Abstract
The paper presents the results of research on the development of a framework and new tools for perceptually oriented visualization of human motion, in particular, a gait. Presented in this paper are new tools for visualizing motion and gait of a human. Their implementation is based on the following principles: i) translational motion component is omitted and time-varying orientations of individual parts of the body are represented by the trajectories of quaternions, ii) the trajectories of quaternions are visualized using a maps: S 3 → ℝ 3 implemented as: orthogonal projection, stereographic projection, Hopf transformation. This paper describes only the basic functionalities of the tool, the rest are easy to elicit from the main application screen. Rotations of a rigid body represented by the ”3D one” about an axis defined by selected vector are presented as an example of using the tool and to facilitate understanding of motion visualization. Finally the exemplary gait visualisations based on three different maps for healthy subjects and patients with impaired movement are presented. Trial carried out using data from the gait laboratory HML show that the best approach to qualitative and quantitative analysis is based on using orthogonal projection. Other types of maps like Hopf and stereographic are difficult to interpret and may be useful in more specific cases.
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References
Carson, M.C., Harrington, M.E., Thompson, N., O’Connor, J.J., Theologis, T.N.: Kinematic analysis of a multi-segment foot model for research and clinical applications: a repeatability analysis. Journal of Biomechanics 34, 1299–1307 (2001)
Eberly, D.: A Linear Algebraic Approach to Quaternions. Magic Software (2002)
Eberly, D.: Quaternion Algebra and Calculus. Magic Software Inc. (2002)
Hanson, A.J.: Visualizing Quaternions. Course Notes for SIGGRAPH 1999 (1999)
Hanson, A.J.: Visualizing Quaternions. Elsevier (2006)
Hanson, A.J., Ishkov, K., Ma, J.: Meshview: Visualizing the Fourth Dimension. Computer Science Department, Indiana University
Hanson, A.J.: Quaternion Rotation Demo, http://www.elsevierdirect.com/Companions/9780120884001/vq/QuatRot/
Hanson, A.J.: Quaternion-Maps, http://www.elsevierdirect.com/companions/9780120884001/vq/Quaternion-Maps/
Hart, J.C., Francis, G.K., Kauffman, L.H.: Visualizing Quaternion Rotation. ACM Transactions on Graphics (1994)
Hart, J.C.: Quaternion Demonstrator, http://graphics.stanford.edu/courses/cs348c-95-fall/software/quatdemo/
Johnson, M.P.: Exploiting Quaternions to Support Expressive Interactive Character Motion. PhD thesis, Massachusetts Institute of Technology (1995)
Vedenev, M.: Quaternions Visualizations in Matlab, http://quaternion.110mb.com
Mosseri, R., Dandoloff, R.: Geometry of entangled states, Bloch spheres and Hopf fibrations. Journal of Physics A: Mathematical and General 34, 10243–10252 (2001)
Gregory, R., Harvey, J.A., Moore, G.: Unwinding strings and T-duality of Kaluza-Klein and H-Monopoles. Advances in Theoretical and Mathematical Physics 1, 283–297 (1997)
Marsden, J., Ratiu, T.: Introduction to Mechanics and Symmetry. Springer, New York (1982)
Szczęsna, A., Słupik, J., Janiak, M.: Quaternion Lifting Scheme for Multi-resolution Wavelet-based Motion Analysis. In: Proceedings of the 1st International Workshop on Computer Vision and Computer Graphics, ThinkMind, ICONS 2012, pp. 223–228 (2012)
Świtoński, A., Stawarz, M., Boczarska-Jedynak, M., Sieroń, A., Polański, A., Wojciechowski, K.: The effectiveness of applied treatment in Parkinson disease based on feature selection of motion activities. Przegląd Elektrotechniczny 88(12b) (2012) ISSN 0033-2097
Stawarz, M., Polański, A., Kwiek, S., Boczarska-Jedynak, M., Janik, Ł., Przybyszewski, A., Wojciechowski, K.: A System for Analysis of Tremor in Patients with Parkinson’s Disease Based on Motion Capture Technique. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds.) ICCVG 2012. LNCS, vol. 7594, pp. 618–625. Springer, Heidelberg (2012)
Stawarz, M., Kwiek, S., Polański, A., Janik, Ł., Boczarska-Jedynak, M., Przybyszewski, A., Wojciechowski, K.: Algorithms for Computing Indexes of Neurological Gait Abnormalities in Patients After DBS Surgery for Parkinson Disease Based on Motion Capture Data. Machine Graphics & Vision, Special Issue (2012)
Szczęsna, A., Słupik, J., Janiak, M.: Quaternion Lifting Scheme for Multi-resolution Wavelet-based Motion Analysis. In: Proceedings of the First International Workshop on Computer Vision and Computer Graphics, VisGra 2012 (2012)
Szczęsna, A., Słupik, J., Janiak, M.: Denoising Motion Data Based on the Quaternion Lifting Scheme Multiresolution Transform. Machine Graphic & Vision, Special Issue (2012)
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Pęszor, D., Małachowski, D., Drabik, A., Nowacki, J.P., Polański, A., Wojciechowski, K. (2014). New Tools for Visualization of Human Motion Trajectory in Quaternion Representation. In: Nguyen, N.T., Attachoo, B., Trawiński, B., Somboonviwat, K. (eds) Intelligent Information and Database Systems. ACIIDS 2014. Lecture Notes in Computer Science(), vol 8398. Springer, Cham. https://doi.org/10.1007/978-3-319-05458-2_59
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DOI: https://doi.org/10.1007/978-3-319-05458-2_59
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