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Cluster-based image segmentation

L. Van Gool, E. Pauwels, G. Frederix, G. Caenen

Recent work on content-based image indexing and retrieval rekindled the interest of the computer vision community for robust and autonomous image segmentation. In this FWO project we focus our attention on the weak segmentation problem where the objective is to delineate regions that enjoy a fair amount of homogeneity with respect to some perceptually salient feature such as colour or texture. As segmentation algorithms try to divide the image into regions that are fairly homogeneous, it therefore makes sense to map the pixels into various feature-spaces (such as colour- or texture-spaces) and look for clusters. Indeed, if in some feature-space pixels are lumped together, this obviously means that, with respect to these features, the pixels are similar. By the same token, image regions that are perceptually salient will map to clusters that (in at least some of the feature-spaces) are clearly segregated from the bulk of the data.

As all this needs to proceed in an unsupervised fashion, it is of paramount importance that we develop a mathematically principled approach that enjoys a consistent performance. To this end we have developed for the case of 1-dimensional numerical features, a non-parametric density estimation that allows us to construct the simplest density that is compatible with the data. In this context, simplicity is interpreted in terms of smoothness, while data-compatibility is determined on the basis of distribution-free statistical test.

Reframed in mathematical terms this gives rise to an optimisation problem that can be solved by geometry-driven diffusion or spline functions. The solution is a denoised model of the actual data that can be used to delineate the clusters. Unfortunately, for higher-dimensional clustering models the mathematical elegance that is characteristic of the 1-dimensional case is lost as the statistical tests become far more involved. For this reason we are working on two approximations. The first one is based on an expansion of the density in terms of Gaussian densities. The second one involves local projections of the high-dimensional data on low-dimensional subspaces and is akin to local PCA methods.