Fusion of images with same or different modalities has been conquering medical imaging field more rapidly due to the presence of highly accessible patients’ information in recent years. For example, cross platform non-rigid registration of CT with MRI images has found a significant role in different clinical application. In some instances labelling of anatomical features by medical experts are also involved to further improve the accuracy and authenticity of the registration. Being motivated by these, we propose a new algorithm to compute diffeomorphic hybrid multi-modality registration with large deformations. Our iterative scheme consists of mainly two steps. First, we obtain the optimal Beltrami coefficient corresponding to the diffeomorphic mapping that exactly superimposes the feature points. The second step detects the intensity difference in the framework of mutual information. A non-rigid deformation which minimizes the intensity difference is then obtained. Experiments have been carried out on both synthetic and real data. Results demonstrate the stability and efficacy of the proposed algorithm to obtain diffeomorphic image registration.

Let fn → f0 be a convergent sequence of rational maps, preserving critical relations, and f0 be geometrically finite with parabolic points. It is known that for some unlucky choices of sequences fn,the Julia sets J(fn) and their Hausdorff dimensions may fail to converge as n → ∞. Our main result here is to prove the convergence of J(fn) and H.dim J(fn) for generic sequences fn. The same conclusion was obtained earlier, with stronger hypotheses on the sequence fn, by Bodart-Zinsmeister and then by McMullen. We characterize those choices of fn by means of flows of appropriate polynomial vector fields (following Douady-Estrada-Sentenac). We first prove an independent result about the (s-dimensional) length of separatrices of such flows, and then use it to estimate tails of Poincar´e series. This, together with existing techniques,provides the desired control of conformal densities and Hausdorff dimensions. Our method may be applied to other problems relatedto parabolic perturbations.

We carry out the programme of R. Liouville [19] to construct an explicit local obstruction to the existence of a Levi–Civita connection within a given projective structure [..] on a surface. The obstruction is of order 5 in the components of a connection in a projective class. It can be expressed as a point invariant for a second order ODE whose integral curves are the geodesics of [..] or as a weighted scalar projective invariant of the projective class. If the obstruction vanishes we find the sufficient conditions for the existence of a metric in the real analytic case. In the generic case they are expressed by the vanishing of two invariants of order 6 in the connection. In degenerate cases the sufficient obstruction is of order at most 8.

We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn’s linearization theorem.

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