大綱

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轉置運算符)

向量使用：點的空間表示；表示數據，沒有空間意義，但是計算仍然有意義

2. 矩陣

矩陣運算：addition, scaling

矩陣範數：

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)}$

矩陣的秩：

• $det(AB) = det(BA)$
• $det(A^-1) = \frac{1}{\det(A)}$
• $det(A^T) = det(A)$
• $det(A) = 0$ 當且僅當$A$是奇異的

矩陣的跡：對角元素的和

特殊矩陣：

• 單位矩陣(Identity Matrix)：對角元素為0，其他元素為1
• 對角矩陣(diagonal matrix)：非對角元素為0
• 對稱矩陣(Symmetric Matrix)：$A^T = A$
• 反對稱矩陣(Skew-symmetric Matrix) $A^T = -A$

[學習筆記] CS131 Computer Vision: Foundations and Applications：Lecture 2 顏色和數學基礎