cs131_CV_lecture2学习笔记（主要介绍颜色编码和最重要的线性代数两个基础）
what is color?
- The result of interaction between physical light in the environment and our visual system.
- A psychological property of our visual experiences when we look at objects and lights, not a physical property of those objects or lights.
Human encoding of color
Color Spaces
- linear space: RGB/CIE XYZ
- nolinear space: HSV
Use of color in computer vision:
- color histogram for indexing and retrieval
- skin detection
- nude people detection
- image segmentation and retrieval
- build apperance models for tracking
- ...
Linear Algebra Primer: Vectors and Matrix
1. 向量
列向量：v∈Rn∗1v=⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢v1v2⋅⋅⋅vn⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥v∈Rn∗1v=[v1v2⋅⋅⋅vn]
行向量：vT∈R1∗nvT=[v1v2...vn]vT∈R1∗nvT=[v1v2...vn] (T转置运算符)
向量使用：点的空间表示；表示数据，没有空间意义，但是计算仍然有意义
2. 矩阵
矩阵运算：addition, scaling
矩阵范数：
one norm：||x||1=∑ni=1|xi|||x||1=∑i=1n|xi|
two norm：$||x||_2 = \sqrt{\sum_{i=1}^n x_i^2}
infinity norm： ||x||inf=max|xi|||x||inf=max|xi|
general P norm：||x||_p = (\sum_{i=1}^n x_i^p)^1/p$
matrix norm：||A||_F = \sqrt{\sum_{i=1}^m \sum_{j = 1}^n A_ij^2 = \sqrt{tr(A^TA)}$
矩阵的秩：
- det(AB)=det(BA)det(AB)=det(BA)
- det(A−1)=1det(A)det(A−1)=1det(A)
- det(AT)=det(A)det(AT)=det(A)
- det(A)=0det(A)=0 当且仅当AA是奇异的
矩阵的迹：对角元素的和
特殊矩阵：
- 单位矩阵(Identity Matrix)：对角元素为0，其他元素为1
- 对角矩阵(diagonal matrix)：非对角元素为0
- 对称矩阵(Symmetric Matrix)：AT=AAT=A
- 反对称矩阵(Skew-symmetric Matrix) AT=−AAT=−A