contour.tex

\documentclass[12pt]{article}

\usepackage{mathtools}


\begin{document}
$$
\nabla f(x,y) 
= 
grad[f(x,y)]
=
\begin{bmatrix}
g_x(x,y)\\
g_y(x,y)
\end{bmatrix}
=
\begin{bmatrix}
\frac{\partial f(x,y)}
{\partial x}\\
\frac{\partial f(x,y)}
{\partial y}
\end{bmatrix}
$$

$$
g_x(x,y) 
= 
\frac{\partial f(x,y)}
{\partial x}
=
f(x+1,y) - f(x,y)
$$

$$
g_y(x,y) 
= 
\frac{\partial f(x,y)}
{\partial y}
=
f(x,y+1) - f(x,y)
$$

DEREVATIVE

$$
\begin{bmatrix}
-1\\1
\end{bmatrix}
\quad
\begin{bmatrix}
-1 & 1
\end{bmatrix}
$$

SOBEL

$$
\begin{bmatrix}
 -1 & \,2 & -1 \\
\,0 & \,0 &\,0 \\
\,1 & \,2 &\,1
\end{bmatrix}
\quad
\begin{bmatrix}
-1 & 0 &  1 \\
-2 & 0 &  2 \\
-1 & 0 &  1
\end{bmatrix}
$$

$$
G 
=
\sqrt{G_x^2 + G_y^2}
\quad
G
=
|G_x| + |G_y|
$$
\end{document}