Cohomological learning of periodic motion

  • Mikael Vejdemo-Johansson
  • Florian T. Pokorny
  • Primoz Skraba
  • Danica Kragic
Original Paper


This work develops a novel framework which can automatically detect, parameterize and interpolate periodic motion patterns obtained from a motion capture sequence. Using our framework, periodic motions such as walking and running gaits or any motion sequence with periodic structure such as cleaning, dancing etc. can be detected automatically and without manual marking of the period start and end points. Our approach constructs an intrinsic parameterization of the motion and is computationally fast. Using this parameterization, we are able generate prototypical periodic motions. Additionally, we are able to interpolate between various motions, yielding a rich class of ‘mixed’ periodic actions. Our approach is based on ideas from applied algebraic topology. In particular, we apply a novel persistent cohomology based method for the first time in a graphics application which enables us to recover circular coordinates of motions. We also develop a suitable notion of homotopy which can be used to interpolate between periodic motion patterns. Our framework is directly applicable to the construction of walk cycles for animating character motions with motion graphs or state machine driven animation engines and processed our examples at an average speed of 11.78 frames per second

Graphical abstract


Periodic motions Circular coordinates Persistent cohomology   Walk cycles Gait parameterization Topological data analysis 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Mikael Vejdemo-Johansson
    • 1
    • 2
  • Florian T. Pokorny
    • 2
  • Primoz Skraba
    • 1
  • Danica Kragic
    • 2
  1. 1.AI LaboratoryJožef Stefan InstituteLjubljanaSlovenia
  2. 2.Computer Vision and Active Perception LabKTH Royal Institute of TechnologyStockholmSweden

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