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Optimal Transport for Manifold-Valued Images 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Fitschen, Jan Henrik Laus, Friederike Schmitzer, Bernhard Univ Kaiserslautern Dept Math Kaiserslautern Germany Univ Munster Inst Computat & Appl Math Munster Germany

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

We introduce optimal transport-type distances for manifold-valued images. To do so we lift the initial data to measures on the product space of image domain and signal space, where they can then be compared by optimal transport with a transport cost that combines spatial distance and signal discrepancy. Applying recently introduced 'unbalanced' optimal transport models leads to more natural results. We illustrate the benefit of the lifting with numerical examples for interpolation of color images and classification of handwritten digits.

关键词： Color space Image Domain Signal space Back Projection Optimal Transport These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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A Unified Hyperelastic Joint Segmentation/Registration Model Based on Weighted Total Variation and Nonlocal Shape Descriptors 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Debroux, Noemie Le Guyader, Carole Normandie Univ INSA Rouen Lab Math 685 Ave Univ F-76801 St Etienne Du Rouvray France

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

In this paper, we address the issue of designing a unified variational model for joint segmentation and registration in which the shapes to be matched are viewed as hyperelastic materials, and more precisely, as Saint Venant-Kirchhoff ones. The dissimilarity measure relates local and global (or region-based) information, since relying on weighted total variation and on a nonlocal shape descriptor inspired by the Chan-Vese model for segmentation. Theoretical results emphasizing the mathematical and practical soundness of the model are provided, among which relaxation, existence of minimizers, analysis of two numerical methods of resolution, asymptotic results and a Gamma-convergence property.

关键词： Segmentation Registration Nonlinear elasticity Saint Venant-Kirchhoff material Quasiconvexity Relaxation Weighted BV space Piecewise constant Mumford-Shah model Nonlocal operators Gamma-convergence Asymptotic results

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Evaluating Data Terms for variational Multi-frame Super-Resolution 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Bodduna, Kireeti Weickert, Joachim Saarland Univ Math Image Anal Grp Fac Math & Comp Sci D-66041 Saarbrucken Germany

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

We present the first systematic evaluation of the data terms for multi-frame super-resolution within a variational model. The various data terms are derived by permuting the order of the blur-, downsample-, and warp-operators in the image acquisition model. This yields six different basic models. Our experiments using synthetic images with known ground truth show that two models are preferable: the widely-used warp-blur-downsample model that is physically plausible if atmospheric blur is negligible, and the hardly considered blur-warp-downsample model. We show that the quality of motion estimation plays the decisive role on which of these two models works best: While the classic warp-blur-downsample model requires optimal motion estimation, the rarely-used blur-warp-downsample model should be preferred in practically relevant scenarios when motion estimation is suboptimal. This confirms a widely ignored result by Wang and Qi (2004). Last but not least, we propose a new modification of the blur-warp-downsample model that offers a very significant speed-up without substantial loss in the reconstruction quality.

关键词： Super-resolution variational methods Inverse problems

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Blind space-Variant Single-Image Restoration of Defocus Blur 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Bar, Leah Sochen, Nir Kiryati, Nahum Tel Aviv Univ Dept Appl Math IL-69978 Tel Aviv Israel Tel Aviv Univ Sch Elect Engn IL-69978 Tel Aviv Israel

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

We address the problem of blind piecewise space-variant image deblurring where only part of the image is sharp, assuming a shallow depth of field which imposes significant defocus blur. We propose an automatic image recovery approach which segments the sharp and blurred sub-regions, iteratively estimates a non-parametric blur kernel and restores the sharp image via a variational non-blind space variant method. We present a simple and efficient blur measure which emphasizes the blur difference of the sub-regions followed by a blur segmentation procedure based on an evolving level set function. One of the contributions of this work is the extension to the space-variant case of progressive blind deconvolution recently proposed, an iterative process consisting of non-parametric blind kernel estimation and residual blur deblurring. Apparently this progressive strategy is superior to the one step deconvolution procedure. Experimental results on real images demonstrate the effectiveness of the proposed algorithm.

关键词： space-variant deblurring Blind deconvolution Blur segmentation

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Vehicle X-ray Scans Registration: A One-Dimensional Optimization Problem 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Marciano, Abraham Cohen, Laurent D. Gadi, Najib Univ Paris 09 PSL Res Univ CNRS CEREMADEUMR 7534 F-75016 Paris France Smiths Detect F-94405 Vitry Sur Seine France

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

Over the years, image registration has been largely employed in medical applications, robotics and geophysics. More recently, it has increasingly drawn attention of security and defense industries, particularly aiming at threat detection automation. This paper first introduces a short overview of mathematical methods for image registration, with a focus on variational approaches. In a second part, a specific registration task is presented: the optimal alignment between X-ray scans of an inspected vehicle and an empty reference of the same car model. Indeed, while being scanned by dedicated imaging systems, the car speed is not necessarily constant which may entail non-rigid deformations in the resulting image. The paper simply addresses this issue by applying a rigid transform on the reference image before using the variational framework solved in one dimension. For convergence and speed purposes, line-search techniques and a multiscale approach are used.

关键词： Image registration variational approach One-dimensional optimization

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Dynamic Texture Recognition Using Time-Causal Spatio-Temporal scale-space Filters 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Jansson, Ylva Lindeberg, Tony KTH Royal Inst Technol Computat Brain Sci Lab Dept Computat Sci & Technol Sch Comp Sci & Commun Stockholm Sweden

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

This work presents an evaluation of using time-causal scale-space filters as primitives for video analysis. For this purpose, we present a new family of video descriptors based on regional statistics of spatio-temporal scale-space filter responses and evaluate this approach on the problem of dynamic texture recognition. Our approach generalises a previously used method, based on joint histograms of receptive field responses, from the spatial to the spatio-temporal domain. We evaluate one member in this family, constituting a joint binary histogram, on two widely used dynamic texture databases. The experimental evaluation shows competitive performance compared to previous methods for dynamic texture recognition, especially on the more complex Dyn-Tex database. These results support the descriptive power of time-causal spatio-temporal scale-space filters as primitives for video analysis.

关键词： Receptive Field Local Binary Pattern Support Vector Machine Classifier Near Neighbour Linear Dynamical System These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Zeune, Leonie van Gils, Stephan A. Terstappen, Leon W. M. M. Brune, Christoph Univ Twente Dept Appl Math NL-7522 NB Enschede Netherlands Univ Twente Dept Med Cell BioPhys NL-7522 NB Enschede Netherlands

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, L-1 data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of L-1-based multi-scale methods with nonlinear spectral decompositions. We compare L-1 with L-2 scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of L-1-TV promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.

关键词： L-1-TV Denoising scale-spaces Nonlinear spectral decomposition Multiscale segmentation Eigenfunction Calibrable sets

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Order-Adaptive Regularisation for variational Optical Flow: Global, Local and in Between 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Maurer, Daniel Stoll, Michael Bruhn, Andres Univ Stuttgart Comp Vis & Intelligent Syst Grp Inst Visualizat & Interact Syst D-70569 Stuttgart Germany

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

Recent approaches for variational motion estimation typically either rely on first or second order regularisation strategies. While first order strategies are more appropriate for scenes with fronto-parallel motion, second order constraints are superior if it comes to the estimation of affine flow fields. Since using the wrong regularisation order may lead to a significant deterioration of the results, it is surprising that there has not been much effort in the literature so far to determine this order automatically. In our work, we address the aforementioned problem in two ways. (i) First, we discuss two anisotropic smoothness terms of first and second order, respectively, that share important structural properties and that are thus particularly suited for being combined within an order-adaptive variational framework. (ii) Secondly, based on these two smoothness terms, we develop four different variational methods and with it four different strategies for adaptively selecting the regularisation order: a global and a local strategy based on half-quadratic regularisation, a non-local approach that relies on neighbourhood information, and a region based method using level sets. Experiments on recent benchmarks show the benefits of each of the strategies. Moreover, they demonstrate that adaptively combining different regularisation orders not only allows to outperform single-order strategies but also to obtain advantages beyond the ones of a frame-wise selection.

关键词： Higher order regularisation variational methods Optical flow

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Nonlinear Spectral Image Fusion 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Benning, Martin Moeller, Michael Nossek, Raz Z. Burger, Martin Cremers, Daniel Gilboa, Guy Schonilibe, Carola-Bibiane Univ Cambridge Wilberforce Rd Cambridge CB3 0WA England Univ Siegen Holderlinstr 3 D-57076 Siegen Germany Technion IIT IL-32000 Haifa Israel Westfalische Wilhelms Univ Einsteinstr 62 D-48149 Munster Germany Tech Univ Munich Boltzmannstr 3 D-85748 Garching Germany

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

In this paper we demonstrate that the framework of non-linear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and edge-preserving spectral TV decomposition allows to select frequencies of a certain image to transfer particular features, such as wrinkles in a face, from one image to another. We illustrate the effectiveness of the proposed approach in several numerical experiments, including a comparison to the competing techniques of Poisson image editing, linear osmosis, wavelet fusion and Laplacian pyramid fusion. We conclude that the proposed spectral TV image decomposition framework is a valuable tool for semi-and fully-automatic image editing and fusion.

关键词： Nonlinear spectral decomposition Total variation regularization Image fusion Image composition Multiscale methods

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Spatio-Temporal scale Selection in Video Data 1

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6th international conference on scale space and variational methods in computer vision (SSVM)

作者： Lindeberg, Tony KTH Royal Inst Technol Computat Brain Sci Lab Dept Computat Sci & Technol Sch Comp Sci & Commun Stockholm Sweden

ISBN: (数字)9783319587714

ISBN: (纸本)9783319587714;9783319587707

We present a theory and a method for simultaneous detection of local spatial and temporal scales in video data. The underlying idea is that if we process video data by spatio-temporal receptive fields at multiple spatial and temporal scales, we would like to generate hypotheses about the spatial extent and the temporal duration of the underlying spatio-temporal image structures that gave rise to the feature responses. For two types of spatio-temporal scale-space representations, (i) a non-causal Gaussian spatio-temporal scale space for offline analysis of pre-recorded video sequences and (ii) a time-causal and time-recursive spatio-temporal scale space for online analysis of real-time video streams, we express sufficient conditions for spatio-temporal feature detectors in terms of spatio-temporal receptive fields to deliver scale covariant and scale invariant feature responses. A theoretical analysis is given of the scale selection properties of six types of spatio-temporal interest point detectors, showing that five of them allow for provable scale covariance and scale invariance. Then, we describe a time-causal and time-recursive algorithm for detecting sparse spatio-temporal interest points from video streams and show that it leads to intuitively reasonable results.

关键词： Temporal scale Video Data Local Extremum scale Covariance scale Selection These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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