@incollection{JuMaurerBreussetal., author = {Ju, Yong Chul and Maurer, Daniel and Breuß, Michael and Bruhn, Andr{\´e}s}, title = {Direct variational perspective shape from shading with Cartesian depth parametrisation}, series = {Perspectives in Shape Analysis, Mathematics and Visualization}, booktitle = {Perspectives in Shape Analysis, Mathematics and Visualization}, editor = {Breuß, Michael and Bruckstein, Alfred and Maragos, Petros and Wuhrer, Stefanie}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-24724-3}, doi = {10.1007/978-3-319-24726-7}, pages = {43 -- 72}, language = {en} } @misc{HoeltgenQueauBreussetal., author = {Hoeltgen, Laurent and Queau, Yvain and Breuß, Michael and Radow, Georg}, title = {Optimised photometric stereo via non-convex variational minimisation}, publisher = {BMVA Press}, address = {York, UK}, pages = {1}, language = {en} } @misc{MaurerJuBreussetal., author = {Maurer, Daniel and Ju, Yong Chul and Breuß, Michael and Bruhn, Andr{\´e}s}, title = {Combining Shape from Shading and Stereo: A Variational Approach for the Joint Estimation of Depth, Illumination and Albedo}, publisher = {BMVA Press}, address = {York, UK}, abstract = {Shape from shading (SfS) and stereo are two fundamentally different strategies for image-based 3-D reconstruction. While approaches for SfS infer the depth solely from pixel intensities, methods for stereo are based on a matching process that establishes correspondences across images. In this paper we propose a joint variational method that combines the advantages of both strategies. By integrating recent stereo and SfS models into a single minimisation framework, we obtain an approach that exploits shading information to improve upon the reconstruction quality of robust stereo methods. To this end, we fuse a Lambertian SfS approach with a robust stereo model and supplement the resulting energy functional with a detail-preserving anisotropic second-order smoothness term. Moreover, we extend the novel model in such a way that it jointly estimates depth, albedo and illumination. This in turn makes it applicable to objects with non-uniform albedo as well as to scenes with unknown illumination. Experiments for synthetic and real-world images show the advantages of our combined approach: While the stereo part overcomes the albedo-depth ambiguity inherent to all SfS methods, the SfS part improves the degree of details of the reconstruction compared to pure stereo methods.}, language = {en} } @misc{WelkKleefeldBreuss, author = {Welk, Martin and Kleefeld, Andreas and Breuß, Michael}, title = {Quantile Filtering of Colour Images via Symmetric Matrices}, series = {Mathematical Morphology - Theory and Applications}, volume = {1}, journal = {Mathematical Morphology - Theory and Applications}, number = {1}, issn = {2353-3390}, doi = {10.1515/mathm-2016-0008}, pages = {136 -- 174}, abstract = {Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2 × 2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these.We consider variants of these filters based on three matrix norms - the nuclear, Frobenius, and spectral norm - and study their differences. We investigate the properties of the quantile and gradient filters and their links to dilation and erosion operators. Using amoeba structuring elements,we devise image-adaptive versions of our quantile and gradient filters. Experiments are presented to demonstrate the favourable properties of the filters, and compare them to existing approaches in colour morphology.}, language = {de} } @inproceedings{RadowBreussHoeltgenetal., author = {Radow, Georg and Breuß, Michael and Hoeltgen, Laurent and Fischer, Thomas}, title = {Optimised Anisotropic Poisson Denoising}, series = {Image Analysis, 20th Scandinavian Conference, SCIA 2017, Troms{\o}, Norway, June 12-14, 2017, Proceedings, Part I}, booktitle = {Image Analysis, 20th Scandinavian Conference, SCIA 2017, Troms{\o}, Norway, June 12-14, 2017, Proceedings, Part I}, editor = {Sharma, Puneet and Filippo, Maria Bianchi}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-59126-1}, doi = {10.1007/978-3-319-59126-1_42}, pages = {502 -- 514}, language = {en} } @inproceedings{DachselBreussHoeltgen, author = {Dachsel, Robert and Breuß, Michael and Hoeltgen, Laurent}, title = {The Classic Wave Equation Can Do Shape Correspondence}, series = {Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017}, booktitle = {Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017}, editor = {Felsberg, Michael and Heyden, Andreas and Kr{\"u}ger, Norbert}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-64688-6}, doi = {10.1007/978-3-319-64689-3_22}, pages = {264 -- 275}, abstract = {A major task in non-rigid shape analysis is to retrieve correspondences between two almost isometric 3D objects. An important tool for this task are geometric feature descriptors. Ideally, a feature descriptor should be invariant under isometric transformations and robust to small elastic deformations. A successful class of feature descriptors employs the spectral decomposition of the Laplace-Beltrami operator. Important examples are the heat kernel signature using the heat equation and the more recent wave kernel signature applying the Schr{\"o}dinger equation from quantum mechanics. In this work we propose a novel feature descriptor which is based on the classic wave equation that describes e.g. sound wave propagation. We explore this new model by discretizing the underlying partial differential equation. Thereby we consider two different time integration methods. By a detailed evaluation at hand of a standard shape data set we demonstrate that our approach may yield significant improvements over state of the art methods for finding correct shape correspondences.}, language = {en} } @inproceedings{DachselBreussHoeltgen, author = {Dachsel, Robert and Breuß, Michael and Hoeltgen, Laurent}, title = {Shape Matching by Time Integration of Partial Differential Equations}, series = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, booktitle = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-58770-7}, doi = {10.1007/978-3-319-58771-4_53}, pages = {669 -- 680}, abstract = {The main task in three dimensional shape matching is to retrieve correspondences between two similar three dimensional objects. To this end, a suitable point descriptor which is invariant under isometric transformations is required. A commonly used descriptor class relies on the spectral decomposition of the Laplace-Beltrami operator. Important examples are the heat kernel signature and the more recent wave kernel signature. In previous works, the evaluation of the descriptor is based on eigenfunction expansions. Thereby a significant practical aspect is that computing a complete expansion is very time and memory consuming. Thus additional strategies are usually introduced that enable to employ only part of the full expansion. In this paper we explore an alternative solution strategy. We discretise the underlying partial differential equations (PDEs) not only in space as in the mentioned approaches, but we also tackle temporal parts by using time integration methods. Thus we do not perform eigenfunction expansions and avoid the use of additional strategies and corresponding parameters. We study here the PDEs behind the heat and wave kernel signature, respectively. Our shape matching experiments show that our approach may lead to quality improvements for finding correct correspondences in comparison to the eigenfunction expansion methods.}, language = {en} } @inproceedings{HoeltgenHarrisBreussetal., author = {Hoeltgen, Laurent and Harris, I. and Breuß, Michael and Kleefeld, Andreas}, title = {Analytic Existence and Uniqueness Results for PDE-Based Image Reconstruction with the Laplacian}, series = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, booktitle = {Scale Space and Variational Methods in Computer Vision, 6th International Conference on Scale Space and Variational Methods in Computer Vision (SSVM 2017, Kolding, Denmark, June 2017), proceedings}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-58770-7}, doi = {10.1007/978-3-319-58771-4_6}, pages = {66 -- 79}, abstract = {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.}, language = {en} } @inproceedings{BreussHoeltgenKleefeld, author = {Breuß, Michael and Hoeltgen, Laurent and Kleefeld, Andreas}, title = {Matrix-Valued Levelings for Colour Images}, series = {Mathematical morphology and its applications to signal and image processing, 13th international symposium, ISMM 2017, Fontainebleau, France, May 15-17, 2017, proceedings}, booktitle = {Mathematical morphology and its applications to signal and image processing, 13th international symposium, ISMM 2017, Fontainebleau, France, May 15-17, 2017, proceedings}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-319-57239-0}, doi = {10.1007/978-3-319-57240-6_24}, pages = {296 -- 308}, abstract = {Morphological levelings represent a useful tool for the decomposition of an image into cartoon and texture components. Moreover, they can be used to construct a morphological scale space. However, the classic construction of levelings is limited to the use of grey scale images, since an ordering of pixel values is required. In this paper we propose an extension of morphological levelings to colour images. To this end, we consider the formulation of colour images as matrix fields and explore techniques based on the Loewner order for formulating morphological levelings in this setting. Using the matrix-valued colours we study realisations of levelings relying on both the completely discrete construction and the formulation using a partial differential equation. Experimental results confirm the potential of our matrix-based approaches for analysing texture in colour images and for extending the range of applications of levelings in a convenient way to colour image processing.}, language = {en} } @misc{BaehrBreussQueauetal., author = {B{\"a}hr, Martin and Breuß, Michael and Qu{\`e}au, Yvain and Sharifi Boroujerdi, Ali and Durou, Jean-Denis}, title = {Fast and accurate surface normal integration on non-rectangular domains}, series = {Computational Visual Media}, volume = {3}, journal = {Computational Visual Media}, number = {2}, issn = {2096-0433}, doi = {10.1007/s41095-016-0075-z}, pages = {107 -- 129}, abstract = {The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness, and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose. To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.}, language = {en} }