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Bézier curves in the space of images 5

Bézier curves in the space of images

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

作者： Effland, Alexander Rumpf, Martin Simon, Stefan Stahn, Kirsten Wirth, Benedikt Institute for Numerical Simulation Universität Bonn Bonn Germany Institute for Computational and Applied Mathematics University of Muenster Muenster Germany

B33;zier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of B33;zier curves to the infinite-dimensional space of images. To this end the space of image... 详细信息

ISBN: (纸本)9783319184609

Bézier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of Bézier curves to the infinite-dimensional space of images. To this end the space of images is equipped with a Riemannian metric which measures the cost of image transport and intensity variation in the sense of the metamorphosis model [MY01]. Bézier curves are then computed via the Riemannian version of de Casteljau’s algorithm, which is based on a hierarchical scheme of convex combination along geodesic curves. Geodesics are approximated using a variational discretization of the Riemannian path energy. This leads to a generalized de Casteljau method to compute suitable discrete Bézier curves in image space. Selected test cases demonstrate qualitative properties of the approach. Furthermore, a Bézier approach for the modulation of face interpolation and shape animation via image sketches is presented. © Springer international Publishing Switzerland 2015.

关键词： Geometry

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The morphological equivalents of relativistic and alpha-scale-spaces 5

The morphological equivalents of relativistic and alpha-scal...

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

作者： Schmidt, Martin Weickert, Joachim Mathematical Image Analysis Group Saarland University Campus E1.7 Saarbrücken66041 Germany

ISBN: (纸本)9783319184609

The relations between linear system theory and mathematical morphology are mainly understood on a pure convolution/dilation level. A formal connection on the level of differential or pseudo-differential equations is still missing. In our paper we close this gap. We establish the sought relation by means of infinitesimal generators, exploring essential properties of the slope and a modified Cramér transform. As an application of our general theory, we derive the morphological counterparts of relativistic scale-spaces and of α-scale-spaces for α ∈ [1/2, ∞). Our findings are illustrated by experiments. © Springer international Publishing Switzerland 2015.

关键词： Mathematical transformations

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A variational model for color assignment 5

A variational model for color assignment

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

作者： Fitschen, Jan Henrik Nikolova, Mila Pierre, Fabien Steidl, Gabriele Department of Mathematics University of Kaiserslautern Kaiserslautern Germany CMLA – CNRS ENS Cachan Cachan France University of Bordeaux CNRS IMB UMR 5251 LaBRI UMR 5800 Talence France

ISBN: (纸本)9783319184609

Color image enhancement is a challenging task in digital imaging with many applications. This paper contributes to image enhancement methods. We propose a new variational model for color improvement in the RGB space based on a desired target intensity image. Our model improves the visual quality of the color image while it preserves the range and takes the hue of the original, badly exposed image into account without amplifying its color artifacts. To approximate the hue of the original image we use the fact that affine transforms are hue preserving. To cope with the noise in the color channels we design a particular coupled TV regularization term. Since the target intensity of the image is unaltered our model respects important image structures. Numerical results demonstrate the very good performance of our method. © Springer international Publishing Switzerland 2015.

关键词： Affine transforms

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IGFTT: Towards an efficient alternative to SIFT and SURF 23

IGFTT: Towards an efficient alternative to SIFT and SURF

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23rd international conference in Central Europe on computer Graphics, Visualization and computer vision, WSCG 2015

作者： De Oliveira, Ícaro Oliveira Fonseca, Keiko Veronica Ono Todt, Eduardo Federal Technological University of Paraná Brazil VRI Research Group Federal University of Paraná Brazil

ISBN: (纸本)9788086943657

The invariant feature detectors are essential components in many computer vision applications, such as tracking, simultaneous localization and mapping (SLAM), image search, machine vision, object recognition, 3D reconstruction from multiple images, augmented reality, stereo vision, and others. However, it is very challenging to detect high quality features while maintaining a low computational cost. scale-Invariant Feature Transform (SIFT) and Speeded-Up Robust Features (SURF) algorithms exhibit great performance under a variety of image transformations, however these methods rely on costly keypoint's detection. Recently, fast and efficient variants such as Binary Robust Invariant Scalable Keypoints (BRISK) and Oriented Fast and Rotated BRIEF (ORB) were developed to offset the computational burden of these traditional detectors. In this paper, we propose to improve the Good Features to Track (GFTT) detector, coined IGFTT. It approximates or even outperforms the state-of-art detectors with respect to repeatability, distinctiveness, and robustness, yet can be computed much faster than Maximally Stable Extremal Regions (MSER), SIFT, BRISK, KAZE, Accelerated KAZE (AKAZE) and SURF. This is achieved by using the search of maximal-minimum eigenvalue in the image on scale-space and a new orientation extraction method based on eigenvectors. A comprehensive evaluation on standard datasets shows that IGFTT achieves quite a high performance with a computation time comparable to state-of-the-art real-time features. The proposed method shows exceptionally good performance compared to SURF, ORB, GFTT, MSER, Star, SIFT, KAZE, AKAZE and BRISK.

关键词： computer vision

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Multiview depth parameterisation with second order regularisation 5

Multiview depth parameterisation with second order regularis...

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

作者： Schroers, Christopher Hafner, David Weickert, Joachim Mathematical Image Analysis Group Saarland University Campus E1.7 Saarbr¨ucken66041 Germany

ISBN: (纸本)9783319184609

In this paper we consider the problem of estimating depth maps from multiple views within a variational framework. Previous work has demonstrated that multiple views improve the depth reconstruction, and that higher order regularisers model a good prior for typical realworld 3D scenes. We build on these findings and stress an important aspect that has not been considered in variational multiview depth estimation so far: We investigate several parameterisations of the unknown depth. This allows us to show, both analytically and experimentally, that directly working with depth values introduces an undesirable bias. As a remedy, we reveal that an inverse depth parameterisation is generally preferable. Our analysis clearly points out its benefits w.r.t. the data and the smoothness term. We verify these theoretical findings by means of experiments. © Springer international Publishing Switzerland 2015.

关键词： Three dimensional computer graphics

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A L1-TV algorithm for robust perspective photometric stereo with spatially-varying lightings 5

A L1-TV algorithm for robust perspective photometric stereo ...

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

作者： Quéau, Yvain Lauze, François Durou, Jean-Denis IRIT UMR CNRS Toulouse5505 France Department of Computer Science University of Copenhagen Copenhagen Denmark

ISBN: (纸本)9783319184609

We tackle the problem of perspective 3D-reconstruction of Lambertian surfaces through photometric stereo, in the presence of outliers to Lambert’s law, depth discontinuities, and unknown spatiallyvarying lightings. To this purpose, we introduce a robust L1-TV variational formulation of the recovery problem where the shape itself is the main unknown, which naturally enforces integrability and permits to avoid integrating the normal field. © Springer international Publishing Switzerland 2015.

关键词： Photometry

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Morphological scale-space operators for images supported on point clouds 5

Morphological scale-space operators for images supported on ...

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

作者： Angulo, Jesús CMM-Centre de Morphologie Mathématique MINES ParisTech PSL-Research University Paris France

ISBN: (纸本)9783319184609

The aim of this paper is to develop the theory, and to propose an algorithm, for morphological processing of images painted on point clouds, viewed as a length metric measure space (X, d, μ). In order to extend morphological operators to process point cloud supported images, one needs to define dilation and erosion as semigroup operators on (X, d). That corresponds to a supremal convolution (and infimal convolution) using admissible structuring function on (X, d). From a more theoretical perspective, we introduce the notion of abstract structuring functions formulated on length metric Maslov idempotent measurable spaces, which is the appropriate setting for (X, d). In practice, computation of Maslov structuring function is approached by a random walks framework to estimate heat kernel on (X, d, μ), followed by the logarithmic trick. © Springer international Publishing Switzerland 2015.

关键词： Mathematical morphology

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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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A linear scale-space theory for continuous nonlocal evolutions 5

A linear scale-space theory for continuous nonlocal evolutio...

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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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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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