Fundamentals on Motion Capture Data

The second part of this monograph deals with content-based analysis and retrieval of 3D motion capture data as used in computer graphics for animating virtual human characters. In this chapter, we provide the reader with some fundamental facts on motion representations. We start with a short introduction on motion capturing and introduce a mathematical model for the motion data as used throughout the subsequent chapters (Sect. 9.1).We continue with a detailed discussion of general similarity aspects that are crucial in view of motion comparison and retrieval (Sect. 9.2). Then, in Sect. 9.3, we formally introduce the concept of kinematic chains, which are generally used to model flexibly linked rigid bodies such as robot arms or human skeletons. Kinematic chains are parameterized by joint angles, which in turn can be represented in various ways. In Sect. 9.4, we describe and compare three important angle representations based on rotation matrices, Euler angles, and quaternions. Each of these representations has its strengths and weaknesses depending on the respective analysis or synthesis application.