Geometry-Aware Graph Transforms for Light Field Compact Representation

Mira Rizkallah, Xin Su, Thomas Maugey, Christine Guillemot

Abstract: This paper addresses the problem of energy compaction of dense 4D light fields by designing geometry-aware local graph-based transforms. Local graphs are constructed on super-rays that can be seen as a grouping of spatially and geometry-dependent angularly correlated pixels. Both non-separable and separable transforms are considered. Despite the local support of limited size defined by the super-rays, the Laplacian matrix of the non-separable graph remains of high dimension and its diagonalization to compute the transform eigenvectors remains computationally expensive. To solve this problem, we then perform the local spatio-angular transform in a separable manner. We show that when the shape of corresponding super-pixels in the different views is not isometric, the basis functions of the spatial transforms are not coherent, resulting in a decreased correlation between spatial transform coefficients. We hence propose a novel transform optimization method that aims at preserving angular correlation even when the shapes of the super-pixels are not isometric. Experimental results show the benefit of the approach in terms of energy compaction. A coding scheme is also described to assess the rate-distortion performances of the proposed transforms and is compared to several state-of-the-art encoders.