I’m implementing a relatively highly cited academic research paper: “Interobserver
Reproducibility of Quantitative Cartilage Measurements: Comparison of B-Spline
Snakes and Manual Segmentation”. In short, the paper outlines how you can get a
B-spline to outline knee cartilage in a 2D slice of an MRI. I am stuck at minimizing the
cost function using gradient descent. I do not know how to gracefully apply a partial derivative to a line integral where the line is a B-spline contour in a 2D image. A full explanation of the problem and my current solution is attached, however I make a poor assumption to get to that solution. If anyone could double check my math or has any ideas I would greatly appreciate it.
Not an answer to your question, but related to segmenting knee cartilage. In this thread, I tried it in 3D:
https://www.researchgate.net/post/How_do_you_segment_femoral_and_tibial_knee_cartilage_individually
Not perfect yet but not bad either...
This links have good information
https://books.google.iq/books?id=NGHjwozI02UC&pg=PA188&lpg=PA188&dq=How+to+take+the+partial+derivative+of+a+line+integral+where+the+line+is+a+B-spline+contour+in+a+2D+image&source=bl&ots=i8qbvPZRJx&sig=ACfU3U3W_1iPx0rVhU2E2VRXYCbCfb-uxQ&hl=ar&sa=X&ved=2ahUKEwjH_sOAoqLqAhURsKQKHUooCXgQ6AEwA3oECAcQAQ#v=onepage&q=How%20to%20take%20the%20partial%20derivative%20of%20a%20line%20integral%20where%20the%20line%20is%20a%20B-spline%20contour%20in%20a%202D%20image&f=false
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