04 December 2020 3 4K Report

Hi everyone,

Im hoping someone can help me better understand the inner workings of the singular value decomposition (SVD).

Given a set of 3D points, I can find and fit the best plane by:

  • representing each point (p) as a N x 3 matrix
  • establishing the centroid (c) of the points
  • translating each point about the centroid (i.e., p - c)
  • using the SVD to evaluate the plane normal (n)

    • While it's clear that the procedural steps allow for the evaluation of p.n = 0, which satisfies the equation of a plane, could anyone break down how the SVD computes the best normal for the plane? Thanks in advance.

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