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
Simple: the Euclidean distance completely ignores the shape when finding a path from the start point to the end point while, for the geodesic distance, the path is constrained to be within the given shape.

That's why the distances at the bottom left of the figure are so different.