Adaptive deformable models

( Benjamin Taton , J.-O. Lachaud )

In image analysis, it is widely assumed that the number of parameters of deformable models is strongly dependent of the image resolution. For highly deformable models, which adapts their topology to their geometrical changes, all explicit and implicit methods have a number of parameters and a time complexity at least linear with the number of pixels or voxels of the component to extract. We show here that a preprocessing of the image can emphasize interesting parts of the image while diminishing the apparent significance of noisy or homogoneous image regions. This zooming effect focuses model parameters and computations on the interesting part of the images. As a consequence, about five time less vertices in 2D and ten times less vertices in 3D are sufficient to extract image components with the same accuracy. Running times are also sped up by a factor ten in 3D.

Embedding the deformable model into a Riemanian metric

In order to have an adaptive deformable model which can still adapt its topology automatically wrt its geometry, we keep the same idea as the explicit model proposed here but the Euclidean distance is replaced by a Riemanian distance computed from the image of interest. All distance constraints are replaced by riemanian distance constraints. The model dynamic is replaced by a riemanian dynamic. As a result, the model density is regular in the Riemanian space but adaptive in the Euclidean space.

Image analysis with the gradient structure tensor

We use a classical tool to detect interesting parts in the image, especially contour information. It is the gradient structure tensor. From this tensor, the riemanian structure tensor is almost readily computed.

Complexity independent from image resolution

For further information, you may consult the PhD thesis of Benjamin Taton [ PhD Thesis PDF | Abstract PDF ].

Lachaud05b , Lachaud04a , Lachaud03d , Taton02b