Hello,
I understand that you want to know about the “graydist” function's output matrix.
T1 = graydist(A,1,1)
The `graydist` function in MATLAB calculates the grayscale distance transform of an input image, where each element in the output matrix (T1) represents the grayscale distance from the corresponding pixel to a reference pixel at coordinates (1,1).
For example, the element T1(1,1) represents the grayscale distance from the pixel at (1,1) in the input image to itself (the reference pixel). Since it's the same pixel, the distance is 0.
The element T1(2,2) represents the grayscale distance from the pixel at (2,2) in the input image to the reference pixel at (1,1). This distance is 4.5.
Similarly, each element in T1 represents the grayscale distance of the corresponding pixel to the reference pixel.
The equation used to calculate grayscale distance in the `graydist` function is based on the geodesic time concept. The equation of geodesic time is as follows:
my understanding of the equation is stated below
A discrete path P of length l going from p to q in a graph G can be defined as a (l+ 1 ) - tuple (
) of vertices of G such that 
, 
=q, and 
defines an arc of G for all i∈ [ 1, l].
) of vertices of G such that , =q, and defines an arc of G for all i∈ [ 1, l]. The time 
necessary to cover a discrete path of length l defined on a discrete grey-scale image f equals the mean of the values off taken two at a time along P:
necessary to cover a discrete path of length l defined on a discrete grey-scale image f equals the mean of the values off taken two at a time along P: 
`
` represents half of the grayscale value at the starting pixel, indicating the "cost" of starting the journey from that pixel.
` represents half of the grayscale value at the starting pixel, indicating the "cost" of starting the journey from that pixel.`
` represents half of the grayscale value at the ending pixel, indicating the "cost" of ending the journey at that pixel.
` represents half of the grayscale value at the ending pixel, indicating the "cost" of ending the journey at that pixel.The summation (∑) adds up the grayscale values of the intermediate pixels (
) along the path (from 
to 
), representing the "cost" of traveling through these pixels.
) along the path (from to ), representing the "cost" of traveling through these pixels.Hope this helps.
