I'm reading about the Fast Marching method and can't figure out how to apply it, until now i think, that in practice, it will be a copy of the Dijkstra algorithm but with a specific distance function, i just can't figure out what is this function, this slide: ENSTA07_Lecture2_4.pdf shows this formula:
$$(max\{max\{\frac{T_{i,j} - T_{i-1,j}}{\Delta x}, 0 \}, -min\{\frac{T_{i+1,j} - T_{i,j}}{\Delta x}, 0\}\})² + (max\{max\{\frac{T_{i,j} - T_{i,j-1}}{\Delta y}, 0 \}, -min\{\frac{T_{i,j+1} - T_{i,j}}{\Delta y}, 0\}\})² = 1 / c²_{i,j}$$
The slide also gives an algorithm to apply the method over a grid: $$T_{i,j} \text{ for each } (i, j) \text{ node}$$ .
I cant understand how to compute the formula for each node, can anyone help?