspondant à une petite oscillation, d'où son nom. Cependant, elle comporte deux différences majeures avec la transformée de Fourier à court terme : elle peut mettre en œuvre une base différente, non forcément sinusoïdale ; il existe une relation entre la largeur de l'enveloppe et la fréquence des oscillations : on effectue ainsi une homothétie de l'ondelette, et non seulement de l'oscillation.
Continuous wavelet transform
In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. The continuous wavelet transform of a function at a scale (a>0) and translational value is expressed by the following integral where is a continuous function in both the time domain and the frequency domain called the mother wavelet and the overline represents operation of complex conjugate.