Image Model | Sahithyan's Notes

An image can be modeled as a function that returns light intensity at a point.

I(x,y)

Analog image model

Here:

$x, y$ : bounded continuous parameters specifying an infinitely small, zero-width region within the image
$I(x,y)$ : intensity at that point, continuous but bounded within intensity limits

The analog image is generated by scanning $x, y$ through their bounds.

$x, y$ are discrete, so each now specifies a small but finite region. $I(x,y)$ returns the average intensity of that region as a discrete value.

I(x,y) \approx \begin{bmatrix} f(0,0) & f(0,1) & \cdots & f(0,n-1) \\ f(1,0) & f(1,1) & \cdots & f(1,n-1) \\ \vdots & \vdots & \ddots & \vdots \\ f(m-1,0) & f(m-1,1) & \cdots & f(m-1,n-1) \end{bmatrix}

Here:

$m, n$ : number of rows and columns, giving the size of the digital image
Each matrix element is a pixel, a discrete approximation of the average intensity of the region it represents