UC Santa Barbara

The focus of this dissertation is the enhancement of prediction and quantization algorithms within the framework of the video-based point cloud compression (V-PCC) standard. The first line of research explores a transform domain prediction strategy specifically tailored for geometry video compression. Standard video codecs rely on simple pixel-copy operations after motion estimation. However, the presence of large homogeneous regions in geometry videos renders this existing prediction strategy sub-optimal. We overcome this limitation by shifting to a transform domain temporal prediction framework, that accounts for spatial as well as temporal block correlations. First, spatial decorrelation is largely achieved by applying the Discrete Cosine Transform (DCT) to source and reference blocks. Subsequently, we employ data-driven temporal correlation filters to predict each transform coefficient of a source block using the corresponding transform coefficient of the best-matching reconstructed reference block. While spatial domain temporal correlations along a motion trajectory appear close to one, true temporal correlations emerge in the frequency domain. Specifically, low frequency components remain highly correlated, whereas high frequency components exhibit significantly lower temporal correlation. This frequency-dependent temporal correlation variation is precisely captured by the trained correlation filters to yield improved predictions. Designing correlation filters is a challenging task due to the complex interdependence between predictions and reconstructions in a video coding system. This issue is addressed using the iterative asymptotic closed-loop (ACL) design paradigm. By fixing the reconstructions across design iterations within the ACL framework, the correlation filters are applied to the exact data statistics used during their optimization. This prevents statistical mismatch between filter design and application, thus ensuring a stable design procedure. The second line of research investigates prediction residual coding in V-PCC. Because V-PCC employs patch-based projection methods to generate geometry and attribute videos, the resulting frames contain large empty regions filled with unoccupied pixels that do not impact the quality of the reconstructed point cloud. While the transmitted binary occupancy map explicitly distinguishes occupied and unoccupied pixels, standard video codecs employing frequency domain transforms are unable to incorporate the spatial domain occupancy information during rate-distortion optimization (RDO). To achieve occupancy-aware compression, we propose an entropy-constrained vector quantization (ECVQ) based methodology as a powerful coding tool. By training an ECVQ based on an occupancy-switched distortion measure - an error metric that ignores the reconstruction quality of the unoccupied pixels - we can make occupancy-aware RD decisions during encoding. Furthermore, because conventional transforms followed by scalar quantization can be mathematically interpreted as a special case of VQ partitioning, our approach theoretically guarantees superior performance. By embedding the design of the proposed occupancy-aware ECVQ within the ACL framework, we ensure a stable system design and establish ECVQ as a highly competitive compression strategy. Finally, to mitigate the issues of exponential growth of codebook size and search complexity that occurs when applying ECVQ to high dimensional residual blocks, we demonstrate the efficacy of entropy-constrained multistage vector quantization (EC-MSVQ). Although this structural constraint introduces a modest drop in RD performance, it achieves significantly lower search and storage complexity. Substantial bitrate savings over the anchor codec illustrate the efficacy of the proposed methods.