[Learning Notes] CS131 computer vision:foundations and applications:lecture 2 color and Math basics

Outline

What is color?

• The result of interaction between physical light in the environment and our visual system.
• A psychological property of our visual experiences if we look at objects and lights, not a physical property of those OB Jects or lights.

Human encoding of color

Color Spaces

• Linear Space:rgb/cie XYZ
• Nolinear SPACE:HSV

Use of the 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. Vectors

Column vectors: $v \in r^{n*1} v = \begin{bmatrix} v_1 \ v_2\\ \cdot \ \cdot \ \cdot \ v_n \end{bmatrix}$

Line vectors: $v ^t \in r^{1*n} v^t = [V_1 v_2 ... v_n]$ (T-transpose operator)

Vector Use: space representation of points, data, no spatial meaning, but calculations still make sense

2. Matrix

Matrix Operations: addition, scaling

Matrix Norm:

One norm:$| | x| | _1 = \sum_{i=1}^n |x_i| $

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)}$

The rank of the matrix:

• $det (AB) = det (BA) $
• $det (a^-1) = \frac{1}{\det (A)}$
• $det (a^t) = det (A) $
• $det (A) = 0$ when and only if $a$ is singular

Trace of the Matrix: the and of the diagonal elements

Special matrices:

• Identity matrix: The diagonal element is 0 and the other element is 1
• Diagonal matrix (Diagonal matrix): 0 for non-diagonal elements
• Symmetric matrix (symmetric matrix): $A ^t = a$
• Anti-call matrix (Skew-symmetric matrix) $A ^t =-a$

[Learning Notes] CS131 computer vision:foundations and applications:lecture 2 color and Math basics