[学习笔记] CS131 Computer Vision: Foundations and Applications：Lecture 2 颜色和数学基础
大纲
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：$v \in R^{n*1} v = \begin{bmatrix} v_1 \\ v_2\\ \cdot \\ \cdot \\ \cdot \\ v_n \end{bmatrix}$
行向量：$v^T \in R^{1*n} v^T = [v_1 v_2 ... v_n]$ (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 = \sum_{i=1}^n |x_i| $
two norm：$||x||_2 = \sqrt{\sum_{i=1}^n x_i^2}
infinity norm： $||x||_inf = max |x_i|$
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：
- $det(AB) = det(BA)$
- $det(A^-1) = \frac{1}{\det(A)}$
- $det(A^T) = det(A)$
- $det(A) = 0$ 当且仅当$A$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)：$A^T = A$
- 反对称矩阵(Skew-symmetric Matrix) $A^T = -A$
