Continuous Greyscale Image 

1 mapping f from a rectangular domain Ω =(0,a₁) X (0,a₂) to a co-domain R

domain Ω is called image domain or image plane.

co-domain specifies grey value usually low grey values are dark, high grey values bright

2 Sampling

 2.1discretization of the domain Ω 

 2.2 image data are only give on a rectangular point within the image domain Ω

 2.3 the grid point is called pixel. 

 2.4 2D images often have equal pixel distance in both directions.

3 Quantisation

 3.1 discretization of the co-domain 

 3.2 if a grey value is encode with a single byte,the discrete codomain is given by {0,1,...255}

 3.3 binary images have the co-domain {0,1}

 3.4 Humans can distinguish only about 40 greyscales.

4 Types of image 

 4.1 m-Dimensional Images 

    m=1 signals  m=2 tow-dimensional images m=3 three-dimensional images

 4.2 Scalar-valued Images

   co-domain in R, for example, greyscale images

 4.3 Vector-valued Images 

   co-domain in Rⁿ , containing n channels for example: Colour images have three channels R G B. Satellite images：different channels represent different frequency bands 

 4.4 Matrix-valued Images

  co-domain in R^{n x m} . For example Diffusion Tensor Magnetic Response Imaging.

4.5 Image Sequence

 this increases the dimensionality of the domain from m to m+1 

summary: Digital images have a discrete domain (sampling) and a discrete co-domain (quantisation)

generalisation of the domain : m-dimensional images , image sequences

generalisation of the co-domain : scalar-valued images, vector-valued images, matrix-valued images.

<数字图像处理1> 数字图像定义(Definition) 类型(Type) 采样 (Sampling) 量化 (Quantisation)