We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes. The RA-GFT is a multiresolution transform, formed by combining spatially localized block transforms. We assume the points are organized by a family of nested partitions represented by a rooted tree. At each resolution level, attributes are processed in clusters using 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. For this, we introduce the $\mathbf{Q}$-normalized graph Laplacian, and propose using its eigenvectors as the block transform. The RA-GFT achieves better complexity-performance trade-offs than previous approaches. In particular, it outperforms the Region Adaptive Haar Transform (RAHT) by up to 2.5 dB, with a small complexity overhead.

中文翻译：

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3d 点云的区域自适应图傅立叶变换

我们引入了区域自适应图傅立叶变换 (RA-GFT) 来压缩 3D 点云属性。RA-GFT 是一种多分辨率变换，由空间局部化块变换组合而成。我们假设这些点是由一棵有根树表示的一系列嵌套分区组织的。在每个分辨率级别，使用块变换在集群中处理属性。每个块变换产生单个近似 (DC) 系数和各种细节 (AC) 系数。DC 系数在树上向上提升到下一个（较低分辨率）级别，在那里可以重复该过程直到到达根。由于簇可能具有不同数量的点，因此每个块变换必须包含每个系数的相对重要性。为此，我们引入了 $\mathbf{Q}$-normalized graph Laplacian，并建议使用其特征向量作为块变换。RA-GFT 比以前的方法实现了更好的复杂性-性能权衡。特别是，它比区域自适应 Haar 变换 (RAHT) 高 2.5 dB，复杂度开销很小。