We propose using the statistical measurement of the sample skewness of the distribution of mean firing rates of a tuning curve to quantify sharpness of tuning. For some features, like binocular disparity, tuning curves are best described by relatively complex and sometimes diverse functions, making it difficult to quantify sharpness with a single function and parameter. Skewness provides a robust nonparametric measure of tuning curve sharpness that is invariant with respect to the mean and variance of the tuning curve and is straightforward to apply to a wide range of tuning, including simple orientation tuning curves and complex object tuning curves that often cannot even be described parametrically. Because skewness does not depend on a specific model or function of tuning, it is especially appealing to cases of sharpening where recurrent interactions among neurons produce sharper tuning curves that deviate in a complex manner from the feedforward function of tuning. Since tuning curves for all neurons are not typically well described by a single parametric function, this model independence additionally allows skewness to be applied to all recorded neurons, maximizing the statistical power of a set of data. We also compare skewness with other nonparametric measures of tuning curve sharpness and selectivity. Compared to these other nonparametric measures tested, skewness is best used for capturing the sharpness of multimodal tuning curves defined by narrow peaks (maximum) and broad valleys (minima). Finally, we provide a more formal definition of sharpness using a shape-based information gain measure and derive and show that skewness is correlated with this definition.

For problems over continuous random variables, MRFs with large cliques pose a challenge in probabilistic inference. Difficulties in performing optimization efficiently have limited the probabilistic models explored in computer vision and other fields. One inference technique that handles large cliques well is Expectation Propagation. EP offers run times independent of clique size, which instead depend only on the rank, or intrinsic dimensionality, of potentials. This property would be highly advantageous in computer vision. Unfortunately, for grid-shaped models common in vision, traditional Gaussian EP requires quadratic space and cubic time in the number of pixels. Here, we propose a variation of EP that exploits regularities in natural scene statistics to achieve run times that are linear in both number of pixels and clique size. We test these methods on shape from shading, and we demonstrate strong performance not only for Lambertian surfaces, but also on arbitrary surface reflectance and lighting arrangements, which requires highly non-Gaussian potentials. Finally, we use large, non-local cliques to exploit cast shadow, which is traditionally ignored in shape from shading.

The success of automated classification hinges on the choice of the representation of the data. Much research has focused on feature extraction techniques that can identify highly informative representations of a dataset. In this paper, we adapt for the purposes of classification a hierarchical Bayesian model developed by Karklin and Lewicki to model the neurophysiological properties of the cortex. The hierarchical nature of the cortex enables it to capture successively abstract and nonlinear features within its stimulus. We show empirically that the properties of natural images that motivated this model are also present in non-homogenous data typical of classification tasks. We also propose a discriminative training method for the model that enables it to preferentially select features that best distinguish the output class labels. Finally, the performance of the model was tested on handwritten digit recognition and face recognition. We found that classification using features extracted from the model achieved greater performance than classification using the nonlinear features of Kernel Fisher Discriminant analysis alone.

A major concern across the globe is the growing number of new chemicals that are brought to use on a regular basis without having any knowledge about their toxic behavior. The challenge here is that the growth in the number of chemicals is fast, and the traditional standards for toxicity testing involve a slow and expensive process of in vivo animal testing. Hence, a number of attempts are being made to find alternate methods of toxicity testing. In this paper we explore Bayesian classifiers and show that if we approximate posterior in the Bayesian classifier with specially crafted basis functions, we can improve upon the performance. We have tested our methods using data sets from the Environmental Protection Agency (EPA). Our experimental study demonstrated the utility of the advanced Bayesian classification approach.

Belief propagation over pairwise connected Markov random fields has become a widely used approach, and has been successfully applied to several important computer vision problems. However, pairwise interactions are often insufficient to capture the full statistics of the problem. Higher-order interactions are sometimes required. Unfortunately, the complexity of belief propagation is exponential in the size of the largest clique. In this paper, we introduce a new technique to compute belief propagation messages in time linear with respect to clique size for a large class of potential functions over real-valued variables. We demonstrate this technique in two applications. First, we perform efficient inference in graphical models where the spatial prior of natural images is captured by 2 times 2 cliques. This approach shows significant improvement over the commonly used pairwise-connected models, and may benefit a variety of applications using belief propagation to infer images or range images. Finally, we apply these techniques to shape-from-shading and demonstrate significant improvement over previous methods, both in quality and in flexibility.

Although there has been substantial progress in understanding the neuro- physiological mechanisms of stereopsis, how neurons interact in a network during stereo computation remains unclear. Computational models on stereopsis suggest local competition and long-range cooperation are impor- tant for resolving ambiguity during stereo matching. To test these predic- tions, we simultaneously recorded from multiple neurons in V1 of awake, behaving macaques while presenting surfaces of different depths rendered in dynamic random dot stereograms. We found that the interaction between pairs of neurons was a function of similarity in receptive fields, as well as of the input stimulus. Neurons coding the same depth experienced common inhibition early in their responses for stimuli presented at their non- preferred disparities. They experienced mutual facilitation later in their re- sponses for stimulation at their preferred disparity. These findings are con- sistent with a local competition mechanism that first removes gross mis- matches, and a global cooperative mechanism that further refines depth es- timates.

This paper explores the statistical relationship between natural images and their underlying range (depth) images. We look at how this relationship changes over scale, and how this information can be used to enhance low resolution range data using a full resolution intensity image. Based on our findings, we propose an extension to an existing technique known as shape recipes [3], and the success of the two methods are compared using images and laser scans of real scenes. Our extension is shown to provide a two-fold improvement over the current method. Furthermore, we demonstrate that ideal linear shape-from-shading filters, when learned from natural scenes, may derive even more strength from shadow cues than from the traditional linear-Lambertian shading cues.