TL;DR
This paper examines a shape inversion formula related to particle density estimation, revealing a distribution that mimics the uniform Haar distribution, thus challenging assumptions in the original method.
Contribution
It introduces a distribution that fakes the Haar uniformity in a shape inversion context, highlighting potential pitfalls in the existing formula.
Findings
Identifies a distribution that imitates Haar uniformity
Challenges assumptions in the shape inversion formula
Provides insights into particle density estimation methods
Abstract
We revisit a shape inversion formula derived by Panaretos in the context of a particle density estimation problem with unknown rotation of the particle. A distribution is presented which imitates, or 'fakes', the uniformity or Haar distribution that is part of that formula.
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