Injection D’a Priori Spatial dans la Construction D’une Hiérarchie Optimale de Régions
This work presents an optimal method of construction of hierarchy of regions with injection of a priori within the framework of the scale set theory. This approach is based on the minimization of an under additive energy in which the spatial a priori is embedded.
In this article, we propose an innovative approach of construction of hierarchy of regions. The building of the hierarchy is based on an energy model and on an optimal merging process. Our objective is to adapt this hierarchy to the complexity of objects composing the image. To reach this objective, we incorporate a spatial a priori which underlines the importance of some objects and structures in the image. In the first part of the article we introduce the multi-scale segmentation paradigm by comparing some existing works. In the second part, some aspects of the Scale-set theory are recalled. In the third part, we present some theoretical aspects of our approach based on the exploitation of a sub additive energy in which we incorporate a spatial energy term. We suggest various ways of building this spatial energy. The last part is devoted to some experimental results.
In a mathematical framework, a set-scale representation is a hierarchy of regions or a monotonous suite of partitions. Most of the existing methods are local and the vertical axe in the hierarchy is not a scale but a level. For this reason we proposed in (Guigues et al., 2006) to represent the image as a hierarchy of regions in which the horizontal cuts are indexed with a scale value or in an other way as a monotonous suite of partitions. The merging process is optimal due to minimization of an energy containing as a classical way, a term of attach to the data and a term of regularization. The energy of regularization is under additive and based on the functional of Mumford-Shah (Mumford et al., 1989) who corresponds to a constant piecewise model of the image. Results are very satisfactory, but we noticed erroneous fusions and premature absorptions (in scale) of relevant structures. These phenomena are understandable because the energies are based on low level attributes and because decisions are local. We thus resolve this problem by injecting a spatial a priori by drawing blobs around relevant structures at high scale. This problem was seldom studied within the framework of the multi-scale segmentation. In our model, spatial a priori is integrated as a spatial energy into the scale set formalism. This spatial energy has to be sub-additive and is incorporated into the regularization term of the Mumford-Shah formula. We defined three types of spatial energies: i) A monopotentialenergy which represents the intensity of the attraction between a region and the blob. This pseudo-attraction will be measured by a potential function of attraction. ii) A multi-potential energy, which, as the mono-potential energy takes into account both the mono-potential energy of the studied region and the energies of the nearby regions. iii) A bi-potential energy based on an attractive intensity between two nearby regions with respect to a blob.
Various experiments have been performed on synthetic and natural images, they illustrate the efficiency and the role of the spatial energy in the hierarchical construction. A spatial energy confers a higher degree of relevance to surrounded objects, their structures resist to the merge processes and persist a longer time in the hierarchy. A top down exploration of the hierarchy allows to find these objects more quickly in cuts containing very few regions (top of the hierarchy). Compared with hierarchy obtained without spatial a priori, the spatial a priori protect objects inside a blob from fusion with regions outside this blob.
In this article, we are within the framework of an interactive segmentation where blob is manually drawn. We also used our algorithm in a embarked system on an intelligent vehicle including two cameras and a radar. The problem is to correctly segment areas containing pedestrians. The echo received by the radar and the multisensor system characteristics are exploited to draw a rectangular blob in the image supplied by one of the cameras. The dimension of the blob is given by the height of a pedestrian computed by taking into account the distance to the obstacle supplied by the radar.
Ce travail présente une méthode de construction optimale de hiérarchie de régions avec injection d’a priori dans le cadre de la théorie ensemble échelle. Cette approche repose sur la minimisation d’une énergie sous-additive qui intègre un a priori spatial.
multiscale segmentation, hierachy of regions, interactive segmentation with spatial priori.
segmentation multi-échelle, hiérarchie de région, segmentation interactive avec a priori spatial.
Cocquerez J., Philipp S. (1995). Analyse d’images : filtrage et segmentation, Masson edn, Paris.
Guigues L., Cocquerez J. P., Le Men H. (2006, April). Scale-Sets Image Analyzis, International Journal of Computer Vision.
Haris K., Estradiadis S. N., Maglaveras N., Katsaggelos A. K. (1998). Hybrid image segmentation using watersheds and fast region merging, IEEE Trans. on Image Processing, vol. 7, n° 12, p. 1684-1699.
Koenderink J. (1984). The structure of images, Biol. Cybern., vol. 50, p. 363-370.
Koenderink J., Van Doorn A. (1999). The structure of locally orderless images, International Journal of Computer Vision, vol. 31, n° 3/2, p. 159-168.
Laurent G. (2003). Modèles Multi-échelles pour la Segmentation d’Images (Multi-Scale Models for Image Segmentation), PhD thesis, Université de Cergy-Pontoise, France, Dec.
Lindeberg T. (1998). Feauture Detection with automatic Scale Selection, Int. J. of Computer Vision.
Mumford D., Shah J. (1989). Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems, Comm. on Pure and Applied Math., vol. 17, n° 4, p. 577-685.
Perona P., Malik J. (1990). Scale space and edge detection using anisotropic diffusion, IEEE trans. on PAMI, vol. 12, n° 1, p. 629-639.
Witkin A. (1983). Scale-space filtering, Proc. of 8th Int. Joint Conf. on Artificial Intell., Karlsruhe, West Germany, vol., p. 1019-1021.
Yousfi K. (2008). Segmentation hiérarchique optimale par injection d’a priori : radiométrique, géométrique ou spatial, PhD thesis, Université de Technologie de Compiègne, 3 novembre.