Evaluating the Overall amount of Variation in an SSM

[Steven A]

Is there a method to evaluate the coefficients created from a statistical shape model into a single value for overall variation represented within that model?

[Marcel Luethi]

Hi Steven

Yes, there are two different ways to do that: Either you sum up the variances of all the points, or you sum up the eigenvalues of the KL basis. Both should give you the same results (as the eigenvalue associated to the i-th basis function in the KL-Expansion is the amount of variance represented by this basis function).

Here is the corresponding code:

def computeTotalVarianceFromPoints(ssm : StatisticalMeshModel) : Double = {
  val variances = for (pId <- ssm.referenceMesh.pointSet.pointIds) yield {
    // variances (x,y,z) for point with id pId
    breeze.linalg.sum(breeze.linalg.diag(ssm.gp.cov(pId, pId)))
  }
  variances.sum
}

def computeTotalVarianceFromKLBasis(ssm : StatisticalMeshModel) : Double = {
  ssm.gp.klBasis.map(basis => basis.eigenvalue).sum
}

Best regards,

Marcel

On Wed, Jun 16, 2021 at 5:41 PM Steven A <steve...@gmail.com> wrote:

Is there a method to evaluate the coefficients created from a statistical shape model into a single value for overall variation represented within that model?

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[Steven A]

Ok thank you very much.