Unlike images which are represented in regular dense grids, 3D point clouds are irregular and unordered, hence applying convolution on them can be difficult. In this paper, we extend the dynamic filter to a new convolution operation, named PointConv. PointConv can be applied on point clouds to build deep convolutional networks. We treat convolution kernels as nonlinear functions of the local coordinates of 3D points comprised of weight and density functions. With respect to a given point, the weight functions are learned with multi-layer perceptron networks and density functions through kernel density estimation. The most important contribution of this work is a novel reformulation proposed for efficiently computing the weight functions, which allowed us to dramatically scale up the network and significantly improve its performance. The learned convolution kernel can be used to compute translation-invariant and permutation-invariant convolution on any point set in the 3D space. Besides, PointConv can also be used as deconvolution operators to propagate features from a subsampled point cloud back to its original resolution. Experiments on ModelNet40, ShapeNet, and ScanNet show that deep convolutional neural networks built on PointConv are able to achieve state-of-the-art on challenging semantic segmentation benchmarks on 3D point clouds. Besides, our experiments converting CIFAR-10 into a point cloud showed that networks built on PointConv can match the performance of convolutional networks in 2D images of a similar structure.

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We propose an unsupervised video segmentation approach by simultaneously tracking multiple holistic figureground segments. Segment tracks are initialized from a pool of segment proposals generated from a figure-ground segmentation algorithm. Then, online non-local appearance models are trained incrementally for each track using a multi-output regularized least squares formulation. By using the same set of training examples for all segment tracks, a computational trick allows us to track hundreds of segment tracks efficiently, as well as perform optimal online updates in closed-form. Besides, a new composite statistical inference approach is proposed for refining the obtained segment tracks, which breaks down the initial segment proposals and recombines for better ones by utilizing highorder statistic estimates from the appearance model and enforcing temporal consistency. For evaluating the algorithm, a dataset, SegTrack v2, is collected with about 1,000 frames with pixel-level annotations. The proposed framework outperforms state-of-the-art approaches in the dataset, showing its efficiency and robustness to challenges in different video sequences.

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