Multiresolution image analysis and synthesis: from axiomatics to applications (CWI.4616)

The notion of "image content" is not uniquely defined: it depends on the resolution level at which an image is being perceived. This phenomenon, that change of resolution (or scale) may give rise to the creation, annihilation, and merging of features, has fascinated various scientists, as well as artists and philosophers. It implies that the perception of a scene at various resolutions may give rise to different outcomes. It has led to an important paradigm in image processing and computer vision: for a comprehensive understanding of a scene, one has to analyse it at a broad range of resolution levels. This results in so-called multiresolution techniques, of which various manifestations can be found in the literature, e.g., quadtrees, pyramids, fractal imaging, scale-spaces, etc. Each of these techniques has its own merits and limitations.

The discovery of wavelets in the last decade has greatly extended the utilisation of multiresolution approaches. The applicability of the wavelet transform to image processing and computer vision is somewhat limited, however, by the fact that it hinges on the linearity assumption: the underlying spaces are linear spaces and the operations involved are linear (averaging, subtraction, convolution).

The morphological approach to image processing is complementary to the linear one in the sense that it considers images as geometrical objects rather than as elements of a linear space. The central idea of mathematical morphology is to examine the geometrical structure of an image by probing it with small patterns, called "structuring elements'", at various locations in the image, just the way a blind man explores the world with the help of his fingers or a stick. By varying the size and shape of the structuring elements, one can extract useful shape information from the image. This procedure results in nonlinear image operators which are well-suited for the analysis of the geometrical and topological structure of an image.

Many of the existing morphological techniques, such as granulometries, skeletons, and alternating sequential filters, are essentially multiresolution techniques. Bearing this in mind, one may wonder: What are the relationships between the existing linear and nonlinear (morphological) multiresolution approaches? Is it possible to unify both approaches into one mathematical framework? Does there exist such a thing as a "morphological wavelet'"? The somewhat ambitious goal of this project is to answer such questions and to apply the results to application areas such image fusion, image coding and compression, and image retrieval (e.g., using textural information).

Meer informatie over dit project is te vinden op de website van het onderzoeksthema Signals and Images benaderen.

Er zijn één bedrijf en twee Nederlandse onderzoeksinstituten bij dit project betrokken.