{"ID":2832878,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.04556","arxiv_id":"2512.04556","title":"DISK: Differentiable Sparse Kernel Complex for Efficient Spatially-Variant Convolution","abstract":"Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations, such as simulated annealing or low-rank decompositions, either lack efficiency or fail to capture non-convex kernels. We introduce a differentiable kernel decomposition framework that represents a target spatially-variant, dense, complex kernel using a set of sparse kernel samples. Our approach features (i) a decomposition that enables differentiable optimization of sparse kernels, (ii) a dedicated initialization strategy for non-convex shapes to avoid poor local minima, and (iii) a kernel-space interpolation scheme that extends single-kernel filtering to spatially varying filtering without retraining and additional runtime overhead. Experiments on Gaussian and non-convex kernels show that our method achieves higher fidelity than simulated annealing and significantly lower cost than low-rank decompositions. Our approach provides a practical solution for mobile imaging and real-time rendering, while remaining fully differentiable for integration into broader learning pipelines.","short_abstract":"Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations, such as simulated annealing or low-rank decompositions, either lack efficiency or...","url_abs":"https://arxiv.org/abs/2512.04556","url_pdf":"https://arxiv.org/pdf/2512.04556v3","authors":"[\"Zhizhen Wu\",\"Zhe Cao\",\"Yuchi Huo\"]","published":"2025-12-04T08:20:07Z","proceeding":"cs.GR","tasks":"[\"cs.GR\",\"cs.CV\"]","methods":"[]","has_code":false}