This partial implementation of a research paper focus on the tools and applications for open curve detection.<br> Given an input image of a simple or complex and unparametrized curve, we would like to automaticaaly derive a discrete parametrisation that fit the 2D curve. The applications are for example in medical image analysis where we would like to derive for example the vessels or aortic valves.
First, we use the Fast-Marching Algorithm to create a distance map on the image. For example, starting from the following:
the Fast-Marching, derives automatically the potential map shown below:
The Fast-Marching algorithm might be implemented via two techniques:
- Djisktra (L1 norm neighborhood)
- Eikonal equation (L2 norm neighborhood)
Using this algorithm, on a open curve:
We derive the chart distance:
And using back propagation to find the geodesic, we find a potential path on the image:
On more complex curves, this technique is not robust, see the following figures:
To avoid this, the authors introduce a method based on intermediary computation of keypoints (kind of step by step geodesic), that will be more robust than the Fast-Marching applied directly.
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Using some conditions specifications on the distance between three following keypoints, we can even
come up with a method where we don't need to specify starting and ending points. See the figures below:
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The program proposed in the notebooks does not go as far as the research paper but the computations are very interesting anyway.