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The [[Jacobian]] ''J'' is the determinant

i.e. the inverse magnification factor equals the absolute value of the Jacobian determinant of the transformation described As the Jacobian determinant above approaches zero, the magnification factor becomes infinit

The [[Jacobian]] (Jacobi determinant) of this transformation from [[Cartesian coordinates]

...V) in the original brain can be calculated by multiplying the GMD with the Jacobian determinants of the deformations used to register the brain to the template ...metimes referred to as Tensor-based morphometry (TBM) -- is based on the [[Jacobian determinant]] of the deformation matrix.

...of the object function be known, but in some situations the derivative or Jacobian may be unavailable or prohibitively expensive to calculate. The cost can be

The weight appearing in the infinitesimal volume element d''V'' is the [[Jacobian]] (the determinant of the Jacobi matrix, which is the square root of the de