statistics on diffeomorphisms via tangent space representations in this paper we present a linear setting for statistical analysis of shape and an optimization approach based on a recent derivation of a conservation of momentum law for the geodesics of diffeomorphic flow once a template is fixed the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point along the geodesic is completely determined by the momentum at the origin through geodesic shooting equations the space of initial momentum provides a linear representation of the nonlinear diffeomorphic shape space in which linear statistical analysis can be applied specializing to the landmark matching problem of computational anatomy we derive an algorithm for solving the variational problem with respect to the initial momentum and demonstrate principal component analysis pca in this setting with three dimensional face and hippocampus databases

recognition of white matter bundles using local and global streamline based registration and clustering virtual dissection of diffusion mri tractograms is cumbersome and needs extensive knowledge of white matter anatomy this virtual dissection often requires several inclusion and exclusion regions of interest that make it a process that is very hard to reproduce across experts having automated tools that can extract white matter bundles for tract based studies of large numbers of people is of great interest for neuroscience and neurosurgical planning the purpose of our proposed method named recobundles is to segment white matter bundles and make virtual dissection easier to perform this can help explore large tractograms from multiple persons directly in their native space recobundles leverages latest state of the art streamline based registration and clustering to recognize and extract bundles using prior bundle models recobundles uses bundle models as shape priors for detecting similar streamlines and bundles in tractograms recobundles is 100 streamline based is efficient to work with millions of streamlines and most importantly is robust and adaptive to incomplete data and bundles with missing components it is also robust to pathological brains with tumors and deformations we evaluated our results using multiple bundles and showed that recobundles is in good agreement with the neuroanatomical experts and generally produced more dense bundles across all the different experiments reported in this paper recobundles was able to identify the core parts of the bundles independently from tractography type deterministic or probabilistic or size thus recobundles can be a valuable method for exploring tractograms and facilitating tractometry studies

locally conformal kahler manifolds with potential a locally conformally kahler lck manifold m is one which is covered by a kahler manifold widetilde m with the deck transformation group acting conformally on widetilde m if m admits a holomorphic flow acting on widetilde m conformally it is called a vaisman manifold neither the class of lck manifolds nor that of vaisman manifolds is stable under small deformations we define a new class of lck manifolds called lck manifolds with potential which is closed under small deformations all vaisman manifolds are lck with potential we show that an lck manifold with potential admits a covering which can be compactified to a stein variety by adding one point this is used to show that any lck manifold m with potential dim m 3 can be embedded into a hopf manifold thus improving similar results for vaisman manifolds ornea and verbitsky math ann 332 121 143 2005

labeling of ambiguous subvoxel fibre bundle configurations in high angular resolution diffusion mri whereas high angular resolution reconstruction methods for diffusion mri can estimate multiple dominant fibre orientations within a single imaging voxel they are fundamentally limited in certain cases of complex subvoxel fibre structures resulting in ambiguous local orientation distribution functions in this article we address the important problem of disambiguating such complex subvoxel fibre tract configurations with the purpose of improving the performance of fibre tractography we do so by extending a curve inference method to distinguish between the cases of curving and fanning fibre bundles using differential geometric estimates in a local neighbourhood the key benefit of this method is the inference of curves instead of only fibre orientations to model the underlying fibre bundles this in turn allows distinct fibre geometries that contain nearly identical sets of fibre orientations at a voxel to be distinguished from one another experimental results demonstrate the ability of the method to successfully label voxels into one of the above categories and improve the performance of a fibre tracking algorithm

an intrinsic characterization of kahler manifolds on etudie la condition de kahler pour une variete complexe compacte on caracterise les varietes complexes compactes qui admettent des metriques de kahler

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

complex geometry of moment angle manifolds moment angle manifolds provide a wide class of examples of non kahler compact complex manifolds a complex moment angle manifold mathcal z is constructed via certain combinatorial data called a complete simplicial fan in the case of rational fans the manifold mathcal z is the total space of a holomorphic bundle over a toric variety with fibres compact complex tori in general a complex moment angle manifold mathcal z is equipped with a canonical holomorphic foliation mathcal f which is equivariant with respect to the mathbb c times m action examples of moment angle manifolds include hopf manifolds of vaisman type calabi eckmann manifolds and their deformations we construct transversely kahler metrics on moment angle manifolds under some restriction on the combinatorial data we prove that any kahler submanifold or more generally a fujiki class mathcal c subvariety in such a moment angle manifold is contained in a leaf of the foliation mathcal f for a generic moment angle manifold mathcal z in its combinatorial class we prove that all subvarieties are moment angle manifolds of smaller dimension and there are only finitely many of them this implies in particular that the algebraic dimension of mathcal z is zero

the polyhedral product functor a method of decomposition for moment angle complexes arrangements and related spaces this article gives a natural decomposition of the suspension of generalized moment angle complexes or partial product spaces which arise as polyhedral product functors described below the geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of goresky macpherson concerning complements of certain subspace arrangements as well as davis januszkiewicz and buchstaber panov concerning moment angle complexes since the stable decompositions here are geometric they provide corresponding homological decompositions for generalized moment angle complexes for any homology theory

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

landmark matching via large deformation diffeomorphisms this paper describes the generation of large deformation diffeomorphisms spl phi spl omega 0 1 sup 3 spl rlhar2 spl omega for landmark matching generated as solutions to the transport equation d spl phi x t dt spl nu spl phi x t t t spl isin 0 1 and spl phi x 0 x with the image map defined as spl phi spl middot 1 and therefore controlled via the velocity field spl nu spl middot t t spl isin 0 1 imagery are assumed characterized via sets of landmarks x sub n y sub n n 1 2 n the optimal diffeomorphic match is constructed to minimize a running smoothness cost spl par l spl nu spl par sup 2 associated with a linear differential operator l on the velocity field generating the diffeomorphism while simultaneously minimizing the matching end point condition of the landmarks both inexact and exact landmark matching is studied here given noisy landmarks x sub n matched to y sub n measured with error covariances spl sigma sub n then the matching problem is solved generating the optimal diffeomorphism spl phi spl circ x 1 spl int sub 0 sup 1 spl nu spl circ spl phi spl circ x t t dt x where spl nu spl circ spl middot argmin sub spl nu spl middot spl int sub 1 sup 1 spl int sub spl omega spl par l spl nu x t spl par sup 2 dxdt spl sigma sub n 1 sup n y sub n spl phi x sub n 1 sup t spl sigma sub n sup 1 y sub n spl phi x sub n 1 conditions for the existence of solutions in the space of diffeomorphisms are established with a gradient algorithm provided for generating the optimal flow solving the minimum problem results on matching two dimensional 2 d and three dimensional 3 d imagery are presented in the macaque monkey

dt refind diffusion tensor registration with exact finite strain differential in this paper we propose the dt refind algorithm for the diffeomorphic nonlinear registration of diffusion tensor images unlike scalar images deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently these methods often approximate the gradient of the objective function in the case of the finite strain fs reorientation strategy we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function by utilizing the closed form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms the resulting registration algorithm is diffeomorphic and fast we contrast the algorithm with a traditional fs alternative that ignores the reorientation in the gradient computation we show that the exact gradient leads to significantly better registration at the cost of computation time independently of the choice of euclidean or log euclidean interpolation and sum of squared differences dissimilarity measure the exact gradient achieves better alignment over an entire spectrum of deformation penalties alignment quality is assessed with a battery of metrics including tensor overlap fractional anisotropy inverse consistency and closeness to synthetic warps the improvements persist even when a different reorientation scheme preservation of principal directions is used to apply the final deformations

some special cremona transformations in this paper we continue the study c f c k s t 1 2 of special cremona transformations i e those whose base scheme y is smooth and connected crauder and katz have completely classified these when dim y 2 our main results classify them when they are quadro quadric theorem 2 6 and when codim y 2 theorem 3 2 in the first case they are just the maps given by systems of quadrics through severi varieties by a result of zak there are just four of these the veronese surface v c p5 the segre embedding of p2 x p2 in p8 the grassmannian g 2 6 in p14 and the 16dimensional e6 variety in p26 and in the second either y is a quintic elliptic scroll in p4 or y is defined in pi by the vanishing of the n x n minors of

large deformation diffeomorphic metric curve mapping we present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping lddmm scheme for computing an optimal transformation between two curves embedded in euclidean space d curves are first represented as vector valued measures which incorporate both location and the first order geometric structure of the curves then a hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves we describe a discretized version of this in which discrete sequences of points along the curve are represented by vector valued functionals this gives a convenient and practical way to define a matching functional for curves we derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in 2 and 3 behaviors of the curve mapping are discussed using 2d curves the applications to shape classification is shown and experiments with 3d curves extracted from brain cortical surfaces are presented

measuring brain variability by extrapolating sparse tensor fields measured on sulcal lines modeling and understanding the variability of brain structures is a fundamental problem in neurosciences improved mathematical representations of structural brain variation are needed to help detect and understand genetic or disease related sources of abnormality as well as to improve statistical power when integrating functional brain mapping data across subjects in this paper we develop a new mathematical model of normal brain variation based on a large set of cortical sulcal landmarks 72 per brain delineated in each of 98 healthy human subjects scanned with 3d mri age 51 8 6 2 years we propose an original method to compute an average representation of the sulcal curves which constitutes the mean anatomy after affine alignment of the individual data across subjects the second order moment distribution of the sulcal position is modeled as a sparse field of covariance tensors symmetric positive definite matrices to extrapolate this information to the full brain one has to overcome the limitations of the standard euclidean matrix calculus we propose an affine invariant riemannian framework to perform computations with tensors in particular we generalize radial basis function rbf interpolation and harmonic diffusion partial differential equations pdes to tensor fields as a result we obtain a dense 3d variability map that agrees well with prior results on smaller subject samples moreover leave one sulcus out tests show that our model is globally able to recover the missing information on brain variation when there is a consistent neighboring pattern of variability finally we propose an innovative method to analyze the asymmetry of brain variability as expected the greatest asymmetries are found in regions that includes the primary language areas interestingly any such asymmetries in anatomical variance if it remains after anatomical normalization could explain why there may be greater power to detect group activation in one hemisphere versus the other in fmri studies

towards a coherent statistical framework for dense deformable template estimation summary the problem of estimating probabilistic deformable template models in the field of computer vision or of probabilistic atlases in the field of computational anatomy has not yet received a coherent statistical formulation and remains a challenge we provide a careful definition and analysis of a well defined statistical model based on dense deformable templates for grey level images of deformable objects we propose a rigorous bayesian framework for which we prove asymptotic consistency of the maximum a posteriori estimate and which leads to an effective iterative estimation algorithm of the geometric and photometric parameters in the small sample setting the model is extended to mixtures of finite numbers of such components leading to a fine description of the photometric and geometric variations of an object class we illustrate some of the ideas with images of handwritten digits and apply the estimated models to classification through maximum likelihood

clinical dt mri estimation smoothing and fiber tracking with log euclidean metrics diffusion tensor magnetic resonance imaging dt mri or dti is an imaging modality that is gaining importance in clinical applications however in a clinical environment data have to be acquired rapidly often at the expense of the image quality this often results in dti datasets that are not suitable for complex postprocessing like fiber tracking we propose a new variational framework to improve the estimation of dt mri in this clinical context most of the existing estimation methods rely on a log gaussian noise gaussian noise on the image logarithms or a gaussian noise that do not reflect the rician nature of the noise in mr images with a low signal to noise ratio snr with these methods the rician noise induces a shrinking effect the tensor volume is underestimated when other noise models are used for the estimation in this paper we propose a maximum likelihood strategy that fully exploits the assumption of a rician noise to further reduce the influence of the noise we optimally exploit the spatial correlation by coupling the estimation with an anisotropic prior previously proposed on the spatial regularity of the tensor field itself which results in a maximum a posteriori estimation optimizing such a nonlinear criterion requires adapted tools for tensor computing we show that riemannian metrics for tensors and more specifically the log euclidean metrics are a good candidate and that this criterion can be efficiently optimized experiments on synthetic data show that our method correctly handles the shrinking effect even with very low snr and that the positive definiteness of tensors is always ensured results on real clinical data demonstrate the truthfulness of the proposed approach and show promising improvements of fiber tracking in the brain and the spinal cord

a new geometric construction of compact complex manifolds in any dimension we consider holomorphic linear foliations of dimension m of mathbb c n with n 2m fulfilling a so called weak hyperbolicity condition and equip the projectivization of the leaf space for the foliation restricted to an adequate open dense subset with a structure of compact complex manifold of dimension n m 1 we show that except for the limit case n 2m 1 where we obtain any complex torus of any dimension this construction gives non symplectic manifolds including the previous examples of hopf calabi eckmann haefliger linear case loeb nicolau linear case and lopez de medrano verjovsky we study some properties of these manifolds that is to say meromorphic functions holomorphic vector fields forms and submanifolds for each manifold we construct an analytic space of deformations of dimension m n m 1 and show that under some additional conditions it is universal lastly we give explicit examples of new compact complex manifolds in particular of connected sums of products of spheres and show the existence of a momentum like map which classifies these manifolds up to diffeomorphism

numerical characterization of the kahler cone of a compact kahler manifold the goal of this work is to give a precise numerical description of the kahler cone of a compact kahler manifold our main result states that the kahler cone depends only on the intersection form of the cohomology ring the hodge structure and the homology classes of analytic cycles if x is a compact kahler manifold the kahler cone k of x is one of the connected components of the set p of real 1 1 cohomology classes which are numerically positive on analytic cycles i e y p 0 for every irreducible analytic set y in x p dim y this result is new even in the case of projective manifolds where it can be seen as a generalization of the well known nakai moishezon criterion and it also extends previous results by campana peternell and eyssidieux the principal technical step is to show that every nef class which has positive highest self intersection numberx n 0 contains a kahler current this is done by using the calabi yau theorem and a mass concentration technique for monge ampere equations the main result admits a number of variants and corollaries including a description of the cone of numerically effective 1 1 classes and their dual cone another important consequence is the fact that for an arbitrary deformation x s of compact kahler manifolds the kahler cone of a very general fibre xt is independent of t i e invariant by parallel transport under the 1 1 component of the gauss manin connection

spatial normalization and averaging of diffusion tensor mri data sets diffusion tensor magnetic resonance imaging dt mri is unique in providing information about both the structural integrity and the orientation of white matter fibers in vivo and through tractography revealing the trajectories of white matter tracts dt mri is therefore a promising technique for detecting differences in white matter architecture between different subject populations however while studies involving analyses of group averages of scalar quantities derived from dt mri data have been performed as yet there have been no similar studies involving the whole tensor here we present the first step towards realizing such a study i e the spatial normalization of whole tensor data sets the approach is illustrated by spatial normalization of 10 dt mri data sets to a standard anatomical template both qualitative and quantitative approaches are described for assessing the results of spatial normalization techniques are then described for combining the spatially normalized data sets according to three definitions of average i e the mean median and mode of a distribution of tensors the current absence of and hence need for appropriate statistical tests for comparison of results derived from group averaged dt mri data sets is then discussed finally the feasibility of performing tractography on the group averaged dt mri data set is investigated and the possibility and implications of generating a generic map of brain connectivity from a group of subjects is considered

registration atlas estimation and variability analysis of white matter fiber bundles modeled as currents this paper proposes a generic framework for the registration the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images this framework is based on the metric on currents for the comparison of fiber bundles this metric measures anatomical differences between fiber bundles seen as global homologous structures across subjects it avoids the need to establish correspondences between points or between individual fibers of different bundles it can measure differences both in terms of the geometry of the bundles like its boundaries and in terms of the density of fibers within the bundle it is robust to fiber interruptions and reconnections in addition a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents first we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects a dense deformation of the underlying white matter is estimated which is constrained by the bundles seen as global anatomical landmarks by contrast the alignment obtained from image registration is driven only by the local gradient of the image second we propose a generative statistical model for the analysis of a collection of homologous bundles this model consistently estimates prototype fiber bundles called template which capture the anatomical invariants in the population a set of deformations which align the geometry of the template to that of each subject and a set of residual perturbations the statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry stretching torque etc and texture fiber density etc third this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability this gives a way to interpret the anatomical features that the model detects consistently across the subjects this may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles

diffeomorphic metric surface mapping in subregion of the superior temporal gyrus this paper describes the application of large deformation diffeomorphic metric mapping to cortical surfaces based on the shape and geometric properties of subregions of the superior temporal gyrus in the human brain the anatomical surfaces of the cortex are represented as triangulated meshes the diffeomorphic matching algorithm is implemented by defining a norm between the triangulated meshes based on the algorithms of vaillant and glaunes the diffeomorphic correspondence is defined as a flow of the extrinsic three dimensional coordinates containing the cortical surface that registers the initial and target geometry by minimizing the norm the methods are demonstrated in 40 high resolution mri cortical surfaces of planum temporale pt constructed from subsets of the superior temporal gyrus stg the effectiveness of the algorithm is demonstrated via the euclidean positional distance distance of normal vectors and curvature before and after the surface matching as well as the comparison with a landmark matching algorithm the results demonstrate that both the positional and shape variability of the anatomical configurations are being represented by the diffeomorphic maps

the homotopy type of the polyhedral product for shifted complexes abstract we prove a conjecture of bahri bendersky cohen and gitler if k is a shifted simplicial complex on n vertices x 1 x n are pointed connected c w complexes and c x i is the cone on x i then the polyhedral product determined by k and the pairs c x i x i is homotopy equivalent to a wedge of suspensions of smashes of the x i s earlier work of the authors dealt with the special case where each x i is a loop space new techniques are introduced to prove the general case these have the advantage of simplifying the earlier results and of being sufficiently general to show that the conjecture holds for a substantially larger class of simplicial complexes we discuss connections between polyhedral products and toric topology combinatorics and classical homotopy theory

deterministic and probabilistic tractography based on complex fibre orientation distributions we propose an integral concept for tractography to describe crossing and splitting fibre bundles based on the fibre orientation distribution function odf estimated from high angular resolution diffusion imaging hardi we show that in order to perform accurate probabilistic tractography one needs to use a fibre odf estimation and not the diffusion odf we use a new fibre odf estimation obtained from a sharpening deconvolution transform sdt of the diffusion odf reconstructed from q ball imaging qbi this sdt provides new insight into the relationship between the hardi signal the diffusion odf and the fibre odf we demonstrate that the sdt agrees with classical spherical deconvolution and improves the angular resolution of qbi another important contribution of this paper is the development of new deterministic and new probabilistic tractography algorithms using the full multidirectional information obtained through use of the fibre odf an extensive comparison study is performed on human brain datasets comparing our new deterministic and probabilistic tracking algorithms in complex fibre crossing regions finally as an application of our new probabilistic tracking we quantify the reconstruction of transcallosal fibres intersecting with the corona radiata and the superior longitudinal fasciculus in a group of eight subjects most current diffusion tensor imaging dti based methods neglect these fibres which might lead to incorrect interpretations of brain functions

on compact complex surfaces of kahler rank one the kahler rank of compact complex surfaces was introduced by harvey and lawson in their 1983 paper on kahler manifolds as a measure of kahlerianity here we give a partial classification of compact complex surfaces of kahler rank 1 these are either elliptic surfaces or hopf surfaces or they admit a holomorphic foliation of a very special type as a consequence we give an affirmative answer to the question raised by harvey and lawson whether the kahler rank is a bimeromorphic invariant

large deformation diffeomorphic metric mapping of vector fields this paper proposes a method to match diffusion tensor magnetic resonance images dt mris through the large deformation diffeomorphic metric mapping of vector fields focusing on the fiber orientations considered as unit vector fields on the image volume we study a suitable action of diffeomorphisms on such vector fields and provide an extension of the large deformation diffeomorphic metric mapping framework to this type of dataset resulting in optimizing for geodesics on the space of diffeomorphisms connecting two images existence of the minimizers under smoothness assumptions on the compared vector fields is proved and coarse to fine hierarchical strategies are detailed to reduce both ambiguities and computation load this is illustrated by numerical experiments on dt mri heart images

real quadrics in cn complex manifolds and convex polytopes in this paper we investigate the topology of a class of non kahler compact complex manifolds generalizing that of hopf and calabi eckmann manifolds these manifolds are diffeomorphic to special systems of real quadrics cn which are invariant with respect to the natural action of the real torus s1 n onto cn the quotient space is a simple convex polytope the problem reduces thus to the study of the topology of certain real algebraic sets and can be handled using combinatorial results on convex polytopes we prove that the homology groups of these compact complex manifolds can have arbitrary amount of torsion so that their topology is extremely rich we also resolve an associated wall crossing problem by introducing holomorphic equivariant elementary surgeries related to some transformations of the simple convex polytope finally as a nice consequence we obtain that affine non kahler compact complex manifolds can have arbitrary amount of torsion in their homology groups contrasting with the kahler situation

resolving fiber crossing using advanced fast marching tractography based on diffusion tensor imaging magnetic resonance diffusion tensor tractography is a powerful tool for the non invasive depiction of the white matter architecture in the human brain however due to limitations in the underlying tensor model the technique is often unable to reconstruct correct trajectories in heterogeneous fiber arrangements such as axonal crossings a novel tractography method based on fast marching fm is proposed which is capable of resolving fiber crossings and also permits trajectories to branch it detects heterogeneous fiber arrangements by incorporating information from the entire diffusion tensor the fm speed function is adapted to the local tensor characteristics allowing in particular to maintain the front evolution direction in crossing situations in addition the fm s discretization error is reduced by increasing the number of considered possible front evolution directions the performance of the technique is demonstrated in artificial data and in the healthy human brain comparisons with standard fm tractography and conventional line propagation algorithms show that in the presence of interfering structures the proposed method is more accurate in reconstructing trajectories the in vivo results illustrate that the elucidated major white matter pathways are consistent with known anatomy and that multiple crossings and tract branching are handled correctly

sparse adaptive parameterization of variability in image ensembles this paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a hamiltonian flow of self interacting particles the proposed approach estimates a template image representative of a given image set an optimal set of control points that focuses on the most variable parts of the image and template to image registrations that quantify the variability within the image set the method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain the optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent the selection of the control points is done by adding a l 1 prior to the objective function which is optimized using the fista algorithm

non kahler manifolds and git quotients bosio generalized the construction by lopez de medrano verjovsky meersseman lvm of a family of non algebraic compact complex manifolds of any dimension we describe how to construct the generalized family from certain geometric invariant theory git quotients we show that bosio s generalization parallels exactly the extension from mumford s git to the more general git developed by bialynicki birula and wi cicka this point of view yields new results on the geometry of lvm and bosio s manifolds