Techniques for Face Motion & Expression Analysis on Monocular Images - 3D Modeling and Animation: Synthesis and Analysis Techniques for the Human Body - page 209

They use the pose information retrieved from one frame to analyze and derive
the pose information on the next one. One of the most extended techniques
involves the use of Kalman filters to predict analytical data, as well as the pose
parameters themselves. We refer the reader to other research (Ström, Jebara,
Basu & Pentland, 1999; Valente & Dugelay, 2001; Cordea, E. M. Petriu,
Georganas, D. C. Petriu & Whalen, 2001) to find related algorithmic details.

Image Processing Algorithms

The complexity of expression analysis is usually simplified by trying to under-
stand either the shape of some parts of the face, the location of very specific
points or the change in magnitude of some characteristic of the area analyzed,
for example, its color. In order to do this, several image-processing techniques
are used and tuned to work on human faces. In this section, we try to summarize
the basics of the most common techniques utilized.

Optical flow

The field of displacement vectors of the objects that compose a scene cannot be
computed directly: we can just find the apparent local motion, also called optical
flow, between two images.
There are two major methods to estimate the optical flow: either we match
objects with no ambiguity from image to image, or we calculate the image
gradients between frames. In the first case, the main goal consists in determining
in one of the studied images the group of points that can be related to their
homologues in the second image, thus giving out the displacement vectors. The
most difficult part of this approach is the selection of the points, or regions, to be
matched. In general, the biggest disadvantage of this kind of method is that it
determines motion in a discrete manner and motion information is only precise
for some of the pixels on the image.
The second technique, the gradient-descent method, generates a more dense
optical flow map, providing information at the pixel level. It is based on the
supposition that the intensity of a pixel I ( x, y, t ) is constant on two consequent
frames, and that its displacement is relatively small. In these circumstances we
verify:

∂ I ∂ I ∂ I

u + v + =

, (1)

∂ x ∂ y ∂ t