An optimization method for elastic shape matching. Application to facial reconstruction
vendredi 30 septembre 2016, 11h00 - 12h00
Shape morphing or matching arises in a wide variety of situations in areas from biomedical engineering to computer graphics and scientific computing.
Beyond the specific stakes to each particular application, the general issue is to find one transformation from a given `template’ shape $\Omega_0$ into a `target’ $\Omega_T$.
Such a transformation may be used as a means to appraise how much $\Omega_0$ and $\Omega_T$ differ from one another – for instance in shape retrieval, classification or recognition – or to achieve physically the transformation from $\Omega_0$ to $\Omega_T$ (in shape registration, reconstruction, or shape simplification).
Our problem is stated as follows : given a `template’ shape $\Omega_0$, numerically described by means of a computational mesh, and a `target’ shape $\Omega_T$, known only via a signed distance function to its boundary, we aim at deforming iteratively the mesh of the template shape into a computational mesh of the target shape. To achieve this goal, we rely on techniques from shape optimization. Under the sole assumption that both shapes share the same topology, the desired transformation is realized as a sequence of elastic displacements, which are obtained by minimizing an energy functional based on the distance between the two shapes.
In doing so, it is expected that the deformation will be easier to achieve in numerical practice, and in particular by limiting the troubles due to mesh tangling.
The proposed method will be used to address the facial reconstruction problem: we aim at virtually reconstructing a face starting fro the sole datum of the underlying raw skull. To achieve this goal, we rely on an original combination of mesh deformation techniques.