1. Spatio-temporal Analysis of Human Movements
B. Bläsing, W. Land, Th. Schack,
O. Strogan, D. Volchenkov

2. Pre-processing the VICON data for human movements.
Markers fixed on clothes are subjected to
movements of clothing,
movements of skin,
movements of body tissues
of order of several cm !
Signals are rather noisy in intensive movements: Velocity, acceleration, jerk
do not have much meaning!
The VICON data should be pre-processed in a statistically consistent way.

3. Subtractive synthesis of kinematic data
The proper decomposition of a movement into the minimal set of independent hierarchically ordered features describing it with a maximal precision.
Spatio-temporally independent features!
Movement
scales
meters
millimeters
Golf
Idea: Cut the noise, reconstruct the movement!
The package for the automated subtractive synthesis of kinematic data has been developed by O. Strogan
“Noise”

4. Complexity of movements
While exploring and exploiting space, a man encodes the environment by movements.
How complex is the code? How many features are important?
Distributions of ranked movement scales (singular values of kinematic data matrix):
Golf
Pirouette en dehors
Gevorg
Adeline
amateur
The straight-lines sign the scale-invariance of movements in experts: they can be performed at any speed – slow or fast. Movements of amateurs cannot be carried at arbitrary rate.
Ranked distributions of movement scales show difference btw men and women, experts and amateurs!

5. Structure of movements
At every scale of movements, markers might be clustered as they move together:
Golf
Head
Head
Torso
Hands
Hands
Legs
Legs
Superior iliac spine
Superior iliac spine
Structures of movements reveal individual differences btw subjects

6. Coordination in movements
The proper decomposition of movements is similar to the Fourier decomposition. However, it results NOT to an infinite number of harmonic modes, BUT to a few anharmonically oscillating features.
Phase portraits: markers are colored
velocity
coordinate
time
phase
Coordination in a movement is achieved by phase modulation and synchronization of anharmonically oscillating features.

7. “Kepler's law” of motion
While synchronized, the friction power absorbed by the floor during one period of oscillations (as a function of frequency) is ever minimal.
time
phase
Johannes Kepler
As the friction power is absent, angular momentum in the movement remains unchanged that can be observed as constancy of equi-affine velocity (the constant areal velocity) during the movement.
Constant equi-affine velocity in human movements was observed by Tamar Flash and coworkers.

8. Analysis of body shape changes
While a human moves, the body shape change due to the well coordinated motor actions. Shape changes can be systematized by the Procrustes analysis subtracting all Euclidean geometrical transformations (translations, dilatations, and mean rotations) that preserve the relative positions of markers.
Amateur
Expert
The diagrams represent
the profiles of the velocity of shape changes for the markers (aligned vertically) tracked at the consequent time frames (aligned horizontally) captured with the time slice of 5 msec.
Pirouette en dehors

9. Analysis of body shape changes
Compositionality, hierarchy and recursion of postures in the pirouettes en dehors executed with 5 rotations by a professional dancer.
The bottom diagram shows the hierarchical structure of active and inertial phases in shape changes for the six right arm markers and includes the timing
for each phase.
The structure of shape changes can be related to the mental representation of the motion structure.
Pirouette en dehors

10. Automated movement recognition