{"ID":2857420,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.09125","arxiv_id":"2510.09125","title":"Polar Separable Transform for Efficient Orthogonal Rotation-Invariant Image Representation","abstract":"Orthogonal moment-based image representations are fundamental in computer vision, but classical methods suffer from high computational complexity and numerical instability at large orders. Zernike and pseudo-Zernike moments, for instance, require coupled radial-angular processing that precludes efficient factorization, resulting in $\\mathcal{O}(n^3N^2)$ to $\\mathcal{O}(n^6N^2)$ complexity and $\\mathcal{O}(N^4)$ condition number scaling for the $n$th-order moments on an $N\\times N$ image. We introduce \\textbf{PSepT} (Polar Separable Transform), a separable orthogonal transform that overcomes the non-separability barrier in polar coordinates. PSepT achieves complete kernel factorization via tensor-product construction of Discrete Cosine Transform (DCT) radial bases and Fourier harmonic angular bases, enabling independent radial and angular processing. This separable design reduces computational complexity to $\\mathcal{O}(N^2 \\log N)$, memory requirements to $\\mathcal{O}(N^2)$, and condition number scaling to $\\mathcal{O}(\\sqrt{N})$, representing exponential improvements over polynomial approaches. PSepT exhibits orthogonality, completeness, energy conservation, and rotation-covariance properties. Experimental results demonstrate better numerical stability, computational efficiency, and competitive classification performance on structured datasets, while preserving exact reconstruction. The separable framework enables high-order moment analysis previously infeasible with classical methods, opening new possibilities for robust image analysis applications.","short_abstract":"Orthogonal moment-based image representations are fundamental in computer vision, but classical methods suffer from high computational complexity and numerical instability at large orders. Zernike and pseudo-Zernike moments, for instance, require coupled radial-angular processing that precludes efficient factorization,...","url_abs":"https://arxiv.org/abs/2510.09125","url_pdf":"https://arxiv.org/pdf/2510.09125v1","authors":"[\"Satya P. Singh\",\"Rashmi Chaudhry\",\"Anand Srivastava\",\"Jagath C. Rajapakse\"]","published":"2025-10-10T08:26:09Z","proceeding":"cs.CV","tasks":"[\"cs.CV\"]","methods":"[]","has_code":false}