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

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[学习笔记] CS131 Computer Vision: Foundations and Applications:Lecture 2 颜色和数学基础_第1张图片

 

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

[学习笔记] CS131 Computer Vision: Foundations and Applications:Lecture 2 颜色和数学基础_第2张图片

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) $A^T = -A$

转载于:https://www.cnblogs.com/vincentcheng/p/7930389.html

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