5,237 research outputs found
Equivariant Fields in an Gauge Theory with new Spontaneously Generated Fuzzy Extra Dimensions
We find new spontaneously generated fuzzy extra dimensions emerging from a
certain deformation of supersymmetric Yang-Mills (SYM) theory with cubic
soft supersymmetry breaking and mass deformation terms. First, we determine a
particular four dimensional fuzzy vacuum that may be expressed in terms of a
direct sum of product of two fuzzy spheres, and denote it in short as . The direct sum structure of the vacuum is revealed
by a suitable splitting of the scalar fields in the model in a manner that
generalizes our approach in \cite{Seckinson}. Fluctuations around this vacuum
have the structure of gauge fields over ,
and this enables us to conjecture the spontaneous broken model as an effective
gauge theory on the product manifold . We support this interpretation by
examining the theory and determining all of the
equivariant fields in the model, characterizing its low energy degrees of
freedom. Monopole sectors with winding numbers are accessed from after suitable projections and subsequently equivariant fields in these
sectors are obtained. We indicate how Abelian Higgs type models with vortex
solutions emerge after dimensionally reducing over the fuzzy monopole sectors
as well. A family of fuzzy vacua is determined by giving a systematic treatment
for the splitting of the scalar fields and it is made manifest that suitable
projections of these vacuum solutions yield all higher winding number fuzzy
monopole sectors. We observe that the vacuum configuration identifies with the bosonic part of the product of two fuzzy
superspheres with supersymmetry and elaborate on this
feature.Comment: 38+1 pages, published versio
Invariant Submanifolds of Generalized Sasakian-Space-Forms
The object of this paper is to study the invariant submanifolds of
generalized Sasakian-space-forms. Here, we obtain some equivalent conditions
for an invariant submanifold of a generalized Sasakian-space-forms to be
totally geodesic.Comment: 11 page
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Coupled PDEs for Non-Rigid Registration and Segmentation
In this paper we present coupled partial differential equations (PDEs) for the problem of joint segmentation and registration. The registration component of the method estimates a deformation field between boundaries of two structures. The desired coupling comes from two PDEs that estimate a common surface through segmentation and its non-rigid registration with a target image. The solutions of these two PDEs both decrease the total energy of the surface, and therefore aid each other in finding a locally optimal solution. Our technique differs from recently popular joint segmentation and registration algorithms, all of which assume a rigid transformation among shapes. We present both the theory and results that demonstrate the effectiveness of the approach
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Estimation of Vector Fields in Unconstrained and Inequality Constrained Variational Problems for Segmentation and Registration
Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well. We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach
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Active Polyhedron: Surface Evolution Theory Applied to Deformable Meshes
This paper presents a novel 3D deformable surface that we call an active polyhedron. Rooted in surface evolution theory, an active polyhedron is a polyhedral surface whose vertices deform to minimize a regional and/or boundarybased energy functional. Unlike continuous active surface models, the vertex motion of an active polyhedron is computed by integrating speed terms over polygonal faces of the surface. The resulting ordinary differential equations (ODEs) provide improved robustness to noise and allow for larger time steps compared to continuous active surfaces implemented with level set methods. We describe an electrostatic regularization technique that achieves global regularization while better preserving sharper local features. Experimental results demonstrate the effectiveness of an active polyhedron in solving segmentation problems as well as surface reconstruction from unorganized points
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Guidewire tracking in x-ray videos of endovascular interventions
We present a novel method to track a guidewire in cardiac xray video. Using variational calculus, we derive differential equations that deform a spline, subject to intrinsic and extrinsic forces, so that it matches the image data, remains smooth, and preserves an a priori length. We analytically derive these equations from first principles, and show how they include tangential terms, which we include in our model. To address the poor contrast often observed in x-ray video, we propose using phase congruency as an image-based feature. Experimental results demonstrate the success of the method in tracking guidewires in low contrast x-ray video
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Graph cuts segmentation using an elliptical shape prior
We present a graph cuts-based image segmentation technique that incorporates an elliptical shape prior. Inclusion of this shape constraint restricts the solution space of the segmentation result, increasing robustness to misleading information that results from noise, weak boundaries, and clutter. We argue that combining a shape prior with a graph cuts method suggests an iterative approach that updates an intermediate result to the desired solution. We first present the details of our method and then demonstrate its effectiveness in segmenting vessels and lymph nodes from pelvic magnetic resonance images, as well as human faces
One-degree-of-freedom motion induced by modeled vortex shedding
The motion of an elastically supported cylinder forced by a nonlinear, quasi-static, aerodynamic model with the unusual feature of a motion-dependent forcing frequency was studied. Numerical solutions for the motion and the Lyapunov exponents are presented for three forcing amplitudes and two frequencies (1.0 and 1.1 times the Strouhal frequency). Initially, positive Lyapunov exponents occur and the motion can appear chaotic. After thousands of characteristic times, the motion changes to a motion (verified analytically) that is periodic and damped. This periodic, damped motion was not observed experimentally, thus raising questions concerning the modeling
The final measurement of by NA48
The direct CP violation parameter Re() has been measured
from the decay rates of neutral kaons into two pions using the NA48 detector at
the CERN SPS. The 2001 running period was devoted to collecting additional data
under varied conditions compared to earlier years (1997-99). The 2001 data
yield the result: Re()=.
Combining this result with that published from the 1997,98 and 99 data, an
overall value of Re()= is
obtained from the NA48 experiment.Comment: 5 pages, 3 figures. Proceedings for the ICHEP02 conferenc
A Variational Approach to the Evolution of Radial Basis Functions for Image Segmentation
In this paper we derive differential equations for evolving radial basis functions (RBFs) to solve segmentation problems. The differential equations result from applying variational calculus to energy functionals designed for image segmentation. Our methodology supports evolution of all parameters of each RBF, including its position, weight, orientation, and anisotropy, if present. Our framework is general and can be applied to numerous RBF interpolants. The resulting approach retains some of the ideal features of implicit active contours, like topological adaptivity, while requiring low storage overhead due to the sparsity of our representation, which is an unstructured list of RBFs. We present the theory behind our technique and demonstrate its usefulness for image segmentation
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