Processing the VICON data for human movements. A case study 7.06.2011 7/6/2011

LFHD RFHD LBHD RBHD C7 T10 CLAV LSHO RSHO RBAK STRN RELB RUPA RFRA RFIN RWRB LPSI RPSI RTHI RWRA LASI RASI LFIN LWRA LELB LUPA LFRA RKNE LKNE LTHI RTIB LTIB RTOE RANK LANK LTOE RHEE LHEE

The VICON data Problem of noise Problem of understanding (analysis & synthesis) Problem of noise Analysis of trajectories Analysis of postures A “posture” - a phase of a motion during which the relative positions of some body parts remain unchanged Decomposition of a motion into a set of spatio-temporally independent hierarchically ordered (space-time scales) movements. Architecture Complexity Spatio-temporal structure Assemblé 100 RBAK THOA CLAV LSHO RSHO C7 LFHD RFHD LBHD RBHD LELB LWRA LWRB LFIN T10 STRN RELB RWRA RWRB RFIN RPSI LPSI RASI LASI LFOA LTHI RTHI LKNE RKNE RANK RTIB LTIB LANK LHEE LTOE RHEE RTOE “Phase space” “Phylogeny” of movements

Decomposition into independent movements 5 turn pirouette Singular Value Decomposition: rotation matrices, the columns of each of them form a set of basis vectors. a scaling matrix;

D = l1u1v*1 + l2u2v*2 + l3u3v*3 +… l1u1v*1 l3u3v*3 l2u2v*2 5 turn pirouette D = l1u1v*1 + l2u2v*2 + l3u3v*3 +… l1u1v*1 l3u3v*3 l2u2v*2

Statistically independent “degrees of freedom” (instantaneous correlations ≡ 0!) LFHD RFHD LBHD RBHD C7 T10 CLAV LSHO RSHO RBAK STRN RELB RUPA RFRA RFIN RWRB LPSI RPSI RTHI RWRA LASI RASI LFIN LWRA LELB LUPA LFRA RKNE LKNE LTHI RTIB LTIB RTOE RANK LANK LTOE RHEE LHEE Decomposition of motion into a set of anharmonic oscillations: time

5 turn pirouette D1 = l1u1v*1

D2 = l1u1v*1 + l2u2v*2 5 turn pirouette

5 turn pirouette D3= l1u1v*1 + l2u2v*2 + l3u3v*3

Phase portraits of markers in a pirouette Coordinate in oscillations 1. 2. 3. velocity velocity velocity

Phase portraits of markers in a pirouette Coordinate in oscillations 4. 5. 6. velocity velocity velocity

Oscillation phases. The evidence of mode coupling Pirouette en dehor, turns TIME Noise 3rd “configuration”

Oscillation phases. The evidence of mode coupling Pirouette en dehor, turns TIME Noise 3rd “configuration”

In each configuration, markers move together Cervical vertebrae 1st configuration 2nd configuration 3rd configuration Left leg Left leg Left hand Left hand Cervical & thoracic vertebrae Clavicles & sternum Right leg Right hand Right hand Right leg thoracic vertebrae Clavicles & sternum

“Eigenmovements” (3rd configuration): Shortlist of markers:

Complexity via scaling factors D =∑k l k u k v* k a student Gevorg Adeline l1> l2 >...l3N ≥ 0 Pirouette: 2 professionals & 1 student

Entropy of trajectories l1> l2 >...l3N ≥ 0 Entropy of trajectories

Entropy of trajectories Assemble Pas Jeté 557 trials Pirouette Échappé Jeté Sauté “White noise” a pendulum

From trajectories to postures 1. Cut off translations and dilatations: While a human dances, the relative positions of markers fixed on the dancers’ body change due to the well coordinated motor actions. In order to detect these changes precisely, we perform a pre-processing of the kinematic data subtracting all Euclidean geometrical transformations (translations, dilatations, and mean rotations) that preserve the relative positions of markers.

2. Subtraction of mean rotations: Procrustes analysis

Signal (velocity) profiles of figure changes Assemblé Sauté

Signal (velocity) profiles of figure changes Pirouette Signal profiles help to indentify the quality of performance

energy configuration

Time-ordering of configurations in professionals 30% 23% 12% 8% ENERGY DECAY

Entropy of postures Jeté Pas Jeté Assemble Pirouette Échappé Sauté No form preserved a spinning top

Conclusions: I still do not know, whether the obtained representations have any relation to a cognitive representation of motion.. I have nothing to say about joined angles … The representations are not intuitively clear.. Phylogeny of markers is different for the different scales (configurations)… Not a biomechanical approach… Problem of filtration (of noise\unsolicited\uninteresting movements) is solved “Postures” can be identified … Compositionality of movements… Entropy-like parameters can be used to classify movements…