[学习笔记] CS131 Computer Vision: Foundations and Applications（Lecture 2 颜色和数学基础） _applications

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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

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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：