Statistical modeling of 3-D natural scenes with application to Bayesian stereopsis

We studied the empirical distributions of luminance, range and disparity wavelet coefficients using a coregistered database of luminance and range images. The marginal distributions of range and disparity are observed to have high peaks and heavy tails, similar to the well-known properties of luminance wavelet coefficients. However, we found that the kurtosis of range and disparity coefficients is significantly larger than that of luminance coefficients. We used generalized Gaussian models to fit the empirical marginal distributions. We found that the marginal distribution of luminance coefficients have a shape parameter p between 0.6 and 0.8, while range and disparity coefficients have much smaller parameters p < 0.32, corresponding to a much higher peak. We also examined the conditional distributions of luminance, range and disparity coefficients. The magnitudes of luminance and range (disparity) coefficients show a clear positive correlation, which means, at a location with larger luminance variation, there is a higher probability of a larger range (disparity) variation. We also used generalized Gaussians to model the conditional distributions of luminance and range (disparity) coefficients. The values of the two shape parameters (p,s) reflect the observed luminance-range (disparity) dependency. As an example of the usefulness of luminance statistics conditioned on range statistics, we modified a well-known Bayesian stereo ranging algorithm using our natural scene statistics models, which improved its performance.