DEVELOPING FOURIER-BASED MODEL USING FEW VARIABLES OBTAINED BY PRINCIPAL COMPONENT ANALYSIS IN RUNNING AT DIFFERENT SPEEDS

Yıl 2010, Cilt: 21 Sayı: 1, 1 - 12, 01.02.2010

Murat Çilli , Serdar Arıtan

Öz

Most of the recent studies focus on human walking and running movements which we often use in daily life and many athletics events. Aim of the study is to reduce dimension of kinematics data by using Principal Component Analysis method and describing human motion at different velocities by low dimensional Fourier model. In order to collect kinematics data of running movement a short distance runner (age:26, height:1.82m, kilo:76kg) was asked to run on treadmill at 8km/h, 12km/h and 16km/h running speed and 6 strides were captured. Principal Components of data including instantaneous postures which were described 3D position values of 16 anatomical markers attached on subject. It was observed that first four Principal Components can cover over 98% of original data and Running at different velocities can be effectively defined by using low-dimensional Fourier series. It was observed that the original spatial locations of the anatomical points which constitute the postures in each instant are coherent with the locations derived from the constructed running model (8km/h, R=0.97, 12km/h, R=0.94 and 16km/h, R=0.93). In this study, it has been determined that human running at varying speeds can be defined with lower dimensional data by modeling the behaviors of the first 4 components derived by using PCA method. Although components derived from PCA do not correspond to a parameter in reality, it can be seen that the second component represents the motion of the feet, the third component represents the motion of the arms and fourth component represents bouncing structure in the running process. The PCs identified in the data belonging to larger amounts of individuals and various positions, can make it possible to classify, analyze, diagnose, compare and collate between movement positions depending on different situations such as gender, running velocity, fatigue, physical structure, injury and well arrangement of technique.

Anahtar Kelimeler

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TEMEL BİLEŞENLER ANALİZİ YARDIMI İLE ELDE EDİLEN DAHA AZ SAYIDA DEĞİŞKEN KULLANILARAK FARKLI HIZLARDA İNSAN KOŞUSUNUN FOURİER TABANLI MODELİNİN OLUŞTURULMASI.

Öz

Günümüzde gerçekleştirilen çalışmaların bir çoğu günlük yaşantımızda ve birçok spor branşında en sık kullandığımız yürüme ve koşu hareketleri üzerine yoğunlaşmaktadır. Bu çalışmada hareket analizi sistemlerinden elde edilen yüksek boyutlardaki kinematik veri setinin boyutlarının Temel Bileşenler Analizi (TBA) yöntemi kullanılarak indirgenmesi ve daha az sayıdaki yeni değişkenler ile farklı koşu hızları için Fourier tabanlı koşu modeli oluşturularak modelde yer alan parametrelerin koşu yapısı üzerindeki etkilerinin incelenmesi amaçlanmıştır. Farklı hızlardaki (8km/s, 12km/s ve 16km/s) koşu hareketine ait kinematik verilerin elde edilmesi amacıyla kısa mesafe koşucusu olan bir atlet (yaş:26, boy:1.82m, kilo:76kg) koşu bandında koşturularak ardışık 6 adımına ait veriler kullanılmıştır. Denek üzerinde işaretlenen 16 anatomik işarete ait 3 Boyutlu (3B) konum değerleri yardımı ile tanımlanan anlık duruşlardan oluşan veri setlerinin temel bileşenleri hesaplanmıştır. İlk dört temel biaçıklaleşenin veri setlerinin %98'inden fazlasını temsil edebildiği gözlenmiştir. Ortalama duruş olarak adlandırılan ilk bileşen ve izleyen ilk 3 bileşenin doğrusal kombinasyonu olarak ifade edilen düşük boyutlardaki Fourier tabanlı koşu modelinin, farklı hızlardaki koşu hareketinin tümü hakkında önemli bilgileri kapsadığı gözlenmiştir. Her bir andaki duruşları oluşturan anatomik noktaların gerçek uzaysal konumları ile ilk 4 bileşen kullanılarak oluşturulan koşu modelinden elde edilen konumların birbirleriyle uyumlu oldukları (8km/s için R=0.97, 12km/s için R=0.94 ve 16km/s için R=0.93) gözlenmiştir. Bu çalışmada insan koşusunun TBA yöntemi ile elde edilen ilk dört bileşenin davranışları modellenerek daha düşük boyutlarda veri setleri ile ifade edilebileceği gözlenmiştir. Her ne kadar TBA'dan elde edilen bileşenler gerçekte bir değişkene karşılık gelmesede, birinci bileşenin ortalama duruş bilgisini ikinci bileşenin ayakların salınımını, üçüncü bileşenin kolların salınımını ve dördüncü bileşenin ise koşunun sıçrama özelliğini temsil edebildikleri düşünülmektedir. Daha fazla sayıdaki birey ve cinsiyet, koşu hızı, yorgunluk, fiziksel yapı, sakatlık, tekniğin düzgünlüğü gibi farklı durumlara ait koşu verileri kullanılarak oluşturulan düşük boyutlardaki koşu modellerinin, sınıflama, analiz, teşhis, karşılaştırma ya da hareket durumları arasında harmanlama yapılabilmesine olanak sağlayacağı düşünülmektedir.

Anahtar Kelimeler

İnsan koşusu, Temel bileşenler analizi, Fourier analizi

Kaynakça

• Ariel BG. (1968). ARIEL Performance Analysis System (APAS) [Bilgisayar yazılımı]. Ariel Dynamics, San Diego: USA.
• Aggarwal JK, Cai Q. (1999). Human motion analysis: a review. Computer Vision and Image Understanding, 73, 428–440.
• Alexander RMc. (2003). Modelling approaches in biomechanics. Philosophical Transactions of the Royal Society London, 358, 1429-1435.
• Amaya K, Bruderlin A, Calvert T. (1996). Emotion from Motion, Graphics Interface ‘96, pp. 222-229.
• Bokman L, Syungkwon R, Park FC. (2005). 2005 IEEE International Conference on Robotics and Automation: Movement primitives, principal component analysis, and the efficient generation of natural motions. Barcelona, Spain.
• Borzelli G, Cappizzo A, Papa E. (1999). Inter- and intra-individual variability of ground reaction forces sit-to-stand with principal component analysis. Medical Engineering&Physics, 21, 235-240.
• Boyle RD. (1998). Scaling additional contributions to principal component analysis, Pattern Recognition, 31, 2047–2053.
• Chen CY, Lee RCT. (1995). A near pattern-matching scheme based upon principal components analysis. Pattern Recognition, 16, 339–345.
• Çilli M, Arıtan, S. (2005). 10th Annual Congress European College of Sport Science: PCA application for modeling and simulation of running patterns. Sirbistan: Belgrade, 13–16 July.
• Çilli M, Arıtan S. (2007). Çok boyutlu kinematik verilerin analizinde temel bileşenler analizi yönteminin kullanılması. Spor Bilimleri Dergisi , 18 (4), 156-166.
• Collins JJ, De Luca CJ. (1993). Open-loop and closedloop control of posture: a random-walk analysis of center-of-pressure trajectories. Experimental Brain Research, 95, 308–318.
• Daffertshofer, A, Lamoth JC, Meijer OG, Beek PJ. (2004). PCA in studying coordination and variability: a tutorial. Clinical Biomechanics, 19, 415-428.
• Hatze H. (1980). A mathematical model for the computational determination of parameter values of anthropomorphic segments. Journal of Biomechanics, 13, (10), 833-843.
• Hollands K, Wing A, Daffertshofer A. (2004). 3rd IEEE EMBSS UK &RI PostGraduate Conference in Biomedical Engineering & Medical Physics: Principal Components Analysis of Contemporary Dance Kinematics. Southampton: University of Southampton, 10-11 August.
• Jason J, Kutch T, Buchanan S. (2002). Fourth World Congress of Biomechanics. Self-organizing maps and the representation of emg signals in terms of muscular synergies, Calgary, Alberta, Canada, 4-9 August.
• Karhunen J, Joutsensalo J. (1995). Generalizations of principal component analysis, optimization problems, and neural networks. Neural Networks, 8, 549–562.
• Kudoh S. (2004). Balance maintenance for human-like models with whole body motion. ( Doctral Thesis, 2005). The Department of Computer Science the Graduate School of Information Science and Technology the University of Tokyo.
• Manly BFJ. (1992). Multivariate Statistical Methods A Premier. London: Chapman & Hall.
• MATLAB [ Bilgisayar Yazılımı], Mathworks Inc., Natick: Ma, USA.
• Murase H, Nayar SK. (1993). In: Fall Symposium: Machine Learning In Computer Vision: Learning and recognition of 3-D objects from brightness images. Raleigh, North Carolina, Fall, 22-24 October.
• Nayar SK, Poggio T. (1996). Early visual learning. Oxford University Press, New York.
• Ormoneit D, Black MJ, Hastie T, Kjellstro¨m H. (2005). Representing cyclic human motion using functional analysis. Image and Vision Computing, 23, 1264–1276.
• Pinkowski B. (1997). Principal component analysis of speech spectrogram images. Pattern Recognition, 30, 777–787.
• Ramsay JO, Munhall KG, Gracco VL, Ostry DJ. (1996). Functional data analyses of lip motion. Journal of the Acoustical Society of America, 99(6), 3718-27.
• Rash G, Campbell K. (2002). Fundamentals of equipment and methodology, Retrieved June 10, 2003, from http://www.gcmas.org/basic_documents.html
• Rodtook S, Rangsanseri Y. (2001). International Conference of information technology coding and computing: Adaptive thresholding of document images based on Laplacian sign.Las Vegas: Nevada, 2-4 April.
• Rosales R, Scarloff S. (2000). IEEE Computer Society Workshop on Human Motion: Specialized mappings and the estimation of human body pose from a single image. Austin, TX, 19-24.
• Sanger TD. (2000). Human Arm Movements Described by a Low-Dimensional Superposition of Principal Components. The Journal of Neuroscience, 20(3), 1066–1072.
• Sanjeev D, Nandedkar D, Sanders B. (1989.). Principal component analysis of the features of concentric needle EMG motor unit action potentials. Muscle & Nerve, John Wiley & Sons, Inc., 12(4), 288 – 293.
• Santello M, Flanders M, Soechting JF. (1998). Postural Hand Synergies for Tool Use. The Journal of Neuroscience, 18(23), 10105–10115.
• Troje FN. (2002a). Decomposing biological motion: A frame work for analysis and synthesis of human gait pattern. Journal of Vision, 2, 371-387.
• Troje FN. (2002b). The little difference: Fourier based synthesis of genderspecific biological motion, In: Rolf P. Würtz, Markus Lappe (Eds.),Dynamic Perception, Berlin: AKA Press, 2002, pp 115-120.
• Unuma M, Anjyo K, Takeuchi R. (1995). Fourier Principles for Emotion-based human Figure Animation. Hitachi Research Laboratory, Hitachi Ltd. ACM.
• Winter DA, Sidwall HG, Hobson DA. (1974), Measurement and reduction of noise in kinematics of locomotion. Journal of Biomechanics, 7, 157-159.
• Yamamoto S, Suto Y, Kawamura H, Hashizume T, Kakurai S, Sugahara S. (1983). Quantitative gait evaluation of hip diseases using principal component analysis. Journal of Biomechanics, 16, (9), 717–726.
• Yamato J, Ohya J, Ishii K. (1992). Recognizing human action in time sequential images using Hidden Markov Model, in Proc. IEEE Conf. CVPR, Champaign, IL, pp. 379–385.
• Yeadon MR. (1990). The simulation of aerial movement- II. A mathematical inertia model of the human body. Journal of Biomechanics, 23, 67-74.
• Zhang Z, Troje FN. (2004). 3D periodic human motion reconstruction from 2D motion sequences, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW’04), 1063-6919/04 IEEE.
• Zhang H, Zhang LO. (2005). ECG analysis based on PCA and Support Vector Machines. International Conference on Neural Networks and Brain ICNN&B ‘05, 2, 743- 747.