how to trace a curve arteries for finding discontinuty

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i have skeleton image of arteries I have to implement following thing on it using mat lab.
1. i have to find out first and last points of arteries
2. i have to find the nearest neighbors along these points and calculate the distance between them i have done first step ...stuck on second step plz helpppppp purpose is to trace the curve and have to find the discontinuity..

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