Image Understanding Applications of Lattice Autoassociative Memories

Multivariate mathematical morphology (MMM) aims to extend the mathematical morphology from gray scale images to images whose pixels are high-dimensional vectors, such as remote sensing hyperspectral images and functional magnetic resonance images (fMRIs). Defining an ordering over the multidimensional image data space is a fundamental issue MMM, to ensure that ensuing morphological operators and filters are mathematically consistent. Recent approaches use the outputs of two-class classifiers to build such reduced orderings. This paper presents the applications of MMM built on reduced supervised orderings based on lattice autoassociative memories (LAAMs) recall error measured by the Chebyshev distance. Foreground supervised orderings use one set of training data from a foreground class, whereas background/foreground supervised orderings use two training data sets, one for each relevant class. The first case study refers to the realization of the thematic segmentation of the hyperspectral images using spatial-spectral information. Spectral classification is enhanced by a spatial processing consisting in the spatial correction guided by a watershed segmentation computed by the LAAM-based morphological operators. The approach improves the state-of-the-art hyperspectral spatial-spectral thematic map building approaches. The second case study is the analysis of resting state fMRI data, working on a data set of healthy controls, schizophrenia patients with and without auditory hallucinations. We perform two experiments: 1) the localization of differences in brain functional networks on population-dependent templates and 2) the classification of subjects into each possible pair of cases. In this data set, we find that the LAAM-based morphological features improve over the conventional correlation-based graph measure features often employed in fMRI data classification.