Hierarchical discriminant analysis for image retrieval

A self-organizing framework for object recognition is described. We describe a hierarchical database structure for image retrieval. The Self-Organizing Hierarchical Optimal Subspace Learning and Inference Framework (SHOSLIF) system uses the theories of optimal linear projection for automatic optimal feature derivation and a hierarchical structure to achieve a logarithmic retrieval complexity. A Space-Tessellation Tree is automatically generated using the Most Expressive Features (MEFs) and the Most Discriminating Features (MDFs) at each level of the tree. The major characteristics of the proposed hierarchical discriminant analysis include: 1) avoiding the limitation of global linear features (hyperplanes as separators) by deriving a recursively better-fitted set of features for each of the recursively subdivided sets of training samples; 2) generating a smaller tree whose cell boundaries separate the samples along the class boundaries better than the principal component analysis, thereby giving a better generalization capability (i.e., better recognition rate in a disjoint test); 3) accelerating the retrieval using a tree structure for data pruning, utilizing a different set of discriminant features at each level of the tree. We allow for perturbations in the size and position of objects in the images through learning. We demonstrate the technique on a large image database of widely varying real-world objects taken in natural settings, and show the applicability of the approach for variability in position, size, and 3D orientation. This paper concentrates on the hierarchical partitioning of the feature spaces.