We discuss a scheme by which we can transfer the deformation of a source face to a target face, using a given set of correspondence pair of points. The target face could be of different, geometry, or transformation.

#### acknowledgement

We would like to thank Lazlo Vespermi of abalone llc for providing us with the source material.

First let us familiarize with some terms.

#### source mesh

A well defined regular facial mesh, resembling a mannequin’s face.

#### target mesh

Target mesh is obtained from real people, using commercial computational photography techniques.

#### neutral state of a mesh

is the un-deformed state of the mesh.

#### feature points set

A set of points in the mesh which denote predetermined features. Shown are the 28 feature points in the source mesh. A feature point for a mesh is represented as an index to the triangles of the mesh, and a three tuple bary-centric co-ordinates in the triangle. The feature points are ordered. Eg: 20th feature point is the left end of the lips.

#### problem specification

The fixed inputs to the system are

* neutral source mesh
* neutral target mesh
* set of 28 feature points for neutral source mesh
* corresponding set of 28 feature points for target neutral mesh


Given the above fixed inputs, for each given deformation of the source mesh, compute the deformation of the target mesh.

#### results

Shown below is a deformation of the source mesh and a corresponding deformation of the target mesh.

#### method

We use the same technique of scattered data interpolation, that is described in Marco Fratarcangeli, Marco Schaerf and Robert Forchheimer:Facial Motion Cloning with Radial Basis Functions in MPEG-4 FBA.

Let us talk about the neutral state. Let $S_j, j=0, 27$ be the set of 28 feature points for the source mesh. Let $T_j, j=0, 27$ be the corresponding set of target feature points.

For any point $Q= [ x, y, z]$ in the source mesh, $G(Q)$ will give the corresponding point in the target mesh.

$G(Q) = \sum_{j=0}^{27}( H_j . R( S_j, Q ) )$ Given two points $P = [x,y,z]$ and $Q = [x',y'z']$, $R(P, Q)$ is a radial basis kernel, which evaluates to a scalar, . $H_j$-s are vectors. By equating $T_i$ with $G(S_i)$ we get a linear set of equations that can be solved to get the unknown $H_j$-s.

#### acknowledgement

We would like to thank Lazlo Vespermi of abalone llc for providing us with the source material.