Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

A Self-Organizing Neural System for Learning to Recognize Textured Scenes

A self-organizing ARTEX model is developed to categorize and classify textured image regions. ARTEX specializes the FACADE model of how the visual cortex sees, and the ART model of how temporal and prefrontal cortices interact with the hippocampal system to learn visual recognition categories and their names. FACADE processing generates a vector of boundary and surface properties, notably texture and brightness properties, by utilizing multi-scale filtering, competition, and diffusive filling-in. Its context-sensitive local measures of textured scenes can be used to recognize scenic properties that gradually change across space, as well a.s abrupt texture boundaries. ART incrementally learns recognition categories that classify FACADE output vectors, class names of these categories, and their probabilities. Top-down expectations within ART encode learned prototypes that pay attention to expected visual features. When novel visual information creates a poor match with the best existing category prototype, a memory search selects a new category with which classify the novel data. ARTEX is compared with psychophysical data, and is benchmarked on classification of natural textures and synthetic aperture radar images. It outperforms state-of-the-art systems that use rule-based, backpropagation, and K-nearest neighbor classifiers.Defense Advanced Research Projects Agency; Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657

A Neural Model of Surface Perception: Lightness, Anchoring, and Filling-in

This article develops a neural model of how the visual system processes natural images under variable illumination conditions to generate surface lightness percepts. Previous models have clarified how the brain can compute the relative contrast of images from variably illuminate scenes. How the brain determines an absolute lightness scale that "anchors" percepts of surface lightness to us the full dynamic range of neurons remains an unsolved problem. Lightness anchoring properties include articulation, insulation, configuration, and are effects. The model quantatively simulates these and other lightness data such as discounting the illuminant, the double brilliant illusion, lightness constancy and contrast, Mondrian contrast constancy, and the Craik-O'Brien-Cornsweet illusion. The model also clarifies the functional significance for lightness perception of anatomical and neurophysiological data, including gain control at retinal photoreceptors, and spatioal contrast adaptation at the negative feedback circuit between the inner segment of photoreceptors and interacting horizontal cells. The model retina can hereby adjust its sensitivity to input intensities ranging from dim moonlight to dazzling sunlight. A later model cortical processing stages, boundary representations gate the filling-in of surface lightness via long-range horizontal connections. Variants of this filling-in mechanism run 100-1000 times faster than diffusion mechanisms of previous biological filling-in models, and shows how filling-in can occur at realistic speeds. A new anchoring mechanism called the Blurred-Highest-Luminance-As-White (BHLAW) rule helps simulate how surface lightness becomes sensitive to the spatial scale of objects in a scene. The model is also able to process natural images under variable lighting conditions.Air Force Office of Scientific Research (F49620-01-1-0397); Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); Office of Naval Research (N00014-01-1-0624

A Self-Organizing System for Classifying Complex Images: Natural Textures and Synthetic Aperture Radar

A self-organizing architecture is developed for image region classification. The system consists of a preprocessor that utilizes multi-scale filtering, competition, cooperation, and diffusion to compute a vector of image boundary and surface properties, notably texture and brightness properties. This vector inputs to a system that incrementally learns noisy multidimensional mappings and their probabilities. The architecture is applied to difficult real-world image classification problems, including classification of synthetic aperture radar and natural texture images, and outperforms a recent state-of-the-art system at classifying natural texturns.Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-91-J-4100); Advanced Research Projects Agency (N00014-92-J-4015); Air Force Office of Scientific Research (F49620-92-J-0225, F49620-92-J-0334); National Science Foundation (IRI-90-00530, IRI-90-24877

A Self-Organizing System for Classifying Complex Images: Natural Textures and Synthetic Aperture Radar

A self-organizing architecture is developed for image region classification. The system consists of a preprocessor that utilizes multi-scale filtering, competition, cooperation, and diffusion to compute a vector of image boundary and surface properties, notably texture and brightness properties. This vector inputs to a system that incrementally learns noisy multidimensional mappings and their probabilities. The architecture is applied to difficult real-world image classification problems, including classification of synthetic aperture radar and natural texture images, and outperforms a recent state-of-the-art system at classifying natural texturns.Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-91-J-4100); Advanced Research Projects Agency (N00014-92-J-4015); Air Force Office of Scientific Research (F49620-92-J-0225, F49620-92-J-0334); National Science Foundation (IRI-90-00530, IRI-90-24877