Computer Vision Foundations · 免费预览
反向积分
把导数写成矩阵，便揭示出积分是它的逆；而在只使用有效差分的情况下，伪逆能把每幅图像恢复到只差一个均值的程度。
1. The derivative as a matrix
The derivative as a matrix
2. The boundary cheat
The boundary cheat
3. What the mean has to do with it
What the mean has to do with it
4. Why the cumulative sum is the inverse
With a zero boundary condition assumed, the inverse of the difference matrix turns out to be the cumulative-sum matrix. Why does summing differences rebuild the signal?
5. What survives reconstruction
A valid-differences pseudoinverse reconstruction is compared with the original signal. What is the guaranteed relationship between the two?
6. The constant that went missing
A three-sample signal reads 1 then 3 then 8. Its mean is 4, its valid differences are 2 then 5, and the pseudoinverse returns minus 3 minus 1 then 4. What single constant added back restores the original signal?