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Oct 22

An Efficient Multilevel Preconditioned Nonlinear Conjugate Gradient Method for Incremental Potential Contact

Incremental Potential Contact (IPC) guarantees intersection-free simulation but suffers from high computational costs due to the expensive Hessian assembly and linear solves required by Newton's method. While Preconditioned Nonlinear Conjugate Gradient (PNCG) avoids Hessian assembly, it has historically struggled with poor convergence in stiff, contact-rich scenarios due to the lack of effective preconditioners; simple Jacobi preconditioners fail to capture the global coupling, while advanced hierarchy-based preconditioners like Multilevel Additive Schwarz (MAS) are computationally prohibitive to rebuild at every nonlinear iteration. We present MAS-PNCG, a method that unlocks the power of hierarchical preconditioning for nonlinear optimization. Our key technical innovation is a Sparse-Input Woodbury update algorithm that incrementally adapts the fine-level MAS components to rapidly evolving contact sets. This bypasses the need for full preconditioner rebuilds, reducing maintenance cost to near-zero while capturing the complex spectral properties of the contact system. Furthermore, we replace heuristic PNCG search directions with a Hessian-aware 2D subspace minimization that optimally combines the preconditioned gradient and previous direction. We also apply a fast per-subdomain conservative CCD method that ensures penetration-free trajectories while avoiding overly restrictive global step sizes. Experiments demonstrate that our MAS-PNCG outperforms state-of-the-art Newton-PCG solvers, GIPC and StiffGIPC, both preconditioned with MAS up to 5.66times and 2.07times respectively.

  • 8 authors
·
Apr 20

CIE XYZ Net: Unprocessing Images for Low-Level Computer Vision Tasks

Cameras currently allow access to two image states: (i) a minimally processed linear raw-RGB image state (i.e., raw sensor data) or (ii) a highly-processed nonlinear image state (e.g., sRGB). There are many computer vision tasks that work best with a linear image state, such as image deblurring and image dehazing. Unfortunately, the vast majority of images are saved in the nonlinear image state. Because of this, a number of methods have been proposed to "unprocess" nonlinear images back to a raw-RGB state. However, existing unprocessing methods have a drawback because raw-RGB images are sensor-specific. As a result, it is necessary to know which camera produced the sRGB output and use a method or network tailored for that sensor to properly unprocess it. This paper addresses this limitation by exploiting another camera image state that is not available as an output, but it is available inside the camera pipeline. In particular, cameras apply a colorimetric conversion step to convert the raw-RGB image to a device-independent space based on the CIE XYZ color space before they apply the nonlinear photo-finishing. Leveraging this canonical image state, we propose a deep learning framework, CIE XYZ Net, that can unprocess a nonlinear image back to the canonical CIE XYZ image. This image can then be processed by any low-level computer vision operator and re-rendered back to the nonlinear image. We demonstrate the usefulness of the CIE XYZ Net on several low-level vision tasks and show significant gains that can be obtained by this processing framework. Code and dataset are publicly available at https://github.com/mahmoudnafifi/CIE_XYZ_NET.

  • 5 authors
·
Jun 22, 2020 1