3D Morphable Model Method

This note is a brief summary of the 3DMM paper A Morphable Model For The Synthesis Of 3D Faces.

Note: I have no idea why there is a “|” following each math environment and “\bold” has no effect, for clarity, see the original version 3D Morphable Model Method.

Prerequisite

• 3D head lase scans
• full correspondence of faces (the method for acquiring this condition is described in the last section of the note.)

Model Construction

The model construction process consists of two steps: compute correspondence and construct model. Notice that these are steps for TRAINING, when the model is constructed, we can apply this model to new faces and scans through matching algorithm.

concept of morphable face model

A face has two major properties: geometry represented as shape-vector $S=(X_{1},Y_{1},Z_{1},X_{2},...,Y_{n},Z_{n})^{T}\in{\Re^{3n}}$ that contains the $X,Y,Z$-coordinates of its $n$ vertices; texture represented as texture-vector $T=(R_{1},G_{1},B_{1},R_{2},...,G_{n},B_{n})^{T}\in{\Re^{3n}}$ that contains the $R,G,B$ color values of the $n$ corresponding vertices. An arbitrary new shapes $S_{model}$ and new texture $T_{model}$ can be expressed in linear combination of the $m$ exemplar faces:

\boldSmod=∑i=1mai\boldSi,\boldTmod=∑i=1mbi\boldTi,∑i=1mai=∑i=