Geometric models with co-occurrence groups

Finding image representations with a dimensionality reduction while maintaining relevant information for classification, remains a major issue. Effective approaches have recently been developed based on locally orderless representations as proposed by Koendering and Van Doom [1]. They observed that high frequency structures are important for recognition but do not need to be precisely located. This idea has inspired a family of descriptors such as SIFT [2] or HOG [3], which delocalize the image information over large neighborhoods, by only recording histogram information. These histograms are usually computed over wavelet like coefficients, providing a multiscale image representation with several wavelets having different orientation tunings. This paper introduces a new geometric image representation obtained by grouping coefficients that have co-occurrence properties across an image class. It provides a locally orderless representation where sparse descriptors are delocalized over groups which optimize the coefficient co-occurrences, and can be interpreted as a form of parcellization [4]. Section 2 reviews wavelet image representations and the notion of sparse geometry through significant sets. Section 3 introduces our co-occurrence grouping model which is optimized with a maximum likelihood approach. Groups are computed from a training sequence in Section 4, using a Bernoulli mixture approximation. Applications to face image compression are shown in Section 5 and the application of this representation is illustrated for MNIST image classifications in Section 6.