Before revision: Topological descriptors  have been shown to be useful for summarizing and differentiating shapes . Related work uses persistence diagrams and Euler characteristic curves to differentiate between shapes and quantifies the number of descriptorsnecessary for shape reconstruction, given certain assumptions such as minimum curvature .
After revision: Topological descriptors , such as persistence diagrams and Euler characteristic curves, have been shown to be useful for summarizing and differentiating shapes . Related work uses persistence diagrams and Euler characteristic curves to differentiate between shapes and quantifies the number of descriptorsnecessary for shape reconstruction, given certain assumptions such as minimum curvature .