Skip to content

Tasks

2022-04-06

  • Write the digital estimators part of the related works
  • Create the section main contributions and paper structure
  • Adapt the paper introduction to the journal we are going to submit (SIAM Journal on Imaging Sciences)

2023-03-23

  • Update image diagram describing our method. Use DGtal to draw a digital board. the idea is that this picture invokes the digital nature of our method in contrast with continuous techniques.
  • Change the order of the text. We decided to first present our method and only at the end we make the link with the mean curvature flow.
  • Update line 228. \(x\) is a point of \(C(0)\) and not $C(1).
  • Put the Neighborhood of Shapes (figure 6.1) in the experimental section. This is not a nice figure to appear as the first result.
  • Think about an illustration that shows how the flow varies according to the radius. In particular, it should be evident that higher the radius (digital radius), higher is the precision. Bear in mind that one can achieve a higher digital radius by two paths: decreasing the grid step or increasing the radius of the estimation disk. Another important evaluation is the ratio between the estimation disk radius and the shape curvature at the point of measure. Jaco suggested to replace one of the graphs on figure 6.2 by another one that display an analytic measure such as Haussdorf distance of the optimal shape.
  • Read and evaluate if this reference pointed by the reviewer is relevant: An efficient iterative thresholding method for image segmentation D Wang, H Li, X Wei, X Wan Journal of Computational Physics 350, 657-667.
  • We need some easy-to-grasp illustration to explain the graph-cut method.
  • Better explain from where it comes the edge capacities used in the graph flow. Point out that this is the approach taken by classical methods in the area. Perhaps indicate the Bayeasian reasoning for them.
  • Start given the edge capacities for the Chan-Vese model. It will be easier to do the translation since we have a mathematical formula for Chan-Vese.
  • Fix issue with graph-flow source code. 
      // contour-correction/model/image/DataDistribution.h:21
  if (pbfgMask.size.dims() > 0 && pbfgMask.size[0] > 0)

  // grabcut/GrabCutApplication.cpp:30 
  if (unknownMask.size > 0)

Weak points

  • Segmentation models based on curvature are particularly praised for their results on segmentation of thin and elongated shapes such as blood vessels.

    • Indeed, in our experiments, we didn't insist in that point. Our experiments lack examples of segmentation of thin and elongated objects. There is a reason for that. The curvature prior is relevant for this task only for models that target a global optimization of the energy. That's not the case of our model. Our model does a local optimization. Eventually it can happen that lead to the optimum value, but that is not the general case. We tried to belittle this by using a different neighborhood of shapes but this has limited impact on the results.
    • There is also another difficulty. Our model is developed for shapes, but thin and elongated objects have a too high perimeter over area ratio and this restrict the estimation disk radius we can use. To better deal with this we need to do some sort of trick in which we identify the thin and elongated shape as a closed curve with some orientation allowing to identify its interior and exterior. Then, during the disk estimation computation we can avoid the problem of a disk cut by two.
    • My suggestion is to explicit mention this weekness in the paper. We should emphasize that our model is shape based and it is not currently possible to handle thin and elongated objects properly, although we can recover some nice results (snake, scisors). We can next point this as a future research direction, because we can have a more general model, curve-based, in which the current one would be a subcase.

  • Comparison with other methods.

    • More than one reviewer asked for a more in-depth comparison between our model and others in the literature.
    • The problem with that is that we need the code to be available. It is very difficult to find papers that link to a public repository.
    • It is not fair to compare our method with curve-based methods. It makes sense to compare it Chan-Vese and Grabcut, though.

  • Clearly present the scope of the work.

    • This work is more about presenting a digital framework to solve a curvature-related problem: segmentation. But the model in itself does not plead to be any better than other existent model.
    • The goal of this work is to convince the readers that a digital framework makes sense to solve the segmentation problem with curvature prior.
    • We do some critics to existing methods such as ADMM algorithms for Euler Elastica. Our aim with this is not to say that we have solve the running time issue with our model, but simply point out that there is a problem and that there is space for alternative solutions. In this paper, we explore a novel solution that uses digital estimators.

  • Missing references:

    • This one was cited by a reviewer to reply to our comment in the text that Threshold Dynamics face some for image processing applications: An efficient iterative thresholding method for image segmentation D Wang, H Li, X Wei, X Wan Journal of Computational Physics 350, 657-667

  • Better explain Graph-Cut

    • The audience of the paper may not be very well familiarized with the graph-cut problem and its algorithms. We should quickly cite the most classical results and the Ford-Fulkerson algorithm.