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Che-Chun Su, Lawrence Cormack, Alan Bovik; Bivariate Statistics and Correlations in Natural Images. Journal of Vision 2014;14(10):651. doi: 10.1167/14.10.651.
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Modeling natural scene statistics and understanding the human vision system have come to be regarded as a dual problem. Great successes have been achieved in the image/video processing and computer vision fields by applying natural scene statistical models to develop perceptually relevant and effective algorithms. However, most natural scene statistical models are characterized only by univariate distributions, while higher-order dependencies between spatially adjacent pixels in natural images are not well-understood or utilized yet. To perform robust bivariate statistical modeling of natural images, we exploited the LIVE Color+3D Database Release-2, which contains 99 pairs of stereoscopic left and right color images with precisely co-registered corresponding ground-truth range maps at a high-definition resolution of 1920x1080. All of the color images were first transformed into the perceptually relevant CIELAB color space. Next, the color images and their corresponding range maps were both subjected to a steerable pyramid wavelet decomposition followed by a divisive normalization using the energies of neighboring coefficients. We examined the statistical relationships between spatially adjacent coefficients over multiple scales and orientations, and modeled the corresponding joint histograms using a bivariate generalized Gaussian distribution (BGGD) augmented by a new correlation model explicitly represented by an exponentiated sine function. To demonstrate the effectiveness of the enhanced BGGD and exponentiated sine correlation models, we applied them to solve a practical problem of depth estimation from monocular natural images. By introducing additional features based on the proposed bivariate statistical models, we boosted the performance of a Bayesian depth estimation framework to achieve better than state-of-the-art performance. We believe that the new bivariate correlation model embeds rich information relating the luminance/chrominance and range information projected from and contained in natural environments. Furthermore, a wide variety of 3D algorithms and applications, e.g., stereoscopic quality assessment, 2D-to-3D video conversion, etc., are to likely benefit from these robust and effective new bivariate statistical models.
Meeting abstract presented at VSS 2014
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