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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Cárdenas, Giovanno Marcelo Weickert, Joachim Schäffer, Sarah Mathematical Image Analysis Group Saarland University Campus E1.7 Saarbrücken66041 Germany

ISBN: (纸本)9783319184609

Most scale-space evolutions are described in terms of partial differential equations. In recent years, however, nonlocal processes have become an important research topic in image analysis. the goal of our paper is to establish well-posedness and scale-space properties for a class of nonlocal evolutions. they are given by linear integro-differential equations with measures. In analogy to Weickert’s diffusion theory (1998), we prove existence and uniqueness, preservation of the average grey value, a maximum–minimum principle, image simplification properties in terms of Lyapunov functionals, and we establish convergence to a constant steady state. We show that our nonlocal scale-space theory covers nonlocal variants of linear diffusion. Moreover, by choosing specific discrete measures, the classical semidiscrete diffusion framework is identified as a special case of our continuous theory. Last but not least, we introduce two modifications of bilateral filtering. In contrast to previous bilateral filters, our variants create nonlocal scale-spaces that preserve the average grey value and that can be highly robust under noise. While these filters are linear, they can achieve a similar performance as nonlinear and even anisotropic diffusion equations. © Springer international Publishing Switzerland 2015.

关键词： Integrodifferential equations

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A geometric formulation of gradient descent for variational problems with moving surfaces

A geometric formulation of gradient descent for variational ...

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5th international conference on scale space and PDE methods in computer vision, scale-space 2005

作者： Solem, Jan Erik Overgaard, Niels Chr. Applied Mathematics Group School of Technology and Society Malmö University Sweden

Developments within the computer vision community have led to the formulation of many interesting problems in a variational setting. this paper introduces the manifold of admissible surfaces and a scalar product on its tangent spaces. this makes it possible to properly define gradients and gradient descent procedures for variational problems involving m-surfaces. these concepts lead to a geometric understanding of current state of the art evolution methods and steepest descent evolution equations. By geometric reasoning, common procedures within the variational level set framework are explained and justified. Concrete computations for a general class of functionals are presented and applied to common variational problems for curves and surfaces. © Springer-Verlag Berlin Heidelberg 2005.

关键词： computer vision

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Discrete orthogonal decomposition and variational fluid flow estimation

Discrete orthogonal decomposition and variational fluid flow...

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5th international conference on scale-space and PDE methods in computer vision

作者： Yuan, J Ruhnau, P Mémin, E Schnörr, C Univ Mannheim Dept Math & Comp Sci Comp Vis Graph & Pattern Recognit Grp D-68131 Mannheim Germany Inst Rech Informat & Syst Aleatoires F-35042 Rennes France

ISBN: (纸本)3540255478

the decomposition of motion vector fields into components of orthogonal subspaces is an important representation for both the analysis and the variational estimation of complex motions. Common finite differencing or finite element methods, however, do not preserve the basic identities of vector analysis. therefore, we introduce in this paper the mimetic finite difference method for the estimation of fluid flows from image sequences. Using this discrete setting, we represent the motion components directly in terms of potential functions which are useful for motion pattern analysis. Additionally, we analyze well-posedness which has been lacking in previous work. Experimental results, including hard physical constraints like vanishing divergence of the flow, validate the theory.

关键词： Flow of fluids

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New approximation of a scale space kernel on SE(3) and applications in neuroimaging 5

New approximation of a scale space kernel on SE(3) and appli...

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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Portegies, Jorg Sanguinetti, Gonzalo Meesters, Stephan Duits, Remco Department of Mathematics and Computer Science Eindhoven University of Technology Eindhoven Netherlands Academic Center for Epileptology Kempenhaeghe and Maastricht UMC+ Heeze Netherlands Department of Biomedical Engineering Eindhoven University of Technology Eindhoven Netherlands

ISBN: (纸本)9783319184609

We provide a new, analytic kernel for scale space filtering of dMRI data. the kernel is an approximation for the Green’s function of a hypo-elliptic diffusion on the 3D rigid body motion group SE(3), for fiber enhancement in dMRI. the enhancements are described by linear scale space PDEs in the coupled space of positions and orientations embedded in SE(3). As initial condition for the evolution we use either a Fiber Orientation Distribution (FOD) or an Orientation Density Function (ODF). Explicit formulas for the exact kernel do not exist. Although approximations well-suited for fast implementation have been proposed in literature, they lack important symmetries of the exact kernel. We introduce techniques to include these symmetries in approximations based on the logarithm on SE(3), resulting in an improved kernel. Regarding neuroimaging applications, we apply our enhancement kernel (a) to improve dMRI tractography results and (b) to quantify coherence of obtained streamline bundles. © Springer international Publishing Switzerland 2015.

关键词： Neuroimaging

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scale-space theory for auditory signals 5

Scale-space theory for auditory signals

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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Lindeberg, Tony Friberg, Anders Department of Computational Biology School of Computer Science and Communication KTH Royal Institute of Technology Stockholm Sweden Department of Speech Music and Hearing School of Computer Science and Communication KTH Royal Institute of Technology Stockholm Sweden

ISBN: (纸本)9783319184609

We show how the axiomatic structure of scale-space theory can be applied to the auditory domain and be used for deriving idealized models of auditory receptive fields via scale-space principles. For defining a time-frequency transformation of a purely temporal signal, it is shown that the scale-space framework allows for a new way of deriving the Gabor and Gammatone filters as well as a novel family of generalized Gammatone filters with additional degrees of freedom to obtain different trade-offs between the spectral selectivity and the temporal delay of time-causal window functions. Applied to the definition of a second layer of receptive fields from the spectrogram, it is shown that the scale-space framework leads to two canonical families of spectro-temporal receptive fields, using a combination of Gaussian filters over the logspectral domain with either Gaussian filters or a cascade of first-order integrators over the temporal domain. these spectro-temporal receptive fields can be either separable over the time-frequency domain or be adapted to local glissando transformations that represent variations in logarithmic frequencies over time. Such idealized models of auditory receptive fields respect auditory invariances, can be used for computing basic auditory features for audio processing and lead to predictions about auditory receptive fields with good qualitative similarity to biological receptive fields in the inferior colliculus (ICC) and the primary auditory cortex (A1). © Springer international Publishing Switzerland 2015.

关键词： Degrees of freedom (mechanics)

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Unsupervised learning using the tensor voting graph 5

Unsupervised learning using the tensor voting graph

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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Deutsch, Shay Medioni, Gérard Computer Science Department Institute for Robotics and Intelligent Systems University of Southern California Los Angeles United States

ISBN: (纸本)9783319184609

Tensor Voting is a local, non parametric method that provides an efficient way to learn the complex geometric manifold structure under a significant amount of outlier noise. the main limitation of the Tensor Voting framework is that it is strictly a local method, thus not efficient to infer the global properties of complex manifolds. We therefore suggest constructing a unique graph which we call the Tensor Voting Graph, in which the affinity is based on the contribution of neighboring points to a point local tangent space estimated by Tensor Voting. the Tensor Voting Graph compactly and effectively represents the global structure of the underlying manifold. We experimentally demonstrate that we can accurately estimate the geodesic distance on complex manifolds, and substantially outperform all state of the art competing approaches, especially when outliers are present. We also demonstrate our method’s superior ability to segment manifolds, first on synthetic data, then on standard data sets for a motion segmentation, with graceful degradation in the presence of noise. © IFIP international Federation for Information Processing 2015.

关键词： Tensors

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Discontinuity-preserving computation of variational optic flow in real-time

Discontinuity-preserving computation of variational optic fl...

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5th international conference on scale-space and PDE methods in computer vision

作者： Bruhn, A Weickert, J Kohlberger, T Schnörr, C Univ Saarland Fac Math & Comp Sci Math Image Anal Grp D-66041 Saarbrucken Germany Univ Mannheim Comp Vis Graph & Pattern Recognit Grp Dept Math & Comp Sci D-68131 Mannheim Germany

ISBN: (纸本)3540255478

variational methods are very popular for optic flow computation: they yield dense flow fields and perform well if they are adapted such that they respect discontinuities in the image sequence or the flow field. Unfortunately, this adaptation results in high computational complexity. In our paper we show that it is possible to achieve real-time performance for these methods if bidirectional multigrid strategies are used. To this end, we study two prototypes: i) For the anisotropic image-driven technique of Nagel and Enkelmann that results in a linear system of equations we derive a regular full multigrid scheme. ii) For an isotropic flow-driven approach with total variation (TV) regularisation that requires to solve a nonlinear system of equations we develop a full multigrid strategy based on a full approximation scheme (FAS). Experiments for sequences of size 160 x 120 demonstrate the excellent performance of the proposed numerical schemes. With frame rates of 6 and 12 dense flow fields per second, respectively, both implementations outperform corresponding modified explicit schemes by two to three orders of magnitude. thus, for the first time ever, real-time performance can be achieved for these high quality methods.

关键词： computer vision optical flow differential techniques variational methods multigrid methods partial differential equations

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A variational image registration approach based on curvature scale space

A variational image registration approach based on curvature...

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5th international conference on scale-space and PDE methods in computer vision

作者： Henn, S Witsch, K Univ Dusseldorf Math Inst D-40225 Dusseldorf Germany

ISBN: (纸本)3540255478

this paper presents a novel scale space approach to obtain a deformation which matches two images acquired from the same or from different medical imaging modalities. the image registration problem is known to be mathematically ill-posed due to the fact that determining the unknown components of the displacements merely from the images is an underdetermined problem. the approach presented here utilizes an auxiliary regularization term, which favors displacements with minimal curvature surface. One of the important aspects of this approach is that the kernel of the Euler-Lagrange equation is spanned by all rigid motions. Hence, the presented approach includes a rigid alignment. A minimizer is determined as the steady-state solution of the Euler-Lagrange equation namely by the biharmonic diffusion equation with higher order boundary conditions. In this framework we give a new interpretation of the underlying regularization parameter alpha. Finally, we present experimental results for registration problems of a Magnetic Resonance Imaging (MRI) (monomodal) registration and for a real computer tomography (CT)-magnetic resonance imaging (multimodal) registration.

关键词： Image processing

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Solving minimal surface problems on surfaces and point clouds 5

Solving minimal surface problems on surfaces and point cloud...

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5th international conference on scale space and variational methods in computer vision, ssvm 2015

作者： Tenbrinck, Daniel Lozes, François Elmoataz, Abderrahim Institute for Computational and Applied Mathematics Westfälische Wilhelms-Universität Münster Einsteinstr. 62 Münster48149 Germany UMR6072 GREYC ENSICAEN Caen France

ISBN: (纸本)9783319184609

Minimal surface problems play an important role not only in physics or biology but also in mathematical signal and image processing. Although the computation of respective solutions is well-investigated in the setting of discrete images, only little attention has been payed to more complicated data, e.g., surfaces represented as meshes or point clouds. In this work we introduce a novel family of discrete total variation seminorms for weighted graphs based on the upwind gradient and incorporate them into an efficient minimization algorithm to perform total variation denoising on graphs. Furthermore, we demonstrate how to utilize the latter algorithm to uniquely solve minimal surface problems on graphs. To show the universal applicability of this approach, we illustrate results from filtering and segmentation of 3D point cloud data. © Springer international Publishing Switzerland 2015.

关键词： Graphic methods

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A multigrid platform for real-time motion computation with discontinuity-preserving variational methods

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international JOURNAL OF computer vision 2006年第3期70卷 257-277页

作者： Bruhn, Andres Weickert, Joachim Kohlberger, Timo Schnoerr, Christoph Univ Saarland Math Image Anal Grp Fac Math & Comp Sci D-66041 Saarbrucken Germany Univ Mannheim Dept Math & Comp Sci Comp Vis Graph & Pattern Recognit Grp D-68131 Mannheim Germany

variational methods are among the most accurate techniques for estimating the optic flow. they yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases-even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 x 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.

关键词： partial differential equations variational methods optic flow multigrid methods

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