Faculty Bibliography

We develop a probability model for natural images, based on empirical observation of their statistics in the wavelet transform domain. Pairs of wavelet coefficients, corresponding to basis functions at adjacent spatial locations, orientations, and scales, are found to be non-Gaussian in both their marginal and joint statistical properties. Specifically, their marginals are heavy-tailed, and although they are typically decorrelated, their magnitudes are highly correlated. We propose a Markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties, and show that it accounts for the statistics of a wide variety of images including photographic images, graphical images, and medical images. In order to directly demonstrate the power of the model, we construct an image coder called EPWIC (embedded predictive wavelet image coder), in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model. Bitplanes are ordered using a greedy algorithm that considers the MSE reduction per encoded bit. The decoder uses the statistical model to predict coefficient values based on the bits it has received. Despite the simplicity of the model, the rate-distortion performance of the coder is roughly comparable to the best image coders in the literature

Adaptation to a moving visual pattern induces shifts in the perceived motion of subsequently viewed moving patterns. Explanations of such effects are typically based on adaptation-induced sensitivity changes in spatio-temporal frequency tuned mechanisms (STFMs). An alternative hypothesis is that adaptation occurs in mechanisms that independently encode direction and speed (DSMs). Yet a third possibility is that adaptation occurs in mechanisms that encode 2D pattern velocity (VMs). We performed a series of psychophysical experiments to examine predictions made by each of the three hypotheses. The results indicate that: (1) adaptation-induced shifts are relatively independent of spatial pattern of both adapting and test stimuli; (2) the shift in perceived direction of motion of a plaid stimulus after adaptation to a grating indicates a shift in the motion of the plaid pattern, and not a shift in the motion of the plaid components; and (3) the 2D pattern of shift in perceived velocity radiates away from the adaptation velocity, and is inseparable in speed and direction of motion. Taken together, these results are most consistent with the VM adaptation hypothesis

We describe a novel formulation of the range recovery problem based on computation of the differential variation in image intensities with respect to changes in camera position. This method uses a single stationary camera and a pair of calibrated optical masks to measure this differential quantity directly. We also describe a variant based on changes in aperture size. The subsequent computation of the range image involves simple arithmetic operations and is suitable for real-time implementation. We present the theory of this technique and show results from a prototype camera that we have constructed