The Topological gesture analysis is a method developed to analyse the topology or the quality of the space of dance gestures in relation to music. The process is another example of cross-modal method that uses information from music and movement (dance) to uncover relationships between music and dance forms in the choreography.
The second figure illustrates the main processes. First the music used in the dance performance is analyzed and relevant cues or markers are collected. These cues can have categories such as the levels of musical meter, used in my PhD research. The idea is to project these cues onto the trajectories of dance body at the same time points remember that music is synched with dance). If the choreography is organized in space according to these cues, it is expected that these categories of cues form point clouds. Further, we can generalized these point clouds in form of simple structures (e.g.: a sphere in figure 4) or more complex structures (e.g.: a convexhull in figure 1). Lobato et al. (2010) used these generalizations to re-synthesize dance movements. In my work I used to analyze the relationship between samba music and dance (Naveda & Leman, 2010), expertise (Naveda & Leman, 2010), and derive theoretical hypotheses (Naveda & Leman 2011).
The video below illustrates the processes involved (see here) for a video translated in Portuguese)