Structural pattern recognition describes and classifies data based on the relationships of features andparts. Topological invariants, like the Euler number, characterize the structure of objects of any dimension.Cohomology can provide more refined algebraic invariants to a topological space than does homology.It assigns 'quantities' to the chains used in homology to characterize holes of any dimension. Graphpyramids can be used to describe subdivisions of the same object at multiple levels of detail. This paperpresents cohomology in the context of structural pattern recognition and introduces an algorithm to efficientlycompute representative cocycles (the basic elements of cohomology) in 2D using a graph pyramid.An extension to obtain scanning and rotation invariant cocycles is given.


Gonzalez-Diaz, R., Ion, A., Iglesias-Ham, M., & Kropatsch, W. G. (2011). Invariant representative cocycles of cohomology generators using irregular graph pyramids. Computer Vision and Image Understanding, 115(7), 1011–1022. https://doi.org/10.1016/j.cviu.2010.12.009