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• Introduction of Riemannian global illumination. • A path tracer algorithm to approximate the solution of the Riemannian global illumination. • A map of the algorithm to the GPU, using the RTX platform. • We apply the Non-Euclidean path tracer to render "Photorealistic" inside views of the 3D flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of the Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries. This paper presents a novel path tracer algorithm for immersive visualization of Riemannian manifolds. To do this, we introduce Riemannian illumination, a generalization of classical Computer Graphics illumination models. In this context, global light transport is expressed by extending the rendering equation to Riemannian manifolds. Using Monte Carlo integration to solve this equation results in the novel path tracer for Non-Euclidean spaces. We discuss its basic principles, as well as the general CPU algorithm. Additionally, we discuss in detail how to implement a GPU version, using the RTX pipeline. Finally, we apply the algorithm to render "photorealistic" inside views of the flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries. [ABSTRACT FROM AUTHOR]

Video segmentation is an important preprocessing step for many computer vision and graphics tasks. Its main goal is to group the voxels in the video volume with similar appearance and motion into spatio-temporally consistent supervoxels. In this paper, we formulate video segmentation as an L 0 gradient minimization problem, so that the spatio-temporal coherence can be effectively enforced through a gradient sparsity pursuit way. In our method, the appearance and motion descriptor space is first built for over-segmented image patches of each video frame. Then the L 0 gradient minimization is performed in the descriptor space, for both spatial and temporal dimensions. To solve the non-convex L 0 norm minimization problem, we extend the fused coordinate descent algorithm from 2D image grids to 3D video volume. We conduct quantitative evaluation of our method in a public video segmentation benchmark LIBSVX. The experimental results demonstrate our superior performance to state-of-the-arts in segmentation accuracy and undersegmentation error, and comparable performance in boundary recall and explained variation. [ABSTRACT FROM AUTHOR]