## General (Non-orthogonal) basis projection

where $m$ can be the non-orthogonal basis column vectors, $x$ is a column vector in global coordinates, $x^{'}$ is a column vector in non-orthogonal basis coordinates. Note the $\left(M^{T}M\right)^{-1}M^{T}$ is the psudo inverse of $M$ when $M$ is not a square matrix.

derivation:

if $M$ is an orthogonal basis, then

re-project:

## From implicit filtering to explicit filtering

[1]Y. Li and S. Osher, “A New Median Formula with Applications to PDE Based Denoising,” Comm. Math. Sciences, vol. 7, pp. 741-753, 2009.

## Computer Vision Matrices 你不能不知道的重要矩陣!

• Camera Matrix
• Fundamental Matrix
• Essential Matrix
• Homography Matrix

## Gauss–Seidel method

Jacobi method中，$x^{(n+1)}$是由$x^{(n)}$全部一口氣帶入原式求得，而Gauss–Seidel method則是依序將已知的$x_{j}^{(n+1)}$帶入得到新的$x_{j+1}^{(n+1)}$