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Global registration of multiple 3D point sets via optimization on a manifold

  • US 7,831,090 B1
  • Filed: 06/30/2006
  • Issued: 11/09/2010
  • Est. Priority Date: 06/30/2006
  • Status: Expired due to Fees
First Claim
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1. A method for registering a plurality of 3D point sets by determining optimal relative positions and orientations of the 3D point sets, comprising:

  • generating, by one or more scanners, a plurality of 3D point sets, each 3D point set representing a view of a surface of an object;

    determining initial values of rotation matrices corresponding to the 3D point sets based on correspondence values of the 3D point sets;

    optimizing a cost function on a product manifold of the rotation matrices using the initial values to determine optimal values of the rotation matrices; and

    calculating optimal values of translation vectors corresponding to the 3D point sets based on the optimal values of the rotation matrices;

    wherein the optimizing step comprises;

    calculating updated values of the rotation matrices based on the initial values to reduce a value of the cost function;

    determining whether the cost function is locally minimized based on the updated values;

    if the cost function is not minimized, setting the initial values to be the updated values and repeating the optimizing step; and

    if the cost function is minimized, determining the updated values to be the optimal values of the rotation matrices;

    wherein the step of calculating updated values of the rotation matrices comprises;

    constructing a local approximation of the cost function in a neighborhood of the initial values on the product manifold;

    calculating a gradient of the local approximation of the cost function;

    calculating a Hessian of the local approximation of the cost function;

    calculating a descent direction based on the gradient of the local approximation of the cost function and the Hessian of the local approximation of the cost function;

    calculating a step length to reduce the cost function based on the calculated descent direction; and

    calculating the updated values on the product manifold using the descent direction and the step length.

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