Deriving Articulated Models from Points

Abstract

One of the dificulties in working with motion capture data is converting from raw data to useful motion. There are essentially two steps in this process, deriving the appropriate model for the motion, and mapping the motion samples to this model in a meaningful way. This project will explore methods for automatically generating a model which can be used to describe the motion samples.

Approach

There are several different levels of this problem. These include:

• Generating correspondences between time instants
• Handling missing data
• Handling outliers
• Determining connectivity

Each of the above problems merits investigation and will be investigated as time permits. The primary focus of this project will be to explore methods of automatically determining connectivity and rigidity properties of the input data to create an articulated model which explains the input.

In general, this is an underdetermined problem. Simply consider the case of motion data collected from two sensors on the hands of an actor. To overcome this problem, various assumptions will be made. In particular, it will be assumed that sensors are placed near all joint locations which need be reconstructed.

Deriving Connectivity

If we have sampled the motion of N points of an articulated object, there are C(N,2) possible connections between all the data points. By tracking the separation of these connections over time we can determine how "stable" or rigid the connection is. The central problem with this approach is handling outliers and missing data. Outliers can skew the rigidity of a particular connection. Missing data must be accounted for in some manner otherwise some connections may be erroneously discarded. Robust statistical techniques must be used to handle outliers, whereas predictive models might prove useful with missing data. [Note: handling missing data once a partial model has been deduced is another option.]

The more rigid the connection the more likely it represents rigid structure in the articulated object. Once rigidity has been determined for each connection, specific connections can be hypothesized to exist. In general, the more rigid the connection the more likely the connection exists.

Each hypothesized connection can be tested in various ways. For example, if the connections represent limbs, the limbs should not pass through one another. The set of all connections should be complete in some sense. Idealy, they should determine a fully connected graph whose topology is identical from frame to frame. This may not always be the case when the data has been corrupted in some manner. It may also not be possible if the data points do not adequatly describe the articulated object, as in the "two hand" example above.

Schedule

I've got three weeks. On your mark get set go!