Collaborators:

Karen Brady, Josiane Zerubia.

Key words:

segmentation, texture, adaptive, wavelet packets, arbitrary regions, boundary wavelets.

Resume:

One of the quantities essential for the segmentation of textured images is the probability of the data in an arbitrary region given that it comes from a specific texture class. Planar parallel textures are, in contrast, defined as translation-invariant measures on the space of infinite images, infinite extendibility being one of the defining criteria for such textures. To get the former from the latter, it is necessary to marginalize away the degrees of freedom outside the region.

Theory:

In the case of Gaussian textures, the probability of the data in a region is itself Gaussian, but with an inverse covariance operator O that depends in a complex way on both the original inverse covariance and the region. In order to work with this measure, it is necessary to diagonalise O. By imposing a weak restriction on the form of the original inverse covariance, O can be approximately diagonalised by a wavelet packet basis. The latter adapts both to the properties of the texture (strong periodicities etc.), thus allowing a more precise description than a fixed basis, and to the geometry of the region, thus allowing a rigorous solution to the "texture boundary" problem. Work continues with the application of the same type of analysis to more sophisticated models.

Practice:

The structure of the basis, and the parameters of the model, are learned by exact MAP estimation. The resulting texture models are used for pixelwise classification with an utility function that depends on the properties of the neighbours of the pixel classified. Work continues with comparative evaluation and with experiments on real images.

Preliminary results:

Publications:

• "Texture Analysis: an Adaptive Probabilistic Approach", Karen Brady, Ian H. Jermyn, Josiane Zerubia, Proceedings of the IEEE International Conference on Image Processing (ICIP), Barcelona, Spain, September 2003. (PDF)