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We study the problem of sparse signal detection on a spatial domain. We propose a novel approach to model continuous signals that are sparse and piecewise-smooth as the product of independent Gaussian (PING) processes with a smooth covariance kernel. The smoothness of the PING process is ensured by the smoothness of the covariance kernels of the Gaussian components in the product, and sparsity is controlled by the number of components. The bivariate kurtosis of the PING process implies that more components in the product results in the thicker tail and sharper peak at zero. We develop an efficient computation algorithm based on spectral methods. The simulation results demonstrate superior estimation using the PING prior over Gaussian process prior for different image regressions. We apply our method to a longitudinal magnetic resonance imaging dataset to detect the regions that are affected by multiple sclerosis computation in this domain. Supplementary materials for this article are available online.
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PhysGaussian: Physics-Integrated 3D Gaussians for Generative Dynamics
We introduce PhysGaussian a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a customized Material Point Method (MPM) our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing marching cubes cage meshes or any other geometry embedding highlighting the principle of "what you see is what you simulate (WS^2)". Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities plastic metals non-Newtonian fluids and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements.
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- PAR ID:
- 10535780
- Publisher / Repository:
- Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2024, pp. 4389-4398
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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