The problem of automatically classifying sensed imagery such as synthetic aperture radar (SAR) into a canonical set of target classes is widely known as automatic target recognition (ATR). A typical ATR algorithm comprises the extraction of a meaningful set of features from target imagery followed by a decision engine that performs class assignment. While ATR algorithms have significantly increased in sophistication over the past two decades, two outstanding challenges have been identified in the rich body of ATR literature: 1) the desire to mine complementary merits of distinct feature sets (also known as feature fusion), and 2) the ability of the classifier to excel even as training SAR images are limited. We propose to apply recent advances in probabilistic graphical models to address these challenges. In particular we develop a two-stage target recognition framework that combines the merits of distinct SAR image feature representations with discriminatively learned graphical models. The first stage projects the SAR image chip to informative feature spaces that yield multiple complementary SAR image representations. The second stage models each individual representation using graphs and combines these initially disjoint and simple graphs into a thicker probabilistic graphical model by leveraging a recent advance in discriminative graph learning. Experimental results on the benchmark moving and stationary target acquisition and recognition (MSTAR) data set confirm the benefits of our framework over existing ATR algorithms in terms of improvement in recognition rates. The proposed graphical classifiers Manuscript are particularly robust when feature dimensionality is high and number of training images is small, a commonly observed constraint in SAR imagery-based target recognition.

The human visual system combines a wide field of view with a high-resolution fovea and uses eye, head, and body movements to direct the fovea to potentially relevant locations in the visual scene. This strategy is sensible for a visual system with limited neural resources. However, for this strategy to be effective, the visual system needs sophisticated central mechanisms that efficiently exploit the varying spatial resolution of the retina. To gain insight into some of the design requirements of these central mechanisms, we have analyzed the effects of variable spatial resolution on local contrast in 300 calibrated natural images. Specifically, for each retinal eccentricity (which produces a certain effective level of blur), and for each value of local contrast observed at that eccentricity, we measured the probability distribution of the local contrast in the unblurred image. These conditional probability distributions can be regarded as posterior probability distributions for the "true" unblurred contrast, given an observed contrast at a given eccentricity. We find that these conditional probability distributions are adequately described by a few simple formulas. To explore how these statistics might be exploited by central perceptual mechanisms, we consider the task of selecting successive fixation points, where the goal on each fixation is to maximize total contrast information gained about the image (i.e., minimize total contrast uncertainty). We derive an entropy minimization algorithm and find that it performs optimally at reducing total contrast uncertainty and that it also works well at reducing the mean squared error between the original image and the image reconstructed from the multiple fixations. Our results show that measurements of local contrast alone could efficiently drive the scan paths of the eye when the goal is to gain as much information about the spatial structure of a scene as possible.

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