Image Model

　　在說明各式各樣的影像處理技術前，必須先瞭解電腦中的影像模型 (Image Model)，如此才能夠進行各樣的影像處理。一般來說，一張數位影像就是許許多多的色點 (pixel) 所構成的圖片，而每一個色點都是由紅、綠、藍（RGB）光的三元色調配出來的，如此便構成了二維的一張影像；我們通常稱這樣的影像是空間中的影像（Spatial domain）。另外，我們有時可以用一些轉換函數（transformation），來抓住影像的特徵，而這些經過轉換後的影像，通常就稱為頻率上的影像（Frequency domain)。（因為這類的轉換函數通常是週期函數）

◎What is a digital image?

A digital image is composed of a set of pixels (picture elements) Each pixel represents a portion of the image in a particular color, or shade of gray.

Resolution: The number of pixels in a given area defines the resolution of a digital image.

Dynamic range: The number of possible colors each pixel can represent is determined by the dynamic range of the image.
RGB colors: 3 colors to represent one pixel.

Dynamic range (bit-depth):

8 bits: 256 colors from an palette
16 bits: 5 bits for Red, 5 bits for Green, 5 bits for Blue
24 bits: 8 bits for Red, 8 bits for Green, 8 bits for Blue

◎Mathematical model (spatial domain)

A digital image = f(x,y)
,where 0≦x＜width, 0≦y＜height,and x, y are discrete.

For a color image f(x,y) is a vector, composed by RGB three components.

◎Transformations (Frequency domain)

Why transformation is necessary?

Capture perceptual features using less bits
- High frequency signals are not sensitive to Human’s eyes. (compression)
- We can represent some features using low frequency signals without losing much information.(feature retrieval, similarity query)
Accelerate convolution operation (only for FFT)
　　f(x)*g(x) ＜＝＞ F(u)G(u)
　　Uppercase letters represent Fourier domain functions.

Some Transforms:

Fourier Transform:
　　
　　
Discrete Cosine Transform (DCT):