Multiresolution linear discriminant analysis: efficient extraction of geometrical structures in images

Currently popular feature extraction tools (e.g., Gabor, wavelet analysis) do not economically represent edges in images. As a step towards solving this problem, the wedgelet transform was recently proposed D.L. Donoho, [1999]; this transform provides nearly optimal representation of objects in the Horizon model, as measured by the minimax mean-squared error. However, there is no reason to assume that the components useful for representing pixel values must also be useful for discriminating between regions in an image. Thus, having the successful extraction of edges as our goal, we propose a novel image analysis method-namely, multiresolution linear discriminant analysis (MLDA). In MLDA, analogously to the wedgelet transform, we seek directions that are efficient for discrimination. The MLDA framework comprises the following components: the MLDA atom, dictionary, tree, graph, and MLDA-based algorithms. In this paper, we explain these components and demonstrate the powerful expressiveness of MLDA, which gives rise to fast geometrical-structure-analysis algorithms.