Standard Formula for the Uniform Shape Component in Landmark Data

摘要: In describing how the shapes of landmark configurations vary, an important role is played by uniform component shape variation. Geometrically, parameterizes changes that leave parallel lines throughout form and so show neither a spatial gradient nor any localization. Algebraically, produced from mean in this way make up linearized subspace, U, our multivariate space vicinity mean, particular corresponds to specimen or group difference can be computed as pair scores (for two-dimensional data) quintet three-dimensional Procrustes projection onto U. The versions crucial are offered currently available program packages inconsistent several aspects. This paper suggests resolution contradictions among these approaches. I introduce nearly exact version it identical two separate previously suggested literature represents more precise estimate for yet another. A somewhat different useful statistical testing. computations demonstrated using growing rat skull data set familiar other canonical demonstrations new geometric methods.