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

作者： Griffin, Lewis D. Lillholm, Martin UCL London England Univ Copenhagen Copenhagen Denmark

We review ideas about the relationship between qualitative description of local image structure and quantitative description based on responses to a family of linear filters. We propose a sequence of three linking hypotheses. The first, the Feature Hypothesis, is that qualitative descriptions arise from a category system on filter-response space. The second, the Icon Hypothesis, is that the partitioning into categories of filter response space is determined by a system of iconic images, one associated with each point of the space. The third, the Texton Hypothesis, is that the correct images to play the role of icons are those that are the most likely explanations of a vector of filter responses. We present results in support of these three hypotheses, including new results on 2-D 1 st order structure.

关键词： computer vision

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Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian 6th

Analytic Existence and Uniqueness Results for PDE-Based Imag...

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

作者： Hoeltgen, Laurent Harris, Isaac Breuss, Michael Kleefeld, Andreas Brandenburg Tech Univ Cottbus Inst Math Pl Deutsch Einheit 1 D-03046 Cottbus Germany Texas A&M Univ Dept Math 621A Blocker Bldg3368 TAMU College Stn TX 77843 USA Forschungszentrum Julich Inst Adv Simulat Julich Supercomp Ctr Wilhelm Johnen Str D-52425 Julich Germany

ISBN: (纸本)9783319587714;9783319587707

Partial differential equations are well suited for dealing with image reconstruction tasks such as inpainting. One of the most successful mathematical frameworks for image reconstruction relies on variations of the Laplace equation with different boundary conditions. In this work we analyse these formulations and discuss the existence and uniqueness of solutions of corresponding boundary value problems, as well as their regularity from an analytic point of view. Our work not only sheds light on useful aspects of the well posedness of several standard problem formulations in image reconstruction but also aggregates them in a common framework. In addition, the performed analysis guides us to specify two new formulations of the classic image reconstruction problem that may give rise to new developments in image reconstruction.

关键词： Partial differential equations Laplace equation Mixed boundary conditions Image reconstruction Image inpainting

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variational perspective shape from shading 5

Variational perspective shape from shading

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

作者： Ju, Yong Chul Bruhn, Andrés Breuß, Michael Computer Vision and Intelligent Systems Group Institute for Visualization and Interactive Systems University of Stuttgart Universitätsstraße 38 Stuttgart70569 Germany Applied Mathematics and Computer Vision Group Institute for Applied Mathematics and Scientic Computing BTU Cottbus-Senftenberg Platz der Deutschen Einheit 1 Cottbus03046 Germany

ISBN: (纸本)9783319184609

Many recent methods for perspective shape from shading (SfS) are based on formulations in terms of partial differential equations (PDEs). However, while the quality of such methods steadily improves, their lacking robustness is still an open issue. In this context, variational methods seem to be a promising alternative, since they allow to incorporate smoothness assumptions that have proven to be useful formany other tasks in computer vision. Surprisingly, however, suchmethods have hardly been considered for perspective SfS so far. In our article we address this problem and develop a novel variational model for this task. By combining building blocks of recent PDE-based methods such as a Lambertian reflectance model and camera-centred illumination with a discontinuitypreserving second-order smoothness term, we obtain a variational method for perspective SfS that offers by construction an improved degree of robustness compared to existing PDE-based approaches. Our experiments confirm the success of our strategy. They show that embedding the assumptions of PDE-based approaches into a variational model with a suitable smoothness term can be very beneficial – in particular in scenarios with noise or partially missing information. © Springer international Publishing Switzerland 2015.

关键词： Cameras

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An Efficient and stable Two-Pixel Scheme for 2D Forward-and-Backward Diffusion 6th

An Efficient and Stable Two-Pixel Scheme for 2D Forward-and-...

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

作者： Welk, Martin Weickert, Joachim Private Univ Hlth Sci Med Informat & Technol Inst Biomed Image Anal Eduard Wallnofer Zentrum 1 A-6060 Hall Tyrol Austria Saarland Univ Math Image Anal Grp Campus E1-7 D-66041 Saarbrucken Germany

ISBN: (纸本)9783319587714;9783319587707

Image enhancement with forward-and-backward (FAB) diffusion is numerically very challenging due to its negative diffusivities. As a remedy, we first extend the explicit nonstandard scheme by Welk et al. (2009) from the 1D scenario to the practically relevant two-dimensional setting. We prove that under a fairly severe time step restriction, this 2D scheme preserves a maximum-minimum principle. Moreover, we find an interesting Lyapunov sequence which guarantees convergence to a flat steady state. Since a global application of the time step size restriction leads to very slow algorithms and is more restrictive than necessary for most pixels, we introduce a much more efficient scheme with locally adapted time step sizes. It applies diffusive two-pixel interactions in a randomised order and adapts the time step size to the specific pixel pair. These space-variant time steps are synchronised at sync times. Our experiments show that our novel two-pixel scheme allows to compute FAB diffusion with guaranteed L-infinity-stability at a speed that can be three orders of magnitude larger than its explicit counterpart with a global time step size.

关键词： Pixels

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Optimising Spatial and Tonal Data for Homogeneous Diffusion Inpainting

Optimising Spatial and Tonal Data for Homogeneous Diffusion ...

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3rd international conference on scale space and variational methods in computer vision

作者： Mainberger, Markus Hoffmann, Sebastian Weickert, Joachim Tang, Ching Hoo Johannsen, Daniel Neumann, Frank Doerr, Benjamin Univ Saarland Fac Math & Comp Sci Math Image Anal Grp Campus E1-1 D-66041 Saarbrucken Germany Max Planck Inst Informat Dept Algorithms & Complex 1 Saarbrucken Germany Tel Aviv Univ Sch Math Sci IL-69978 Tel Aviv Israel Univ Adelaide Sch Comp Sci Adelaide SA 5005 Australia

ISBN: (纸本)9783642247842

Finding optimal inpainting data plays a key role in the field of image compression with partial differential equations (PDEs). In this paper, we optimise the spatial as well as the tonal data such that an image can be reconstructed with minimised error by means of discrete homogeneous diffusion inpainting. To optimise the spatial distribution of the inpainting data, we apply a probabilistic data sparsification followed by a nonlocal pixel exchange. Afterwards we optimise the grey values in these inpainting points in an exact way using a least squares approach. The resulting method allows almost perfect reconstructions with only 5% of all pixels. This demonstrates that a thorough data optimisation can compensate for most deficiencies of a suboptimal PDE interpolant.

关键词： image compression partial differential equations (PDEs) inpainting optimisation homogeneous diffusion

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Extraction of the Intercellular Skeleton from 2D Images of Embryogenesis Using Eikonal Equation and Advective Subjective Surface Method

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2nd international conference on scale space and variational methods in computer vision

作者： Bourgine, Paul Frolkovic, Peter Mikula, Karol Peyrieras, Nadine Remesikova, Mariana Ecole Polytech CNRS CREA 1 Rue Descartes F-75005 Paris France Slovak Tech Univ Dept Mat SL-81368 Bratislava Slovakia CNRS DEPSNGIF Ave Terasse F-91198 Gif Sur Yvette France

ISBN: (纸本)9783642022555

We suggest an efficient method for automatic detection of the intercellular skeleton in microscope images of early embryogenesis. The method is based on the solution of two advective PDEs. First, we solve numerically the time relaxed eikonal equation in order to obtain the signed distance function to a given set - a set of points representing cell centers or a set of closed curves representing segmented inner borders of cells. The second step is a segmentation process driven by the advective version of subjective surface equation where the velocity field is given by the gradient of the computed distance function. The first equation is discretized by Rouy-Tourin scheme and we suggest a fixing strategy that significantly improves the speed of the computation. The second equation is solved using a classical upwind strategy. We present several test examples and we show a practical application - the intercellular skeleton extracted from a 2D image of a zebrafish embryo.

关键词： Velocity

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PDE Evolutions for M-Smoothers: From Common Myths to Robust Numerics 7th

PDE Evolutions for M-Smoothers: From Common Myths to Robust ...

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7th international conference on scale space and variational methods in computer vision (SSVM)

ISBN: (纸本)9783030223687;9783030223670

Local M-smoothers constitute an interesting and important class of image processing techniques with many connections to other methods. In our paper we derive a family of partial differential equations (PDEs) that result as limiting processes from M-smoothers which are based on local order-p means within a disc the radius of which tends to zero. The order p may take any nonzero value > -1. Thus, we also allow negative values which have never been considered before. In contrast to results from the literature, we show in the space-continuous case that mode filtering does not arise for p -> 0, but for p -> -1. Extending our filter class to p-values smaller than - 1 allows to include e.g. the classical image sharpening flow of Gabor. Since our PDE class is highly anisotropic and may contain backward parabolic operators, designing adequate numerical methods is difficult. We present an L-infinity-stable explicit finite difference scheme that satisfies a discrete maximum-minimum principle, is fairly efficient, and offers excellent rotation invariance. Although it solves parabolic PDEs, it makes consequent use of stabilisation concepts from the numerics of hyperbolic PDEs. Our experiments show that the PDEs forp < 1 are of specific interest: Their backward parabolic term creates favourable sharpening properties, while they appear to maintain the strong shape simplification properties of mean curvature motion.

关键词： M-smoother Partial differential equation Mode filter Backward parabolic operator Anisotropy Finite difference methods Shape analysis

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Geodesics in Shape space via variational Time Discretization

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7th international conference on Energy Minimization methods in computer vision and Pattern Recognition

作者： Wirth, Benedikt Bar, Leah Rumpf, Martin Sapiro, Guillermo Univ Bonn Inst Numer Simulat D-5300 Bonn Germany Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

ISBN: (纸本)9783642036408

A variational approach to defining geodesics in the space of implicitly described shapes is introduced in this paper. The proposed framework is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 1-1 property of the induced flow in shape space. For decreasing time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the shape space. Considering shapes as boundary contours, the proposed shape metric is identical to a physical dissipation in a viscous fluid model of optimal transportation. If the pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional, for decreasing time step size one obtains an additional optical flow term controlling the transport of the shape by the underlying motion field. The implementation of the proposed approach is based oil a level set representation of shapes, which allows topological transitions along the geodesic path. For the spatial discretization a finite element approximation is employed both for the pairwise deformations and for the level set representation. The numerical relaxation of the energy is performed via all efficient multi-scale procedure in space and time. Examples for 2D and 3Dd shapes underline the effectiveness and robustness of the proposed approach.

关键词： Non Newtonian flow

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Elimination of artifacts due to occlusion and discretization problems in image space blurring techniques

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GRAPHICAL MODELS 2005年第6期67卷 584-599页

作者： Barsky, BA Tobias, MJ Chu, DP Horn, DR Univ Calif Berkeley Div Comp Sci Berkeley CA 94720 USA Univ Calif Berkeley Sch Optometry Berkeley CA 94720 USA Univ Calif Los Angeles Dept Comp Sci Los Angeles CA 90095 USA

Traditional computer graphics methods render images that appear sharp at all depths. Adding blur can add realism to a scene, provide a sense of scale, and draw a viewer's attention to a particular region of a scene. Our image-based blur algorithm needs to distinguish whether a portion of an image is either from a single object or is part of more than one object. This motivates two approaches to identify objects after an image has been rendered. We illustrate how these techniques can be used in conjunction with our image space method to add blur to a scene. (c) 2005 Elsevier Inc. All rights reserved.

关键词： image forming and processing visual perception

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scale space and variational methods in computer vision 1

Scale Space and Variational Methods in Computer Vision

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丛书名： Lecture Notes in computer Science

1000年

作者： Tatiana A. Bubba Romina Gaburro Silvia Gazzola Kostas Papafitsoros Marcelo Pereyra Carola-Bibiane Schönlieb

ISBN: (数字)9783031923661

ISBN: (纸本)9783031923654

The two-volume set LNCS 15667 and 15668 constitutes the proceedings of the 10th international conference on scale space and variational methods in computer vision, SSVM 2025, which took place in Dartington, UK, in May 2025. The total of 63 full papers accepted in the proceedings were carefully reviewed and selected from 81 submissions. They were organized in topical sections as follows: Part I: Inverse Problems in Imaging; machine and deep learning in imaging; Part II: Optimization for imaging: theory and methods; scale space, PDES, flow, motion and registration.

关键词： computer Imaging, vision, Pattern Recognition and Graphics Signal, Image and Speech Processing computer Communication Networks computer Applications Machine Learning Mathematics of Computing

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