LanguageMusicDance Phonemes& Letters Pitches& Notes ? Phonetic & Grammar Rules of harmony ?

Spatio-temporal Analysis of Human Movements in Classical Dance D. Volchenkov, B. Bläsing The Center of Excellence Cognitive Interaction Technology (CITEC) Universität Bielefeld

LanguageMusicDance LettersNotes ? Phonetic & Grammar Rules of harmony ? Although communication by the spoken and written languages& music have been paid much attention, little is known about the information aspects of body language and dance movements. A reliable compact representation of human movements remains questionable.

Movement concepts determined by professionals are not as “physically” independent as letters or notes. Movement concepts determined by professionals are not as “physically” independent as letters or notes. Interpretation of notations is sensitive to the personal body experience & the personal experience to perceive and understand own movements. Interpretation of notations is sensitive to the personal body experience & the personal experience to perceive and understand own movements. Laban Movement Analysis Benesh Movement Notation DanceWriting of Valerie Sutton Eshkol-Wachman Movement Notation etc… Compact representations of human movements

1.How to assess the architecture of human motion directly from the kinematic data; 2.How to quantify the complexity of movements; 3.Does a dance figure contain a quantifiable amount of information? Whether a dance can contain a message? Whether a dance can contain a message? A “posture” - a phase of a movement during which the relative positions of some body parts remain unchanged We decompose the kinematic signal into a few hierarchically ordered localized coherent modes – postures and trajectories – and study its complexity

To identify the spatio-temporal characteristics of ballet figures, we collected 3D kinematic data (557 trials processed) using a VICON motion capture system with 12 infrared cameras tracked the movement of 42 passive retro-reflective body markers placed at selected points of the body by an expert, for the basic ballet movements, performed by 11 students (aged years, 9 girls) aspiring to a career of professional dancers, as well as the two professional dancers (1 man, 1 woman).

LFHDRFHDLBHDRBHD C7 T10 CLAV LSHO RSHO RBAK RSHO STRN RELB RUPA RFRA RFIN RWRB LPSI RPSI RTHI RWRA LASIRASI LFIN LWRA RWRA LELB LUPA LFRA RKNE RKNELKNE LTHI RTIBLTIBRTIB RTOE RANK LANK LTOE RHEE LHEE

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

D = 1 u 1 v* 1 +  2 u 2 v* 2 +  3 u 3 v* 3 +… 1 u 1 v* 1 1 u 1 v* 1 2 u 2 v* 2 2 u 2 v* 2 3 u 3 v* 3 3 u 3 v* 3 5 turn pirouette

D 1 = 1 u 1 v* 1 5 turn pirouette

D 2 = 1 u 1 v* 1 +  2 u 2 v* 2 5 turn pirouette

D 3 = 1 u 1 v* 1 +  2 u 2 v* 2 +  3 u 3 v* 3 5 turn pirouette

Phase portraits of markers in a pirouette coordinatecoordinatecoordinatecoordinate coordinatecoordinatecoordinatecoordinate velocityvelocityvelocity

1 st configuration Dynamical phenogram of markers in pirouettes neighbor-joining clustering method time path D 1 = 1 u 1 v* 1 The phenogram represents the hierarchy of paths along the trajectories of the 1 st configuration.

3 rd configuration neighbor-joining clustering method Dynamical phenogram of markers in pirouettes UPGMA (Unweighted Pair Group Method with Arithmetic Mean) elbows wrists fingers Right leg Left foot head 3 u 3 v* 3 3 u 3 v* 3

1  2  3N ≥ 0 Complexity via scaling factors Pirouette: 2 professionals & 1 student D =∑ uv* D =∑ k k u k v* kGevorgAdeline a student

1  2  3N ≥ 0 Entropy of trajectories

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

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. 1. Cut off translations and dilatations:

2. Subtraction of mean rotations: Procrustes analysis

Assemblé Sauté

Signal profiles help to indentify the quality of performance Pirouette

configuration energy

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

A concluding metaphor Cape Verde Islands, Atlantic Wind flow von Karman cloud streets