FKAConv: Feature-Kernel Alignment for Point Cloud Convolution

Recent state-of-the-art methods for point cloud processing are based on the notion of point convolution, for which several approaches have been proposed. In this paper, inspired by discrete convolution in image processing, we provide a formulation to relate and analyze a number of point convolution methods. We also propose our own convolution variant, that separates the estimation of geometry-less kernel weights and their alignment to the spatial support of features. Additionally, we define a point sampling strategy for convolution that is both effective and fast. Finally, using our convolution and sampling strategy, we show competitive results on classification and semantic segmentation benchmarks while being time and memory efficient.