# Geometry-Aware Graph Transforms for Light Field Compact Representation

## TL;DR

This paper introduces geometry-aware local graph transforms for 4D light fields, optimizing energy compaction and correlation preservation through a novel transform method, and demonstrates improved rate-distortion performance over existing codecs.

## Contribution

It proposes a new geometry-aware transform optimization method for non-isometric super-pixels, enhancing energy compaction in light field compression.

## Key findings

- Improved energy compaction with the proposed transforms.
- Enhanced correlation preservation for non-isometric super-pixels.
- Better rate-distortion performance compared to HEVC and JPEG Pleno VM 1.1.

## Abstract

The 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 eigen vectors 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 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 perfomances of the proposed transforms and is compared to state of the art encoders namely HEVC and JPEG Pleno VM 1.1.