{"id":147,"date":"2022-07-21T19:30:21","date_gmt":"2022-07-21T18:30:21","guid":{"rendered":"https:\/\/wp.coventry.domains\/e2edu\/?page_id=147"},"modified":"2022-08-22T19:51:24","modified_gmt":"2022-08-22T18:51:24","slug":"movement-analysis","status":"publish","type":"page","link":"https:\/\/wp.coventry.domains\/e2edu\/movement-analysis\/","title":{"rendered":"Movement Analysis"},"content":{"rendered":"\n

This article discusses how raw motion data that has been obtained through motion capture can be processed to extract higher level movement attributes.<\/p>\n\n\n\n

Raw Motion Capture Data<\/h3>\n\n\n\n

The data obtained through motion capture typically represents a temporal sequence of positions and rotations of body joints. Joint positions are represented as three-dimensional vectors. Joint orientation are represented as quaternions <\/a>which are four dimensional vectors out of which three dimensions are complex numbers. This type of data lends itself to reconstruct a so called skeleton representations of poses. <\/p>\n\n\n

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Example of a skeleton representation of a pose obtained through motion capture. Joints are represented here as balls and bones as cones. Contrary to the joints, the bones are not directly part of the recording but are reconstructed afterwards based on the hierarchy of joints. <\/figcaption><\/figure>\n<\/div>\n\n\n

Physical Quantities<\/h3>\n\n\n\n

Information about body motion can only be indirectly obtained by calculating how joint positions and orientations change from frame to frame. Some of the more intuitively understandable physical quantities that describe aspects of motion are velocity, acceleration, and jerk. Velocity describes how positions change over time, acceleration describes how velocity changes over time, and jerk describes how acceleration changes over time. <\/p>\n\n\n

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Graphs depicting temporal sequences of physical values that correspond to derivatives of each other. Image from \u00a9Vernier<\/a>.<\/figcaption><\/figure>\n<\/div>\n\n\n

There are two types of motion data that are of interest in motion capture. One deals with how joints positions change over time and the other how joint rotations change over time. In the first case, we are dealing linear derivatives such as linear velocity, linear acceleration, and linear jerk. In the second case, we are dealing with angular derivatives, i.e. angular velocity, angular acceleration, and angular jerk. <\/p>\n\n\n\n

Linear derivatives can easily be obtained by calculating the discrete derivative of the joint positions with regards to time. The equations for this are as follows:<\/p>\n\n\n

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Linear velocity calculated from position difference <\/figcaption><\/figure>\n<\/div>\n\n
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Linear acceleration calculated from velocity difference<\/figcaption><\/figure>\n<\/div>\n\n
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Linear jerk calculated from acceleration difference<\/figcaption><\/figure>\n<\/div>\n\n\n

Angular derivatives can be obtained in a similar manner by calculating the discrete derivative of the joint orientations with regards to time. The equations for this are as follows:<\/p>\n\n\n

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Angular velocity calculated from rotation difference<\/figcaption><\/figure>\n<\/div>\n\n
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Angular acceleration calculated from angular velocity difference<\/figcaption><\/figure>\n<\/div>\n\n
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Angular jerk calculated from angular acceleration difference<\/figcaption><\/figure>\n<\/div>\n\n\n

Laban Effort Factors<\/h3>\n\n\n\n

While physical quantities of motion are easy to compute from raw motion capture data, these quantities are not necessarily particularly meaningful for dance. Dancers and choreographers often think about body movement in terms of more qualitative aspects such as its expressive, aesthetic, or communicative properties. An article on movement representation<\/a> provides information about some aspects of movements that dancers we worked with refer to. There is also an article available that describes more general movement qualities<\/a> in dance. <\/p>\n\n\n\n

For the purpose of movement analysis, the formalisations introduced by the Laban Movement Analysis<\/a> (LMA) system has informed fields such as robotics and human computer interaction. Central to LMA are four categories that formalise different aspects of the human body: Body, Space, Shape, and Effort. <\/p>\n\n\n\n

The Effort category describes aspects that relate to the dynamics, energy, and inner intention of movement, all of which contribute to the expressivity of movement. This category is subdivided into four Effort Factors: Space, Weight, Time, Flow. Each Factor possesses two opposing dimensions. <\/p>\n\n\n\n