What are MREPS
MREPS are medial representations, composed out of one or more medial sheets. Medial sheets contain medial atoms, each of which live in a new coordinate system: <x, r, F, theta>. These coordinates define each medial atom by:
- Translation (position)
- Local size
- Local frame (local orientation): twisting and bending
- Boundary angulation
This is an 8 tuple. A medial sheet with n medial atoms therefore defines a point in 8n dimensional curved space. The space is curved because rotations do not combine linearily.
The surface is defined implicitly and computed by Catmull-Clark subdivision.
Objects are defined by a hierarchy of figures, the position and orientation of subfigures are defined relative to their host figure.
Why MREPS can be useful for representing faces
- Because faces look blobby, but are not jelly!
- MREPS allow local deformations: translations, twisting and bending, magnifications
- The host-subfigure hierarchy naturally reflects the bone-muscle relationship:
- Muscles don't move independently to the underlying face
- Muscles only influence each other locally
Animating face MREPS
- Shortest paths in the curved MREP space are called geodesics
- Interpolation between 2 MREPS (keyframes) yields naturally smooth animation sequences
- Less manual tweaking of the path
- Keyframes can be further apart
- Statistical analysis of the atoms distribution in 8n-dimensional space: we can extract the principal modes of variation in a set of head expressions
First task: build a generic head MREP
Modeling and animating expressions
Modeling:
- The principal geodesics correspond to the principal modes of variation: blend between them.
- Interpolate along the geodesics between the coordinates of 2 keyframe MREPS