Deep learning models have greatly improved the accuracy of point cloud classification. Nevertheless, existing deep learning models are vulnerable to data corruptions such as Gaussian noise and outliers which are inevitable in real-world point cloud collection. To address this challenge, we develop a novel point cloud classification model that is robust to data corruptions, with permutohedral lattice-based representation and density-improved hierarchical feature extraction. Specifically, raw noisy point clouds are firstly projected into a regular per-mutohedral lattice space to obtain the quantized representations. Subsequently, we propose to leverage the local density to improve the farthest point sampling (FPS) and spectral graph convolution for robust hierarchical feature extraction, inspired by that the local point density implicitly reveals the reliability and semantic information of each point. The local density can be efficiently calculated from the permutohedral lattice-based representation. Extensive experiments on the benchmark dataset (i.e., ModelNet-C) verify the robustness of the proposed model. In comparison to the state-of-the-art methods, the proposed model achieves superior performance on the corrupted dataset while maintaining competitive classification accuracy on the clean dataset.

Entropy modeling plays an important role in estimating the rates of latent representations and optimizing the rate-distortion performance for learned image compression. Autoregression modules are demonstrated to eliminate spatial/channel-wise redundancy of latent representations in fixed-rate learned image compression. However, it cannot be efficiently achieved in progressive coding due to the high computational complexity raised by element-wise probability prediction. In this paper, we propose a learned progressive image compression method that enables spatial autoregression for entropy modeling. Specifically, we develop a novel codeword alignment scheme to prevent coding redundancy and achieve efficient autoregression of latent representations in different quality layers. Consequently, conditional probability estimation for the latent prediction can be achieved based on spatial autoregression in a layer-wise manner. We further extend the proposed method by dead-zone quantizers to obtain promoted rate-distortion performance. The proposed method is a successful attempt to enable spatial autoregression in learned progressive coding and further bridge the performance gap with fixed-rate models. Experimental results show that it outperforms traditional methods such as JPEG and BPG, as well as recent fine-grained learned progressive coding models DPICT and PLONQ in terms of rate-distortion performance.

A graph is called supereulerian if it has a spanning eulerian subgraph. A graph is said to be hamiltonian if it has a spanning cycle. A nontrivial path is called a branch if it has only internal vertices of degree two and end vertices of degree not two. Let S be a set of branches of G, then S is called a branch cut if G−S has more components than G. A minimal branch cut is called a branch-bond. In this paper, we characterize one or pairs of those forbidden subgraphs that force a 2-edge-connected graph satisfying that every odd branch-bond has an edge branch to be supereulerian. We also characterize one or pairs of those forbidden subgraphs that force a 2-connected supereulerian graph to be hamiltonian.