# What is different between Euclidean distance and the Geodesic distance?

We have two kinds of distance in image: Euclidean distance and the Geodesic distance. What is different between them? Could you show mathematic formula or visualization to make it clear? The reference said

Difference between the Euclidean distance and the Geodesic distance calculated with the Fast Marching Method. The Geodesic distance is the distance of the minimum length inside the figure path and the Euclidean distance is the straight line distance

This is example

• @MoonLee : As the text associated with equation (2) says, (2) is the same as the Euclidean distance of $\gamma = 0$. Otherwise, yes, equation (2) is aimed at finding the geodesic distance. – Peter K. Jan 14 at 19:51