Google Research

Region Adaptive Graph Fourier Transform for 3D Point Clouds

  • Antonio Ortega
  • Benjamin Girault
  • Eduardo H Pavez Carvelli
  • Phil Chou
International Conference on Image Processing (ICIP), IEEE (2020)


We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes. We assume the points are organized by a family of nested partitions represented by a tree. The RA-GFT is a multiresolution transform, formed by combining spatially localized block transforms. At each resolution level attributes are processed in clusters by a set of block transforms. Each block transform produces a single approximation (DC) coefficient, and various detail (AC) coefficients. The DC coefficients are promoted up the tree to the next (lower resolution) level, where the process can be repeated until reaching the root. Since clusters may have a different numbers of points, each block transform must incorporate the relative importance of each coefficient, as well as their local geometry relations. For this, we introduce the Q-normalized graph Laplacian, and propose using its eigenvectors as the block transform. The RA-GFT outperforms the Region Adaptive Haar Transform (RAHT) by up to 2.5 dB, with a small complexity overhead.

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