We propose a complete system to enable progressive coding with quality scalability of the mesh geometry, in MPEG's state-of-the-art Video-based Dynamic Mesh Coding (V-DMC) framework. In particular, we propose an alternative method for encoding the subdivision wavelet coefficients in V-DMC, using a zerotree coding approach that works directly in the native 3D mesh space. This allows us to identify parent-child relationships amongst the wavelet coefficients across different subdivision levels, which can be used to achieve an efficient and versatile coding mechanism. We demonstrate that, given a starting base mesh, a target subdivision surface and a desired maximum number of zerotree passes, our system produces an elegant and visually attractive lossy-to-lossless mesh geometry reconstruction with no further user intervention. Moreover, lossless coefficient encoding with our approach requires nearly the same bitrate as the default displacement coding methods in V-DMC. Yet, our approach provides several quality resolution levels embedded in the same bitstream, while the current V-DMC solutions encode a single quality level only. To the best of our knowledge, this is the first time that a zerotree-based method has been proposed and demonstrated to work for the compression of dynamic time-varying meshes, and the first time that an embedded quality-scalable approach has been used in the V-DMC framework.

This paper addresses the problem of compressing the colour attributes of dynamic dense point clouds. Inter-frame prediction and motion compensation are key to removing temporal redundancies and thereby reaching major compression gains. For that purpose, an attribute compression scheme combining intra-frame and motion-compensated inter-frame predictions is presented. It is built upon the Test Model developed by MPEG within the Geometry-based Point Cloud Compression (G-PCC) activity to encode dense dynamic point clouds. More precisely, a motion-compensated inter-frame prediction is introduced into the RAHT encoding scheme, leveraging the local motion field already present in the geometry encoder. The best prediction mode according to rate-distortion optimization is decided at each node of the octree, encoded by means of arithmetic coding using a binary prediction tree and signalled to the decoder. Experimental results are provided using the MPEG test sequences and common test conditions. They demonstrate very significant compression gains, with average BD-Rates of −15.2%, −18.3% and −18.1 % on Y, Cb and Cr colour components respectively, when compared with the current scheme with intra-frame only attribute compression.

In this paper, we introduce a novel 6-D representation of plenoptic point clouds, enabling joint, non-separable transform coding of plenoptic signals defined along both spatial and angular (viewpoint) dimensions. This 6-D representation, which is built in a global coordinate system, can be used in both multi-camera studio capture and video fly-by capture scenarios, with various viewpoint (camera) arrangements and densities. We show that both the Region-Adaptive Hierarchical Transform (RAHT) and the Graph Fourier Transform (GFT) can be extended to the proposed 6-D representation to enable the non-separable transform coding. Our method is applicable to plenoptic data with either dense or sparse sets of viewpoints, and tocompleteorincompleteplenoptic data, while the state-of-the-art RAHT-KLT method, which is separable in spatial and angular dimensions, is applicable only tocompleteplenoptic data. The “complete” plenoptic data refers to data that has, for each spatial point, one colour for every viewpoint (ignoring any occlusions), while “incomplete” data has colours only for thevisiblesurface points at each viewpoint. We demonstrate that the proposed 6-D RAHT and 6-D GFT compression methods are able to outperform the state-of-the-art RAHT-KLT method on 3-D objects with various levels of surface specularity, and captured with different camera arrangements and different degrees of viewpoint sparsity.

The recently introduced plenoptic point cloud representation marries a 3D point cloud with a light field. Instead of each point being associated with a single colour value, there can be multiple values to represent the colour at that point as perceived from different viewpoints. This representation was introduced together with a compression technique for the multi-view colour vectors, which is an extension of the RAHT method for point cloud attribute coding. In the current paper, we demonstrate that the best-proposed RAHT extension, RAHT-KLT, can be improved by performing a prior subdivision of the plenoptic point cloud into clusters based on similar colour values, followed by a separation of each cluster into specular and diffuse components, and coding each component separately with RAHT-KLT. Our proposed improvements are shown to achieve better rate-distortion results than the original RAHT-KLT method.

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are functions defined not just on a finite set of points, but throughout space. As in regression analysis, volumetric functions are continuous functions that are able to interpolate values on a finite set of points as linear combinations of continuous basis functions. Using a B-spline wavelet basis, we are able to code volumetric functions representing both geometry and attributes. Geometry compression is addressed in Part II of this paper, while attribute compression is addressed in Part I. Attributes are represented by a volumetric function whose coefficients can be regarded as a critically sampled orthonormal transform that generalizes the recent successful region-adaptive hierarchical (or Haar) transform to higher orders. Experimental results show that attribute compression using higher order volumetric functions is an improvement over the first order functions used in the emerging MPEG Point Cloud Compression standard.

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are functions defined not just on a finite set of points, but throughout space. As in regression analysis, volumetric functions are continuous functions that are able to interpolate values on a finite set of points as linear combinations of continuous basis functions. Using a B-spline wavelet basis, we are able to code volumetric functions representing both geometry and attributes. Attribute compression is addressed in Part I of this paper, while geometry compression is addressed in Part II. Geometry is represented implicitly as the level set of a volumetric function (the signed distance function or similar). Experimental results show that geometry compression using volumetric functions improves over the methods used in the emerging MPEG Point Cloud Compression (G-PCC) standard.

A recently-introduced coder based on region-adaptive hierarchical transform (RAHT) is being considered as a standard for the compression of point cloud attributes at moving picture experts group. The RAHT coefficients can be encoded in many ways and the transform is based on a series of orthogonal 2 × 2 transform matrices with geometry-dependent floating-point entries. In order to remove computation ambiguity and facilitate deployment, fixed-point operations are often preferred. In this letter, we present an alternative RAHT description that allows for fixed-point implementation of its transform steps. It is based on matrix decompositions akin to lifting steps and a scaling of the quantization steps. Results are presented to show that the new fixed-point transform is, in practical terms, equivalent to the floating-point RAHT. For that we use a reasonable number of precision bits for the integer operations, e.g. 8 b or more.

For applications such as virtual reality and mobile mapping, point clouds are an effective means for representing 3-D environments. The need for compressing such data is rapidly increasing, given the widespread use and precision of these systems. This paper presents a method for compressing organized point clouds. 3-D point cloud data is mapped to a 2-D organizational grid, where each element on the grid is associated with a point in 3-D space and its corresponding attributes. The data on the 2-D grid is hierarchically partitioned, and a Bezier patch is fit to the 3-D coordinates associated with each partition. Residual values are quantized and signaled along with data necessary to reconstruct the patch hierarchy in the decoder. We show how this method can be used to process point clouds captured by a mobile-mapping system, in which laser-scanned point locations are organized and compressed. The performance of the patch-fitting codec exceeds or is comparable to that of an octree-based codec.