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What is the Jacobian, and how does it relate to VBM and regional gray matter volume or density?
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Jacobian
In neuroimaging, we use the term “Jacobian” to mean the determinant of the Jacobian matrix, which is a term from vector calculus. The Jacobian matrix is calculated at each voxel as a vector representation of the deformation field (“field” for short) represented by the a warping - usually spatial normalization. Think of the “field” as a vector (x,y,z) that describes the direction and size of warping that voxel has to undergo to be moved into normalized space.
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