danoan / graph-flow Goto Github PK

Similar as it is done with shape evolution, implement a benchmark for contour-correction across the releases.

Currently a whole disk is intersected for every computation of the balance coefficient.

Contours are a sequence of adjacent pixels, so we can optimize this computation. We need to compute a full intersection of the disk at the very first balance coefficient computation. All the others can be derived from a delta from the previous one. This delta refers to the pixels in the contour of the disk.

This improvement removes the quadratic slow down we observe as the disk size increases.

I propose an alternative optimization strategy.

Currently, the optimization band is computed relative to the current contour. Therefore, it changes at every iteration. Instead, the strategy proposed here consists in fixing a (possibly) large optimization band until no improvement is found.

A great advantage of this approach is that the optimization graph is created a single time until the optimization band is changed.

Graph coefficients define candidate shapes for energy validation.
Validation coefficients evaluates the quality of the candidate.

By separating graph coefficients from validation ones, we can force the candidate selection to favor the regularization terms while the validation coefficients favors the data terms instead.

Remove dependency from DIPaCUS and from geoc

the estimation of curvature and local length can be computed more efficiently by using standard functions of the DGtal library.

A naive implementation could be the following:

1. Run a contour-detection algorithm (likely one is biased to form closed contours)
2. Invert the image to obtain the connected digital sets
3. For each connected digital set, choose some strategy to select seeds in the interior (foreground) and in the outer (background) of the set.
4. Run the graph-flow for each connected digital set

An alternative to that:

1. Create an hierarchy (watershed segmentation)
2. Pick some nodes of the hierarchy to execute graph-flow
3. Select the best graph-flow result

The data term may be defined like this: For the closed areas, select random seeds and compute a mixed gauss distribution (similar to classical graph cut)

It may be possible to optimize the contour extraction by considering the previously extracted contours and the optimization band used

Currently, the length component is only computed at the validation step. No length component is considered in the computation of the minimum cut.

This improvement aims to implement a very simple length penalization component in the capacity function, by simply adding a constant (weigthed by the length penalization parameter alpha) in the capacity function of each edge.

Ideally, we should use a convergent estimator, such as the one proposed by Boykov.

Take advantage of the multigrid estimators and run the algorithm in reduced image scales to obtain approximated solutions. Greater resolutions can also be used to obtain a refined contour correction by the elastica energy.