Persistent Barcodes for Shapes by Gunnar Carlsson, Afra Zomorodian, Anne Collins and Leonides Guibas (Eurographics Symposium on Geometry Processing, 2004).
This is a meaty paper with an express purpose of introducing us to topology concepts that help us classify shapes based on their global connectedness. The authors aim to leverage local and global information to characterize shapes. A core concept introduced is that of the filtered tangent complex, which is a family of spaces paramterized by curvature. A story of the curvature of the space at every point. A family of spaces paramerterized by curvature. When we apply our tools of homology to this family of spaces we can derive a persistence module that reveals even further information about a space.
The applications the authors suggest that the application to makng sesne of noisy data is possible. Including coordinating spaces.