Point and Edge Detection - Experiments

Point Detection

Below is an example of point detection.

$(\begin{matrix} -1 & -1 & -1 \\ -1 & 8 & -1 \\ -1 & -1 & -1 \end{matrix})$

Kernel for point detection

Below is an example of edge detection using Sobel, Prewitt, and Roberts filter.

Sobel filter uses two kernels to calculate derivatives of each pixel: horizontal and vertical. Then, we combine those results to get magnitude.

Horizontal

$(\begin{matrix} 1 & 0 & -1 \\ 2 & 0 & -2 \\ 1 & 0 & -1 \end{matrix})$

Kernel for horizontal Sobel filter

Vertical

$(\begin{matrix} 1 & 2 & 1 \\ 0 & 0 & 0 \\ -1 & -2 & -1 \end{matrix})$

Kernel for vertical Sobel filter

Magnitude

$\sqrt{x^{2} + y^{2}}$

Prewitt filter acts like Sobel filter, but does not focus on the middle.

Horizontal

$(\begin{matrix} 1 & 0 & -1 \\ 1 & 0 & -1 \\ 1 & 0 & -1 \end{matrix})$

Kernel for horizontal Prewitt filter

Vertical

$(\begin{matrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ -1 & -1 & -1 \end{matrix})$

Kernel for vertical Prewitt filter

Magnitude

$\sqrt{x^{2} + y^{2}}$

Roberts filter uses diagonals instead of x and y axis.

45 degrees

$(\begin{matrix} 1 & 0 \\ 0 & -1 \end{matrix})$

Kernel for 45 degrees Roberts filter

135 degrees

$(\begin{matrix} 0 & 1 \\ -1 & 0 \end{matrix})$

Kernel for 135 degrees Roberts filter

Magnitude

$\sqrt{x^{2} + y^{2}}$