Shape analysis is a mathematical framework that focuses on the study of geometric shapes and their properties, particularly how they can be represented, compared, and transformed. This field is crucial for understanding the underlying structure of Riemannian metrics, as it allows for the quantification of shapes in a way that respects the geometric features encoded in the metric. By examining shapes in this context, we can gain insights into their intrinsic properties and how they interact with one another under various transformations.
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