Image digitization

The image plane is realized through a linear plane of photo-sensor which translate light in voltage quantities suitable for computer processing

Sampling

The image information is sampled both horizontally and vertically in order to obtain a 2D $M\times N$ array of values suitable for processing

$$ I(x,y) \Rightarrow \begin{bmatrix} I(0,0) & I(0,1) & …. & I(0,M-1)\ … & … & … & … \ I(N-1,0) & I(N-1,1) & …. & I(N-1,M-1)\ \end{bmatrix} $$

Quantization

In this phase the values of a single cell are quantize in $l=2^{m}$ different levels called gray levels , where $m$ is the number of bits used to represent the image, with this the space occupancy of one image is the following

$$ B = M\times N\times m $$

Image quality

in order to increase the quality of the representation more bits need to be used, ether increasing $M$ or $N$ (the matrix dimensions) or increasing $m$ (the quality of representation of the single point)