IEEE Trans Image Process - Geodesic active fields--a geometric framework for image registration.

Tópicos

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Resumo

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.

Resumo Limpo

paper present novel geometr framework call geodes activ field general imag registr imag registr one look under deform field best map one imag onto anoth classic illpos invers problem usual solv ad regular term propos multipl coupl registr term regular term turn equival emb deform field weight minim surfac problem deform field driven minim flow toward harmon map correspond solut registr problem propos approach registr share close similar wellknown geodes activ contour model imag segment segment term edg detector function coupl regular term length function via multipl well matter fact propos geometr model actual exact mathemat general vector field weight length problem curv surfac introduc caselleskimmelsapiro energi deform field measur polyakov energi weight suitabl imag distanc borrow standard registr model investig three differ weight function squar error approxim absolut error monomod imag local joint entropi multimod imag compar special stateoftheart method tailor specif applic geometr framework involv import contribut first general formul registr work parametriz smooth differenti surfac includ nonflat multiscal imag latter case multiscal imag regist scale simultan relat space scale intrins account second method best knowledg first reparametr invari registr method introduc literatur third multipl coupl registr term ie local imag discrep regular term natur result datadepend tune regular strength final choos metric deform field one can freeli interpol classic gaussian interest anisotrop tvlike regular

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