Analyse multiechelle, vision stereo et ondelettes
Lecture notes in mathematicsPublished 1 January 1990
Jacques Froment, Jean‐Michel Morel
Citations3
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
Dans cette conférence nous commençons par décrire le programme de recherches de David Marr, basé sur l'hypothèse de l'existence d'une ”vision bas niveau” accessible à la formalisation mathématique. Ensuite nous examinons les développements qui ont conduit à la notion d'analyse multiéchelle, et nous discutons les rapports qu'entretient avec celle-ci la théorie des ondelettes. Nous continuons en décrivant les premiers résultats obtenus sur un aspect applicatif particulièrement prometteur des ondelettes en traitement d'images : la compression. Nous concluons cet exposé, étayé d'images expérimentales, par quelques commentaires sur l'apport de la théorie des ondelettes aux problèmes de vision.
Keywords
Computer Science
IEEE Transactions on Pattern Analysis and Machine IntelligenceA theory for multiresolution signal decomposition: the wavelet representation
21,081 Citations1989Stéphane Mallat
It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/Sup j/ can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions.
IEEE Transactions on Pattern Analysis and Machine IntelligenceStochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images
17,980 Citations1984Stuart Geman, Donald Geman
The analogy between images and statistical mechanics systems is made and the analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations, creating a highly parallel ``relaxation'' algorithm for MAP estimation.
IEEE Transactions on Pattern Analysis and Machine IntelligenceScale-space and edge detection using anisotropic diffusion
12,040 Citations1990Pietro Perona, Jitendra Malik
IEEE Transactions on Information TheoryThe wavelet transform, time-frequency localization and signal analysis
6,448 Citations1990Ingrid Daubechies
Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied and the notion of time-frequency localization is made precise, within this framework, by two localization theorems.
Proceedings of the Royal Society of London. Series B, Biological sciencesTheory of edge detection
6,193 Citations1980David Marr, Ellen C. Hildreth
The theory of edge detection explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround ∇2G filters acting on the image forms the basis for a physiological model of simple cells.
Elsevier eBooksDigital Picture Processing
4,622 Citations1982
The rapid rate at which the field of digital picture processing has grown in the past five years had necessitated extensive revisions and the introduction of topics not found in the original edition.
SIAM Journal on Mathematical AnalysisDecomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape
3,559 Citations1984A. Großmann, J. Morlet
Biological CyberneticsThe structure of images
2,406 Citations1984Jan J. Koenderink
It is shown that any image can be embedded in a one-parameter family of derived images (with resolution as the parameter) in essentially only one unique way if the constraint that no spurious detail should be generated when the resolution is diminished, is applied.
Elsevier eBooksSCALE-SPACE FILTERING
2,353 Citations1987Andrew Witkin
Scale-space filtering is a method that describes signals qualitatively, managing the ambiguity of scale in an organized and natural way.
Transactions of the American Mathematical SocietyMultiresolution approximations and wavelet orthonormal bases of 𝐿²(𝑅)
2,109 Citations1989Stéphane Mallat
From any multiresolution approximation, one can derive a function >i/(x) called a wavelet such that {V2~Ji//(2Jx - k)),k )6Z2 is an orthonormal basis of L2(R), which provides a new approach for understanding and computing wavelet Orthonormal bases.
DSpace@MIT (Massachusetts Institute of Technology)Finding Edges and Lines in Images
807 Citations1983John Canny
This thesis is an attempt to formulate a set of edge detection criteria that capture as directly as possible the desirable properties of an edge operator.
Elsevier eBooksRepresentations based on Zero-crossings in Scale-Space
134 Citations1987Robert A. Hummel
It is shown that the evolution property of level-crossing in scale-space is equivalent to the maximum principle, and it is argued that gradient information along the zero-crossings is needed, and that although such information more than suffices, the representation is still not stable.
Shape Information From Shading: A Theory About Human Perception
108 Citations2005Alex Pentland
A closed-form solution to the problem of extracting shape information from image shading is derived that does not employ an assumption about surface smoothness and so is directly applicable to complex natural surfaces such as hair or cloth.
Towards Real-time Trinocular Stereo
15 Citations2005Charles Hansen, Nicholas Ayache +1 more
An innovative method for the reconstruction of 3-D seginents which provides better results and a new validation technique based on the observation that neighbors in the image should be neighbors in space are developed.
How the Delaunay Triangulation Can Be used For Representing Stereo Data
12 Citations2005E. Le Bras-Mehlman, Michel Schmitt +2 more
A coherent method of interpolating 3D data obtained for example by stereo, with a polyhedral surface by means of the Delaunay Triangulation, which is intrinsically discontinuity preserving and can be used for the integration of multiple viewpoints is proposed.