RBF Interpolated Level Sets
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:
- 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.
- Periodic re-initialisation of the level set function is no longer necessary.
- More complex topological changes, such as holes within objects, are comfortably found.
- The active contour and surface models using this technique are initialisation independent.
- 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 Snake | Evolving Contours | Stabilised 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
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Example results - more results without initialisation using the proposed method
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Example results by proposed method - 3D images
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| Initial deformable surface | Evolving deformable surface | Stabilised surface | Stabilised surface with inside hole |
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| Recovering object with arbitrary initialisation |
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| Recovering a complex 3D shape |
Publications
- Xianghua Xie and Majid Mirmehdi, Radial Basis Function based Level Set Interpolation and Evolution for Deformable Modelling, Image and Vision Computing, volume 29, issues 2-3, 167 - 177, February 2011.
- Xianghua Xie and Majid Mirmehdi, Implicit Active Model using Radial Basis Function Interpolated Level Sets, In Proceedings of the 18th British Machine Vision Conference, pages 1040-1049, BMVA press, September 2007.