Missing one term in the geodesic distance

[John1231983]

In the original paper, the geodesic distance is defined:

while it is defined as below in your paper

it shows that you are missing the first term in the formular. Is it right? As mentioned in the original paper, the first term is Euclidean distance.

[taigw]

@John1231983 (2) can be seen as an extreme version of (1). Here (2) is fully defined based on Geodesic and (1) contains information of Euclidean distance (not purely geodesic). In my code I defined a parameter lamb which balances the two terms:

`def geodesic_distance_2d(I, S, lamb, iter):

'''

get 2d geodesic disntance by raser scanning.

I: input image

S: binary image where non-zero pixels are used as seeds

lamb: weighting betwween 0.0 and 1.0

      if lamb==0.0, return spatial euclidean distance without considering gradient

      if lamb==1.0, the distance is based on gradient only without using spatial distance

iter: number of iteration for raster scanning.

'''

return geodesic_distance.geodesic2d_raster_scan(I,S, lamb, iter)`

[John1231983]

Thanks for your reply. But I did not find any lamb term in your equation (2). I mean if lamb is 0.5, then two terms contributes equally and it should be appear in the equation

[taigw]

equation (2) is the case of lamb == 1.0

[John1231983]

@taigw : It is clear now. So, can your code can produce the results likes eq. (1) in case of lamb = 0.5? It means I want to consider the first term also.

[taigw]

Yes, you can set lamb to 0.5 to obtain a mixture of the two terms. I have updated the 2D example as you can see in the readme file.