In this paper, we investigate the problem of analyzing theshape of obstacle-avoiding paths in a space. Given a d-dimensional spacewith holes, representing obstacles, we ask if certain paths are equivalent,informally if one path can be continuously deformed into another,within this space. Algebraic topology is used to distinguish between topologicallydifferent paths. A compact yet complete signature of a path isconstructed, based on cohomology theory. Possible applications includeassisted living, residential, security and environmental monitoring. Numericalresults will be presented in the final version of this paper.


Dlotko, P., Kropatsch, W., & Wagner, H. (2011). Characterizing Obstacle- Avoiding Paths using Cohomology Theory. In Lecture Notes in Computer Science (pp. 310–317). Proc. CAIP 2011 - 14th International Conference on Computer Analysis of Images and Patterns, LNCS 6854, Ainhoa Berciano et al. Eds./Springer. http://hdl.handle.net/20.500.12708/53908