Fundamentals on Motion Capture Data

Abstract

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. 9.1 Motion Capture Data There are many ways to generate motion capture data using, e.g., mechanical , magnetic, or optical systems, each technology having its own strengths and weaknesses. For an overview and a discussion of the pros and cons of such systems we refer to Wikipedia [215]. We exemplarily discuss an optical marker-based technology, which yields very clean and detailed motion capture data. Here, the actor is equipped with a set of 40-50 retro-reflective markers attached to a suit. These markers are tracked by an array of 6-12 calibrated high-resolution cameras at a frame rate of up to 240 Hz, see Fig. 9.1. From the recorded 2D images of the marker positions, the system can then reconstruct the 3D marker positions with high precision (present systems have a resolution of less than a millimeter). Then, the data are cleaned with the aid of semi-automatic gap filling algorithms exploiting kinematic constraints. Cleaning is