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Fast methods for convolution and correlation underlie a variety of applications in computer vision and graphics, including efficient filtering, analysis, and simulation. However, standard convolution and correlation are inherently limited to fixed filters: spatial adaptation is impossible without sacrificing efficient computation. In early work, Freeman and Adelson have shown how steerable filters can address this limitation, providing a way for rotating the filter as it is passed over the signal. In this work, we provide a general, representation-theoretic, framework that allows for spatially varying linear transformations to be applied to the filter. This framework allows for efficient implementation of extended convolution and correlation for transformation groups such as rotation (in 2D and 3D) and scale, and provides a new interpretation for previous methods including steerable filters and the generalized Hough transform. We present applications to pattern matching, image feature description, vector field visualization, and adaptive image filtering.
LiDAR point-cloud segmentation is an important problem for many applications. For large-scale point cloud segmentation, the textit{de facto} method is to project a 3D point cloud to get a 2D LiDAR image and use convolutions to process it. Despite the
Spatially-adaptive normalization (SPADE) is remarkably successful recently in conditional semantic image synthesis cite{park2019semantic}, which modulates the normalized activation with spatially-varying transformations learned from semantic layouts,
Convolutional neural networks (CNNs) have made great breakthroughs in 2D computer vision. However, the irregular structure of meshes makes it hard to exploit the power of CNNs directly. A subdivision surface provides a hierarchical multi-resolution s
As a variant of standard convolution, a dilated convolution can control effective receptive fields and handle large scale variance of objects without introducing additional computational costs. To fully explore the potential of dilated convolution, w
Most existing human pose estimation (HPE) methods exploit multi-scale information by fusing feature maps of four different spatial sizes, ie $1/4$, $1/8$, $1/16$, and $1/32$ of the input image. There are two drawbacks of this strategy: 1) feature map