Computer Vision Foundations · free preview
Reconstruction and Interpolation
Ideal reconstruction cuts one spectral copy with a frequency box, whose space-domain shape is the sinc, and every practical interpolator is a cheap local approximation of it.
1. The ideal is a box, lived as a sinc
The ideal is a box, lived as a sinc
2. One sinc per sample
One sinc per sample
3. The price of the ideal
The price of the ideal
4. The local rogues' gallery
The local rogues' gallery
5. Why each sample owns its point
In sinc reconstruction, every sample plants a scaled sinc centered at itself. Why does the final curve pass exactly through every sample value?
6. Choosing a cheap kernel
An image must be upscaled in real time inside a GPU sampler, where only tiny local kernels are affordable. What is the honest trade among box, triangle, and Lanczos?
7. The sinc at an integer
Write the value of sinc(1), where sinc(t) = sin(πt)/(πt).
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