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.
"Fake uniformity in a shape inversion formula." Braz. J. Probab. Stat. 33 (3) 549 - 557, August 2019. https://doi.org/10.1214/18-BJPS402