Normal Distribution on the Rotation Group So(3)

By D. Nikolayev, Tatjana I. Savyolov. 1997

We study the normal distribution on the rotation group SO(3). If we take as the normal distribution on the rotation group the distribution defined by the central limit theorem in Parthasarathy (1964) rather than the distribution with density analogous to the normal distribution in Eucledian space, then its density will be different from the usual (1/2πσ) exp⁡(−(x−m)2/2σ2) one. Nevertheless, many properties of this distribution will be analogous to the normal distribution in the Eucledian space. It is possible to obtain explicit expressions for density of normal distribution only for special cases. One of these cases is the circular normal distribution.

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Citations in the corpus

DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking (2022, methodology): “The diffusion kernel on SO (3) is given by the IGSO (3) distribution [10, 11] and its score is ) , where R ′ = R ( ω ˆ ω ) R is the result of applying Euler vector ω ˆ ω to R .”
SE(3) diffusion model with application to protein backbone generation (2023, unknown): “3.3 agrees with previous proposed expressions of the law of the Brownian motion (Nikolayev & Savyolov, 1970; Leach et al., 2022) up to a two-fold deceleration of time.”