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P. Dlotko, W. Kropatsch, H. Wagner:
"Characterizing Obstacle- Avoiding Paths using Cohomology Theory";
Talk: CAIP 2011 - 14th International Conference on Computer Analysis of Images and Patterns, Seville, Spanien; 2011-08-29 - 2011-08-31; in: "Lecture Notes in Computer Science", Proc. CAIP 2011 - 14th International Conference on Computer Analysis of Images and Patterns, LNCS 6854, Ainhoa Berciano et al. Eds./Springer, Seville, Spanien (2011), ISBN: 978-3-642-23671-6; 310 - 317.

In this paper, we investigate the problem of analyzing the
shape of obstacle-avoiding paths in a space. Given a d-dimensional space
with 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 topologically
different paths. A compact yet complete signature of a path is
constructed, based on cohomology theory. Possible applications include
assisted living, residential, security and environmental monitoring. Numerical
results will be presented in the final version of this paper.

obstacle-avoidance, cohomology generators, trajectory planning problem.