Alexander Effland, Sebastian Neumayer and Martin Rumpf Convergence of the Time Discrete Metamorphosis Model on Hadamard Manifolds 2019 https://arxiv.org/abs/1902.10930
Alexander Effland, Erich Kobler, Thomas Pock, Marko Rajković and Martin Rumpf Image Morphing in Deep Feature Spaces: Theory and Applications 2019 https://arxiv.org/abs/1910.12672
Alexander Effland, Erich Kobler, Anne Brandenburg, Teresa Klatzer, Leonie Neuhäuser, Michael Hölzel, Jennifer Landsberg, Thomas Pock and Martin Rumpf Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data International Journal of Computer Assisted Radiology and Surgery, 14(4): 587--599 2019 https://dx.doi.org/10.1007/s11548-019-01919-z
Alexander Effland, Erich Kobler, Thomas Pock and Martin Rumpf Time Discrete Geodesics in Deep Feature Spaces for Image Morphing In Lellmann, Jan and Burger, Martin and Modersitzki, Jan, editor, Scale Space and Variational Methods in Computer Vision
page 171--182.
Publisher: Springer International Publishing
2019 https://dx.doi.org/10.1007/978-3-030-22368-7_14
2018
Alexander Effland, Martin Rumpf and Florian Schäfer Image extrapolation for the time discrete metamorphosis model -- existence and applications SIAM J. Imaging Sci. 2018 https://arxiv.org/abs/1705.04490
2017
Benjamin Berkels, Michael Buchner, Alexander Effland, Martin Rumpf and Steffen Schmitz-Valckenberg GPU Based Image Geodesics for Optical Coherence Tomography In Bildverarbeitung für die Medizin, Informatik aktuell
page 68--73.
Publisher: Springer
2017 http://dx.doi.org/10.1007/978-3-662-54345-0_21
Alexander Effland, Martin Rumpf and Florian Schäfer Time discrete extrapolation in a Riemannian space of images In Proc. of International Conference on Scale Space and Variational Methods in Computer Vision, Volume 10302
page 473--485.
Publisher: Springer, Cham
2017 https://dx.doi.org/10.1007/978-3-319-58771-4_38
2015
Benjamin Berkels, Alexander Effland and Martin Rumpf A Posteriori Error Control for the Binary Mumford-Shah Model ArXiv Preprint 2015 http://arxiv.org/abs/1505.05284
Abstract: The binary Mumford-Shah model is a widespread tool for image segmentation and can be considered as a basic model in shape optimization with a broad range of applications in computer vision, ranging from basic segmentation and labeling to object reconstruction. This paper presents robust a posteriori error estimates for a natural error quantity, namely the area of the non properly segmented region. To this end, a suitable strictly convex and non-constrained relaxation of the originally non-convex functional is investigated and Repin's functional approach for a posteriori error estimation is used to control the numerical error for the relaxed problem in the $L^2$-norm. In combination with a suitable cut out argument, a fully practical estimate for the area mismatch is derived. This estimate is incorporated in an adaptive meshing strategy. Two different adaptive primal-dual finite element schemes, and the most frequently used finite difference discretization are investigated and compared. Numerical experiments show qualitative and quantitative properties of the estimates and demonstrate their usefulness in practical applications.
Benjamin Berkels, Alexander Effland and Martin Rumpf Time Discrete Geodesic Paths in the Space of Images SIAM J. Imaging Sci., 8(3): 1457-1488 2015 http://dx.doi.org/10.1137/140970719
Abstract: In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and effective variational time discretization of geodesics paths is proposed. This requires to minimize a discrete path energy consisting of a sum of consecutive image matching functionals over a set of image intensity maps and pairwise matching deformations. For square-integrable input images the existence of discrete, connecting geodesic paths defined as minimizers of this variational problem is shown. Furthermore, Γ-convergence of the underlying discrete path energy to the continuous path energy is proved. This includes a diffeomorphism property for the induced transport and the existence of a square-integrable weak material derivative in space and time. A spatial discretization via finite elements combined with an alternating descent scheme in the set of image intensity maps and the set of matching deformations is presented to approximate discrete geodesic paths numerically. Computational results underline the efficiency of the proposed approach and demonstrate important qualitative properties.
Alexander Effland, Martin Rumpf, Stefan Simon, Kirsten Stahn and Benedikt Wirth Bézier curves in the space of images In Proceedings Scale Space and Variational Methods in Computer Vision, Volume 9087 of Lecture Notes in Computer Science
page 372-384.
Publisher: Springer International
2015 http://dx.doi.org/10.1007/978-3-319-18461-6_30
Abstract: 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 by Miller and Younes. 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.