L'analyse d'image touche a l'heure actuelle de nombreux domaines, avec des objectifs aussi varies que l'aide au diagnostic pour les images medicales, la vision artificielle en robotique ou l'analyse des ressources terrestres a partir des images prises par satellite. Le but du traitement de ces images est a la fois simple dans son concept et difficile dans sa realisation. Simple en effet, puisqu'il s'agit de reconnaitre des objets que notre systeme visuel percoit rapidement, du moins pour la majorite d'entre eux. Difficile cependant, car dans la grande quantite d'informations contenues dans l'image, il faut extraire des elements pertinents pour l'application visee et ceci independamment de la qualite de l'image. L'analyse d'image s'est donc dotee d'outils et de methodes puissants issus de domaines aussi varies que les mathematiques, le traitement du signal, ou l'informatique. Cet ouvrage presente un des aspects les plus importants du traitement des images : la " segmentation ". Il recapitule d'abord les grandeurs observables et calculables sur une image et les algorithmes de manipulation des structures de donnees associees. Il detaille ensuite les traitements preliminaires, tels le filtrage du bruit et les deux types d'approche de la segmentation, l'extraction des contours et celle des regions. Chacune fait l'objet d'une etude theorique et de nombreux resultats illustrent les performances. Une des originalites de l'ouvrage est l'etude comparative des differentes techniques appliquees sur un meme corpus d'images reelles.

https://hal.archives-ouvertes.fr/hal-00706168/document

Analyse d'images: filtrage et segmentation

A unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis is presented. The unification requires a set-theoretic methodology, where signals are modeled as sets, systems (signal transformations) are viewed as set mappings, and translational-invariant systems are uniquely characterized by special collections of input signals. This approach leads to a general representation theory, in which any translation-invariant, increasing, upper semicontinuous system can be presented exactly as a minimal nonlinear superposition of morphological erosions or dilations. The theory is used to analyze some special cases of image/signal analysis systems, such as morphological filters, median and order-statistic filters, linear filters, and shape recognition transforms. Although the developed theory is algebraic, its prototype operations are well suited for shape analysis; hence, the results also apply to systems that extract information about the geometrical structure of signals. >

/pdf/a-representation-theory-for-morphological-image-and-signal-3nod3hexrq.pdf

A representation theory for morphological image and signal processing

Summary form only given. Two approaches have been used in the past to design rank-order-based nonlinear filters to enhance or restore images: the structural approach and the estimation approach. The first approach requires structural descriptions of the image and the process which has altered it, whereas the second required statistical descriptions. The many different classes of rank-order-based filters that have been developed over the last few decades have been reviewed in the context of these two approaches. One of these filter classes, stack filters, has been investigated. These filters, which are defined by a weak superposition property and an ordering property, contain all compositions of 2D rank-order operations. The recently developed theory of minimum-mean-absolute-error (MMAE) stack filtering has been extended to two dimensions. A theory of optimal stack filtering under structural constraints and goals has been developed for the structural approach to image processing. These two optimal stack filtering theories have been combined into a single design theory for rank-order-based filters. >

Optimal stack filtering and the estimation and structural approaches to image processing

It is shown that four composite morphological systems, namely morphological edge detection, peak/valley extraction, skeletonization, and shape-size distributions obey a weak linear superposition, called threshold-linear superposition. The output image signal or measurement from each system is shown to be the sum of outputs due to input binary images that result from thresholding the input gray-level image at all levels. These results are generalized to a vector space formulation, e.g. to any finite linear combination of simple morphological systems. Thus many such systems processing gray-level images are reduced to corresponding binary image processing systems, which are easier to analyze and implement. >

Threshold superposition in morphological image analysis systems

This paper presents a unifying theory for many concepts and operations encountered in or related to morphological image and signal analysis. This unification requires a set-theoretic methodology, where signals are modeled as sets, systems (signal transformations) are viewed as set mappings, and translation-invariant systems are uniquely characterized by special collections of input signals. This approach leads to a general representation theory, in which any translation-in- variant, increasing, upper semicontinuous system can be represented exactly as a minimal nonlinear superposition of morphological erosions or dilations. In this representation, many similarities and a few differences are observed between systems processing binary or multi- level signals, and continuous-domain or discrete-domain signals. The theory is used to analyze some special cases of image/signal analysis systems, such as morphological filters, median and order-statistic fil- ters, linear filters, and shape recognition transforms. Although the de- veloped theory is algebraic, its prototype operations are well suitable for shape analysis; hence, the results of this study also apply to systems that extract information about the geometrical structure of signals. Zndex Terms-Imagelsignal processing, mathematical morphology, nonlinearllinear filtering, shape analysis, systems representation.

A Representation Theory for Morphological Image and Signal Processing

A hybrid optical/electronic system performs median filtering and related ranked-order operations using threshold decomposition to encode the image. Threshold decomposition transforms the nonlinear neighborhood ranking operation into a linear space-invariant filtering step followed by a point-to-point threshold comparison step. Spatial multiplexing allows parallel processing of all the threshold components as well as recombination by a second linear space-invariant filtering step. An incoherent optical correlation system performs the linear filtering, using a magnetooptic spatial light modulator as the input device and a computergenerated hologram in the filter plane. Thresholding is done electronically. By adjusting the value of the threshold, the same architecture is used to perform median, minimum, and maximum filtering of images.

Jan P. Allebach

Papers

Optical median filtering using threshold decomposition