Abstract
The statistical properties of image formation in the natural environment have been an important driving force of the evolution of biological vision systems. Luminance features in natural scenes have been studied extensively in recent years. In fact, the bandwidths, orientation tuning, and shapes of receptive fields are closely related to the spatial and spectral properties of natural luminance distributions. With recent advances and products based on light detection and ranging (lidar) technology, researchers have also begun to make progress on understanding the statistical properties of three dimensional visual features. We studied distributions of luminance, disparity, and range gradient magnitudes using a co-registered database of luminance and range natural images. We found that the 2D (luminance) and 3D (disparity or range) edge distributions can be well modeled as one-sided generalized Gaussian distributions with varying shape parameters. Through a simple thresholding process, we found that the probability of observing a strong luminance edge at supra-threshold 3D discontinuities is about 3 times greater than that of observing homogeneous luminance. Conversely, the probability of a strong, perceivable 3D edge at supra-threshold luminance discontinuities is about 5 times greater than that at homogeneous luminance regions. Interestingly, we also have observed a monotonic relationship between 3D gradient magnitudes and luminance gradient magnitudes at supra-threshold luminance discontinuities, suggesting that monocular luminance information may play a role in depth perception. However, we did not observe a clear dependency between the strength of luminance edges and the strength of 3D edges at supra-threshold 3D discontinuities. We applied the statistical relationship between luminance gradient magnitudes and disparity gradient magnitudes in a Bayesian model of stereopsis. Direct comparison of the model's performance with and without the 2D-3D gradient dependency directly demonstrates the benefit of using these statistical relationships in recovering the 3D structure of the environment from 2D image data.