Efficient Description, Modeling, and Recognition of Natural Imagery via a Local Basis Library

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9973032The investigator develops adaptive, hierarchical, and computationally efficient algorithms for description, modeling, and recognition of natural imagery by tightly combining computational harmonic analysis techniques and the insight derived from the study of biological vision systems. The specific study aims are to: 1) Investigate the elementary image features that efficiently characterize a given image class, and develop computationally efficient stochastic image models using these features for simulation; 2) Develop hierarchical algorithms to extract high-level complex features by integrating the elementary features for building better stochastic models; and 3) Investigate the effectiveness of such stochastic models for recognizing and classifying different image classes. Throughout this study the investigator fully utilizes the so-called local basis library as a basic tool to extract elementary features that are the expansion coefficients (or nonlinear functions of such coefficients) of an image with respect to the bases contained in this library. This local basis library consists of a collection of the local basis dictionaries (such as wavelet packets, local cosine, local Fourier, and brushlets) whose basis elements are localized in both space and spatial frequency. Each dictionary in turn contains a huge number of orthogonal or biorthogonal bases, and is equipped with a fast numerical algorithm to select a best basis tailored to a given task and to a given set of images by optimizing task-specific criterion. In Aim 1, the investigator specifically selects the local features from the library by explicitly reducing the redundancy and statistical dependence among them, and investigate the importance of the sparsity and statistical independence for image representation and description. Then, he analyzes the effectiveness of such features by constructing simple stochastic models by assuming mutual independence or pairwise dependence among them. In Aim 2, the investigator integrates local features studied in Aim 1 to extract high-level complex features by applying the localized versions of the Karhunen-Loeve transform directly on those local features, and incorporates such features into the stochastic models. In Aim 3, the investigator examines the effectiveness of combining the localized versions of the linear discriminant analysis and the models obtained by Aims 1 and 2, for extracting the key discriminant local features.Results of the project will be useful for those who routinely work on image-based diagnostics such as radiologists and geologists. Radiologists use very subtle features of mammograms to determine whether the patients have benign or malignant tumors. Exploration geologists use images of multiple scales ranging from actual rock samples to seismic images to determine whether a specific subsurface layer contains oil or gas. Although these experts have highly trained eyes and have accumulated large databases of images in their minds through training and experience, their diagnostic rules are often of qualitative nature. The investigator believes that the above feature extraction tools will help these experts move their diagnostic methods from a qualitative regime to a quantitative one. In fact, given a specific class of images (e.g., a collection of mammograms representing malignant tumors), the above algorithms may allow these experts to build stochastic models that specify the statistical dependency of critical features of the images and to create new sample images from these models. This ability to create new simulated images at will is indispensable for assessing the variability of the features and images. If an expert can give a correct diagnosis for these simulated images, then this implies that the implicit diagnostic rules in their minds are encoded as an explicit stochastic model built on features computed by these feature extraction tools. This may lead to the development of a distributed digital image diagnostic system, where imaging devices and the diagnostic engines/knowledge bases are remotely located. One can easily imagine the usefulness of such systems in medicine, geophysical exploration, and other fields requiring image diagnostics.