DISK: Differentiable Sparse Kernel Complex for Efficient Spatially-Variant Convolution
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| Format: | Preprint |
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2025
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| _version_ | 1866911695395356672 |
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| author | Wu, Zhizhen Cao, Zhe Huo, Yuchi |
| author_facet | Wu, Zhizhen Cao, Zhe Huo, Yuchi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_04556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DISK: Differentiable Sparse Kernel Complex for Efficient Spatially-Variant Convolution Wu, Zhizhen Cao, Zhe Huo, Yuchi Graphics Computer Vision and Pattern Recognition 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. |
| title | DISK: Differentiable Sparse Kernel Complex for Efficient Spatially-Variant Convolution |
| topic | Graphics Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2512.04556 |