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Michael Miller - One of the best experts on this subject based on the ideXlab platform.

  • Principal Component Based Diffeomorphic Surface Mapping
    IEEE transactions on medical imaging, 2011
    Co-Authors: Anqi Qiu, Laurent Younes, Michael Miller
    Abstract:

    We present a new diffeomorphic surface mapping algorithm under the framework of large deformation diffeomorphic metric mapping (LDDMM). Unlike existing LDDMM approaches, this new algorithm reduces the complexity of the estimation of diffeomorphic transformations by incorporating a shape prior in which a nonlinear diffeomorphic shape space is represented by a linear space of Initial momenta of diffeomorphic geodesic flows from a fixed template. In addition, for the first time, the diffeomorphic mapping is formulated within a decision-theoretic scheme based on Bayesian modeling in which an empirical shape prior is characterized by a low dimensional Gaussian distribution on Initial Momentum. This is achieved using principal component analysis (PCA) to construct the eigenspace of the Initial Momentum. A likelihood function is formulated as the conditional probability of observing surfaces given any particular value of the Initial Momentum, which is modeled as a random field of vector-valued measures characterizing the geometry of surfaces. We define the diffeomorphic mapping as a problem that maximizes a posterior distribution of the Initial Momentum given observable surfaces over the eigenspace of the Initial Momentum. We demonstrate the stability of the Initial Momentum eigenspace when altering training samples using a bootstrapping method. We then validate the mapping accuracy and show robustness to outliers whose shape variation is not incorporated into the shape prior.

  • Statistics on computational anatomy: from template estimation to geodesically controlled diffeomorphic active shapes
    2011
    Co-Authors: Michael Miller
    Abstract:

    This thesis addresses two important problems in the domain of statistical analysis on anatomical shapes: template estimation and PCA representation of diffeomorphic deformation. Geodesic shooting provides a new philosophy for statistical analysis on anatomical shapes. According to the Momentum conservation law, given a template, a diffeomorphic trajectory is uniquely determined by the Initial Momentum. Thus, statistics on the nonlinear space of diffeomorphims can be studied via the linear tangent space. We present a Bayesian model for template estimation for 3D images in CA. It is assumed that observed images are generated by deforming the template through Gaussian distributed random Initial momenta. The template is modeled as a deformation from a given hypertemplate with Initial Momentum μ, which has a Gaussian prior. We employ a variant of EM (MAEM) procedure, and approximate the conditional expectation by Dirac measure. This leads to an image matching problem with a Jacobian weight term. We derive a weighted Euler-Lagrange equation and develop a numerical algorithm to solve it. The results of template estimation for hippocampus and cardiac data are presented. The Bayesian framework and MAEM scheme have also been applied to template estimation for surfaces and have been validated with caudate, thalamus and hippocampus surface data, showing its effectiveness and convergence, and also experimentally proved to be robust to variations in the choice of the hypertemplate. The other major topic of this thesis is Geodesically Controlled Diffeomorphic Active Shapes (GDAS). The motivation of GDAS is to learn shape variability from training samples and describe this variability by low dimensional data. For the "shape statistics", we map a template to each surface in the training set and obtain its corresponding Initial Momentum vector. We perform PCA on these Initial Momentum vectors and define in this way a subspace for shape deformation. Any new Initial Momentum is projected onto this subspace and is represented by a small number of PCA coefficients. Applications of GDAS usually boil down to finding the optimal coefficients minimizing an energy term. The energy turns out to have a common pattern: it is a combination of a coefficient regulation term and a mismatch term. The latter is a functional of the deformed surface. We derive a general gradient descent procedure for GDAS optimization and apply this procedure in the context of 3D medical image segmentation and PCA based surface matching.

  • Large Deformation Diffeomorphism and Momentum Based Hippocampal Shape Discrimination in Dementia of the Alzheimer type
    IEEE transactions on medical imaging, 2007
    Co-Authors: Lei Wang, Can Ceritoglu, Laurent Younes, F. Beg, Tilak Ratnanather, John C. Morris, John G. Csernansky, Michael Miller
    Abstract:

    In large-deformation diffeomorphic metric mapping (LDDMM), the diffeomorphic matching of images are modeled as evolution in time, or a flow, of an associated smooth velocity vector field v controlling the evolution. The Initial Momentum parameterizes the whole geodesic and encodes the shape and form of the target image. Thus, methods such as principal component analysis (PCA) of the Initial Momentum leads to analysis of anatomical shape and form in target images without being restricted to small-deformation assumption in the analysis of linear displacements. We apply this approach to a study of dementia of the Alzheimer type (DAT). The left hippocampus in the DAT group shows significant shape abnormality while the right hippocampus shows similar pattern of abnormality. Further, PCA of the Initial Momentum leads to correct classification of 12 out of 18 DAT subjects and 22 out of 26 control subjects

  • statistics on diffeomorphisms via tangent space representations
    NeuroImage, 2004
    Co-Authors: Marc Vaillant, L. Younes, Michael Miller, Alain Trouve
    Abstract:

    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.

Sebastian Eckart - One of the best experts on this subject based on the ideXlab platform.

  • Holographic angular streaking of electrons and the Wigner time delay
    Physical Review Research, 2020
    Co-Authors: Sebastian Eckart
    Abstract:

    For a circularly polarized single-color field at a central frequency of $2\omega$ the final electron Momentum distribution upon strong field ionization does not carry any information about the phase of the Initial Momentum distribution. Adding a weak, co-rotating, circularly polarized field at a central frequency of $\omega$ gives rise to a sub-cycle interference pattern (holographic angular streaking of electrons (HASE)). This interference pattern allows for the retrieval of the derivative of the phase of the Initial Momentum distribution after tunneling $\phi^{\prime}_{\mathrm{off}}(p_i)$. A trajectory-based semi-classical model (HASE model) is introduced which links the experimentally accessible quantities to $\phi^{\prime}_{\mathrm{off}}(p_i)$. It is shown that a change in $\phi^{\prime}_{\mathrm{off}}$ is equivalent to a displacement in position space $\Delta x$ of the Initial wave packet after tunneling. This offset in position space allows for an intuitive interpretation of the Wigner time delay $\Delta \tau_W$ in strong field ionization for circularly polarized single-color fields. The influence of Coulomb interaction after tunneling is investigated quantitatively.

  • Direct Experimental Access to the Nonadiabatic Initial Momentum Offset upon Tunnel Ionization.
    Physical review letters, 2018
    Co-Authors: Sebastian Eckart, K. Fehre, Nicolas Eicke, A. Hartung, Jonas Rist, D. Trabert, Nico Strenger, Andreas Pier, L. Ph. H. Schmidt, Till Jahnke
    Abstract:

    We report on the nonadiabatic offset of the Initial electron Momentum distribution in the plane of polarization upon single ionization of argon by strong field tunneling and show how to experimentally control the degree of nonadiabaticity. Two-color counter- and corotating fields (390 and 780 nm) are compared to show that the nonadiabatic offset strongly depends on the temporal evolution of the laser electric field. We introduce a simple method for the direct access to the nonadiabatic offset using two-color counter- and corotating fields. Further, for a single-color circularly polarized field at 780 nm, we show that the radius of the experimentally observed donutlike distribution increases for increasing Momentum in the light propagation direction. Our observed Initial Momentum offsets are well reproduced by the strong-field approximation. A mechanistic picture is introduced that links the measured nonadiabatic offset to the magnetic quantum number of virtually populated intermediate states.

R Leonhardt - One of the best experts on this subject based on the ideXlab platform.

V. M. Ristić - One of the best experts on this subject based on the ideXlab platform.

  • Influence of Ponderomotive Potential and NonZero Initial Momentum of Ejected Electron on Transition Rate in Multiphoton Ionization
    Acta Physica Polonica A, 2013
    Co-Authors: T. B. Miladinović, V.m. Petrović, V. M. Ristić
    Abstract:

    The multiphoton ionization of neutral atoms irradiated by photons is an interesting topic for experimental and also theoretical examination. We study the in uence of ponderomotive potential and non-zero Initial Momentum of ejected electrons on transition rate, and also on the generalized cross-section in the case of a multiphoton ionization process. Also, we study how the transition rate depends on the number of absorbed photons.

  • THE ROLE OF THE NON-ZERO Initial Momentum ANDMODIFIED IONIZATION POTENTIAL IN THE CORRECTED AMMOSOV-DELONE-KRAINOV THEORY
    2013
    Co-Authors: M. M. Radulović, T. B. Miladinović, V. M. Ristić
    Abstract:

    In this paper the dependence of corrected Ammosov-Delone-Krainov (cADK) ionization probability on ion net charge Z , on modified ionization potential mod E and on non-zero Initial Momentum p in the case of linearly polarized laser field is examined. The physical system in question is the potassium atom irradiated by CO2 laser, with intensities that ranged from 14 2 10 W cm to 16 2 5 10 W cm × . It turns out that dominant ionization probability, for a given intensity of laser field, depends on Z and p , i.e. of an electron that awaits next step in sequential process of ionization. The influence of modified ionization potential on ionization probability is most readily apparent in the case of high laser intensities that vary from 15 2 10 W cm to

  • Calculating Ionization Transition Rate for Circularly Polarized Fields, Including Non-Zero Initial Momentum
    Acta Physica Polonica A, 2009
    Co-Authors: V. M. Ristić, T. B. Miladinović, M. M. Radulović
    Abstract:

    Potassium atoms in circularly polarized laser field whose intensity (I) varies from 2 × 10 W/cm to 2.5 × 10 W/cm were studied. In the case when there is zero Initial Momentum, transition rate (that depends only on I) exhibits standard behaviour: as I increases, so thus the rate, until it reaches its maximum value at 1.1× 10 W/cm; after that, rate diminishes as I increases. In the case of non-zero Initial Momentum, transition rate (that now depends on I but additionally on Initial Momentum, too) exhibits following behaviour: dependence of the rate on I follows standard pattern, it rises with increase of I until it reaches its maximum, and then diminishes. But with increase of Momentum, ionization rate gradually diminishes.

  • Transition Rate Dependence on the Non-Zero Initial Momentum in the ADK-Theory
    Acta Physica Polonica A, 2007
    Co-Authors: V. M. Ristić, T. B. Miladinović, M. M. Radulović
    Abstract:

    Tunneling regime, introduced by Keldysh, in the interaction of strong lasers with atoms has been now accepted as the reliable method for describing processes when low frequency lasers are involved. Yet it was always assumed that the ionized electrons are leaving the atom with zero Initial Momentum. Because we are interested in how non-zero Momentum influences the transition probability of tunnel ionization, we obtained the exact expression for the Momentum. Here the estimation of the transition probability with nonzero Momentum included was conducted. Potassium atoms in the laser field whose intensity varied from 10 W/cm to 10 W/cm were studied. It seems that all energy of laser field is used for tunneling ionization process at the beginning of laser pulse — ionization probability is large. After that, with further action of laser pulse, ionization probability decreases, probably because part of laser pulse energy is used for increasing Momentum of ejected electrons, leaving smaller amounts of light quanta available for ionization of remaining electrons. If laser pulse lasts long enough, then the amounts of light quanta available for ionization become larger, resulting in increase in ionization probability, now with greater starting energy of ejected electrons.

Mark Sadgrove - One of the best experts on this subject based on the ideXlab platform.