We proposed a novel method to perform implicit modelling using the radial basis functions (RBFs), which is able to handle more complex topological changes, in particular perturbation away from the evolving front. This allows the initial contour or surface to be placed arbitrarily in the image. Compared to conventional level set based active models, our method has the following advantages:

  1. The evolution of the level set function is considered as an ODE problem rather than a much more difficult PDE problem, which is efficient and does not suffer from self-flattening while evolving, thus avoids large numerical errors.
  2. Periodic re-initialisation of the level set function is no longer necessary.
  3. More complex topological changes, such as holes within objects, are comfortably found.
  4. The active contour and surface models using this technique are initialisation independent.
  5. The computational grid can be much coarser, hence it is computationally cheaper when updating the level set function, particularly in high dimensional spaces.

Example results - complex topological changes

 Initial SnakeEvolving ContoursStabilised Snake
Conventional level set method
Proposed method

Example results - real image - horse

Conventional level set based active contour
Proposed method

Example results - real image - flower

Conventional level set based active contour
Proposed method

Example results - real image - brain

Conventional level set based active contour
Proposed method

Example results - initialisation invariancy using the proposed method

Uniformly distributed circles
Parallel lines
No initialization

Example results - more results using the proposed method

Example results - more results without initialisation using the proposed method

Example results by proposed method - 3D images

Initial deformable surfaceEvolving deformable surfaceStabilised surfaceStabilised surface with inside hole
Recovering object with arbitrary initialisation
Recovering a complex 3D shape

Publications

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