Challenges in Reconstructing Shapes from Euler Characteristic Curves

Understand

Shape recognition and classification is a problem with a wide variety of applications.

• Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances.
• In this abstract, we explore the use of a finite number of Euler Characteristic Curves (ECC) to reconstruct plane graphs.
• We highlight difficulties that occur when attempting to adopt approaches for reconstruction with persistence diagrams to reconstruction with ECCs.