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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轉置運算子)
向量使用:點的空間表示;表示資料,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:
- $det(AB) = det(BA)$
- $det(A^-1) = \frac{1}{\det(A)}$
- $det(A^T) = det(A)$
- $det(A) = 0$ 若且唯若$A$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