A Unified Theory of Image Scaling: Point Spread Functions, Discrete Kernels, and Scale-Spaces
We derive the optically aligned system of image-scaling operators $\mathbf{K}_s$ that reproduces optical zoom (exact zoom-out, canonical zoom-in), by identifying a Huygens-like consistency principle in which each pixel acts as a secondary source. The system is determined in closed form by the camera's point spread function (PSF), itself the operator $\mathbf{K}_0$. The operators compose, $\mathbf{K}_{s'} \circ \mathbf{K}_s = \mathbf{K}_{ss'}$ (with band projection for down-up), and account for both upscaling and downscaling, which form a Moore-Penrose pseudoinverse pair, $\mathbf{K}_{1/s} = \mathbf{K}_s^\dagger$. We show that image scaling, as routinely practiced, is neither optically fai...
| Authors | Assaf Shocher |
|---|---|
| Primary category | eess.IV |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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