Patent ID: 8275204

Claim:
A method for estimating the joint radiometric and geometric deformations of an image of an object using a radiometry-first approach comprising: (a) analyzing a first observation h of an image, about a known m-dimensional signal g, of the form h ( x )= Q ( g ( A ( x )))+η( x ) =Q∘g∘A+η, where Q is a non-linear mapping of the intensities (radiometry), A is an affine (geometric) transformation, and η is an additive noise; (b) estimating the joint radiometric and geometric deformations of the first observation without limitations on the magnitude of the geometric or radiometric deformations; and (c) analyzing the deformations of the first observation in comparison to a second observation of an object to determine whether the first observation and the second observation are of the same object; wherein (i) the sample distribution transformation T is invariant under right-hand affine compositions: T(g∘A)=Tg, and T(W∘g)=[Tg]∘W −1 for any strictly increasing continuous function W:R→R such that W(0)=0; (ii) applying T to the (noiseless) relation h=Q∘g∘A, to obtain Th=[Tg]∘Q −1 ; (iii) using the transformation T to convert a functional relation expressed by a left-hand composition (“radiometric deformation”) into a new functional relation expressed by a right-hand composition (“geometric deformation”) so equation H(t)=[G∘Q −1 ](t)=G(Q −1 (t)) describes a new, one-dimensional, “time-domain” registration problem and any suitable (parametric or non-parametric) registration method may be used to recover (estimate) Q −1 ; (iv) producing linear constraints on Q, enabling the explicit recovery of Q −1 in terms of solving a linear system of equations, as follows: ∫ R ⁢ wo ⁢ H ~ = [ ∫ R ⁢ e 1 ⁡ ( wo ⁢ G ~ ) ⁢ L ⁢ ∫ R ⁢ e M ⁡ ( wo ⁢ G ~ ) ] ⁢ [ b 1 ⋮ b M ] (v) once the radiometric deformation Q (or equivalently its inverse Q −1 ) is recovered, rewriting h=Q∘g∘A, as h = ( Q ∘ g ) ︸ known ∘ A ; and (vi) reducing the problem to a strictly geometric problem where A is recovered.