@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} } @misc{HoeltgenPeterBreuss, author = {Hoeltgen, Laurent and Peter, Pascal and Breuß, Michael}, title = {Clustering-based quantisation for PDE-based image compression}, series = {Signal, Image and Video Processing}, volume = {12}, journal = {Signal, Image and Video Processing}, number = {3}, issn = {1863-1703}, doi = {10.1007/s11760-017-1173-9}, pages = {411 -- 419}, abstract = {Optimal known pixel data for inpainting in compression codecs based on partial differential equations is real-valued and thereby expensive to store. Thus, quantisation is required for efficient encoding. In this paper, we interpret the quantisation step as a clustering problem. Due to the global impact of each known pixel and correlations between spatial and tonal data, we investigate the central question, which kind of feature vectors should be used for clustering with popular strategies such as k-means. Our findings show that the number of colours can be reduced significantly without impacting the reconstruction quality. Surprisingly, these benefits are negated by an increased coding cost in compression applications.}, language = {en} } @misc{HoeltgenBreussHeroldetal., author = {Hoeltgen, Laurent and Breuß, Michael and Herold, Gert and Sarradj, Ennes}, title = {Sparse ℓ1 regularisation of matrix valued models for acoustic source characterisation}, series = {Optimization and Engineering}, volume = {19}, journal = {Optimization and Engineering}, number = {1}, issn = {1389-4420}, doi = {10.1007/s11081-017-9357-2}, pages = {39 -- 70}, abstract = {We present a strategy for the recovery of a sparse solution of a common problem in acoustic engineering, which is the reconstruction of sound source levels and locations applying microphone array measurements. The considered task bears similarities to the basis pursuit formalism but also relies on additional model assumptions that are challenging from a mathematical point of view. Our approach reformulates the original task as a convex optimisation model. The sought solution shall be a matrix with a certain desired structure. We enforce this structure through additional constraints. By combining popular splitting algorithms and matrix differential theory in a novel framework we obtain a numerically efficient strategy. Besides a thorough theoretical consideration we also provide an experimental setup that certifies the usability of our strategy. Finally, we also address practical issues, such as the handling of inaccuracies in the measurement and corruption of the given data. We provide a post processing step that is capable of yielding an almost perfect solution in such circumstances.}, language = {en} } @inproceedings{BaehrDachselBreuss, author = {B{\"a}hr, Martin and Dachsel, Robert and Breuß, Michael}, title = {Fast Solvers for Solving Shape Matching by Time Integration}, series = {Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria}, booktitle = {Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria}, editor = {Welk, Martin and Urschler, Martin and Roth, Peter M.}, publisher = {Verlag der TU Graz}, address = {Graz}, isbn = {978-3-85125-603-1}, doi = {10.3217/978-3-85125-603-1-14}, pages = {65 -- 72}, abstract = {The main task in three-dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three-dimensional objects. An important building block of many methods constructed to achieve this goal is a simplified shape representation called feature descriptor, which is invariant under almost isometric transformations. A recent feature descriptor relies on the full numerical integration of the geometric heat equation. This approach involves to solve a system of linear equations with multiple right-hand sides. To this end, it is necessary to find a fast and accurate numerical scheme in conjunction with the solution of a sparse linear system and many different right sides. In this paper we evaluate direct, iterative and model order reduction (MOR) methods and their influence to shape correspondence applications which will be validated on standard shape data sets with different resolutions.}, language = {en} } @inproceedings{DachselBreussHoeltgen, author = {Dachsel, Robert and Breuß, Michael and Hoeltgen, Laurent}, title = {A Study of Spectral Expansion for Shape Correspondence}, series = {Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria}, booktitle = {Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria}, editor = {Welk, Martin and Urschler, Martin and Roth, Peter M.}, publisher = {Verlag der TU Graz}, address = {Graz}, isbn = {978-3-85125-603-1}, doi = {10.3217/978-3-85125-603-1-15}, pages = {73 -- 79}, abstract = {The main task in three dimensional non-rigid shape correspondence is to retrieve similarities between two or more similar three dimensional objects. A useful way to tackle this problem is to construct a simplified shape representation, called feature descriptor, which is invariant under deformable transformations. A successful class of such feature descriptors is based on physical phenomena, concretely by the heat equation for the heat kernel signature and the Schr{\"o}dinger equation for the wave kernel signature. Both approaches employ the spectral decomposition of the Laplace-Beltrami operator, meaning that solutions of the corresponding equations are expressed by a series expansion in terms of eigenfunctions. The feature descriptor is then computed at hand of those solutions. In this paper we explore the influence of the amount of used eigenfunctions on shape correspondence applications, as this is a crucial point with respect to accuracy and overall computational efficiency of the method. Our experimental study will be performed at hand of a standard shape data set.}, language = {en} } @inproceedings{SharifiBoroujerdiKhanianBreuss, author = {Sharifi Boroujerdi, Ali and Khanian, Maryam and Breuß, Michael}, title = {Deep Interactive Region Segmentation and Captioning}, series = {2017 13th International Conference on Signal-Image Technology \& Internet-Based Systems (SITIS), Jaipur, India}, booktitle = {2017 13th International Conference on Signal-Image Technology \& Internet-Based Systems (SITIS), Jaipur, India}, publisher = {IEEE}, address = {Piscataway, NJ}, isbn = {978-1-5386-4283-2}, doi = {10.1109/SITIS.2017.27}, pages = {103 -- 110}, abstract = {Based on recent developments in dense image captioning, it is now possible to describe every object of a photographed scene with a caption while objects are determined by bounding boxes. However, the user interpretation of such an output is not trivial due to the existence of many overlapping bounding boxes. Furthermore, in current captioning frameworks, the user is not able to involve personal preferences to exclude areas that are out of interest. In this paper, we propose a novel hybrid deep learning architecture for interactive region segmentation and captioning whereby the user is able to specify an arbitrary region of the image that should be highlighted and described. To this end, we trained three different highly deep architectures on our special training data to identify the User Intention Region (UIR). In parallel, a dense image captioning model is utilized to locate all the objects of the scene by drawing bounding boxes and produce their linguistic descriptions. During our fusion approach, the detected UIR will be explained with the caption of the best match bounding box. To the best of our knowledge, this is the first work that provides such a comprehensive output. Our experiments show the superiority of the proposed approach over state-of-the-art interactive segmentation methods on several well-known segmentation benchmarks. In addition, replacement of the bounding boxes with the result of the interactive segmentation leads to a better understanding of the dense image captioning output as well as an enhancement in object localization accuracy.}, language = {en} } @inproceedings{SchefflerMansouriYarahmadiBreussetal., author = {Scheffler, Robert and Mansouri Yarahmadi, Ashkan and Breuß, Michael and K{\"o}hler, Ekkehard}, title = {A Graph Theoretic Approach for Shape from Shading}, series = {Energy minimization methods in computer vision and pattern recognition , 11th International Conference, EMMCVPR 2017, Venice, Italy, October 30 - November 1, 2017}, booktitle = {Energy minimization methods in computer vision and pattern recognition , 11th International Conference, EMMCVPR 2017, Venice, Italy, October 30 - November 1, 2017}, editor = {Pelillo, Marcello and Hancock, Edwin}, publisher = {Springer}, address = {Cham}, isbn = {978-3-319-78198-3}, doi = {10.1007/978-3-319-78199-0_22}, pages = {328 -- 341}, abstract = {Resolving ambiguities is a fundamental problem in shape from shading (SFS). The classic SFS approach allows to reconstruct the surface locally around singular points up to an ambiguity of convex, concave or saddle point type. In this paper we follow a recent approach that seeks to resolve the local ambiguities in a global graph-based setting so that the complete surface reconstruction is consistent. To this end, we introduce a novel graph theoretic formulation for the underlying problem that allows to prove for the first time in the literature that the underlying surface orientation problem is NP-complete. Moreover, we show that our novel framework allows to define an algorithmic framework that solves the disambiguation problem. It makes use of cycle bases for dealing with the graph construction and enables an easy embedding into an optimization method that amounts here to a linear program.}, language = {en} } @misc{KhanianSharifiBoroujerdiBreuss, author = {Khanian, Maryam and Sharifi Boroujerdi, Ali and Breuß, Michael}, title = {Photometric stereo for strong specular highlights}, series = {Computational Visual Media}, volume = {4}, journal = {Computational Visual Media}, number = {1}, issn = {2096-0433}, doi = {10.1007/s41095-017-0101-9}, pages = {83 -- 102}, abstract = {Photometric stereo is a fundamental technique in computer vision known to produce 3D shape with high accuracy. It uses several input images of a static scene taken from one and the same camera position but under varying illumination. The vast majority of studies in this 3D reconstruction method assume orthographic projection for the camera model. In addition, they mainly use the Lambertian reflectance model as the way that light scatters at surfaces. Thus, providing reliable photometric stereo results from real world objects still remains a challenging task. We address 3D reconstruction by use of a more realistic set of assumptions, combining for the first time the complete Blinn-Phong reflectance model and perspective projection. Furthermore, we compare two different methods of incorporating the perspective projection into our model. Experiments are performed on both synthetic and real world images; the latter do not benefit from laboratory conditions. The results show the high potential of our method even for complex real world applications such as medical endoscopy images which may include many specular highlights.}, 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 Joint Variational Method for Estimating Depth, Illumination and Albedo}, series = {International Journal of Computer Vision}, volume = {126}, journal = {International Journal of Computer Vision}, number = {12}, issn = {0920-5691}, doi = {10.1007/s11263-018-1079-1}, pages = {1342 -- 1366}, 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. This difference in approaching the reconstruction problem yields complementary advantages that are worthwhile being combined. So far, however, most "joint" approaches are based on an initial stereo mesh that is subsequently refined using shading information. In this paper we follow a completely different approach. We propose a joint variational method that combines both cues within a single minimisation framework. 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 resulting model in such a way that it jointly estimates depth, albedo and illumination. This in turn makes the approach applicable to objects with non-uniform albedo as well as to scenes with unknown illumination. Experiments for synthetic and real-world images demonstrate the benefits of our combined approach: They not only show that our method is capable of generating very detailed reconstructions, but also that joint approaches are feasible in practice.}, language = {en} } @misc{BreussKemmVogel, author = {Breuß, Michael and Kemm, Friedemann and Vogel, Oliver}, title = {A numerical study of Newton interpolation with extremely high degrees}, series = {Kybernetika : international journal published by Institute of Information Theory and Automation}, volume = {54}, journal = {Kybernetika : international journal published by Institute of Information Theory and Automation}, number = {2}, issn = {0023-5954}, doi = {10.14736/kyb-2018-2-0279}, pages = {279 -- 288}, abstract = {In current textbooks the use of Chebyshev nodes with Newton interpolation is advocated as the most efficient numerical interpolation method in terms of approximation accuracy and computational effort. However, we show numerically that the approximation quality obtained by Newton interpolation with Fast Leja (FL) points is competitive to the use of Chebyshev nodes, even for extremely high degree interpolation. This is an experimental account of the analytic result that the limit distribution of FL points and Chebyshev nodes is the same when letting the number of points go to infinity. Since the FL construction is easy to perform and allows to add interpolation nodes on the fly in contrast to the use of Chebyshev nodes, our study suggests that Newton interpolation with FL points is currently the most efficient numerical technique for polynomial interpolation. Moreover, we give numerical evidence that any reasonable function can be approximated up to machine accuracy by Newton interpolation with FL points if desired, which shows the potential of this method.}, language = {en} } @misc{HoeltgenBreussRadow, author = {Hoeltgen, Laurent and Breuß, Michael and Radow, Georg}, title = {Towards PDE-Based Video Compression with Optimal Masks and Optic Flow}, series = {Scale Space and Variational Methods in Computer Vision : 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 - July 4, 2019, Proceedings}, journal = {Scale Space and Variational Methods in Computer Vision : 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30 - July 4, 2019, Proceedings}, editor = {Lellmann, Jan and Burger, Martin and Modersitzki, Jan}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-22367-0}, doi = {10.1007/978-3-030-22368-7_7}, pages = {79 -- 91}, abstract = {Lossy image compression methods based on partial differential equations have received much attention in recent years. They may yield high quality results but rely on the computationally expensive task of finding optimal data. For the possible extension to video compression, the data selection is a crucial issue. In this context one could either analyse the video sequence as a whole or perform a frame-by-frame optimisation strategy. Both approaches are prohibitive in terms of memory and run time. In this work we propose to restrict the expensive computation of optimal data to a single frame and to approximate the optimal reconstruction data for the remaining frames by prolongating it by means of an optic flow field. We achieve a notable decrease in the computational complexity. As a proof-of-concept, we evaluate the proposed approach for multiple sequences with different characteristics. We show that the method preserves a reasonable quality in the reconstruction, and is very robust against errors in the flow field.}, language = {en} } @misc{RadowBreuss, author = {Radow, Georg and Breuß, Michael}, title = {Variational Optical Flow: Warping and Interpolation Revisited}, series = {Computer Analysis of Images and Patterns 18th International Conference, CAIP 2019, Salerno, Italy, September 3-5, 2019, Proceedings, Part I}, journal = {Computer Analysis of Images and Patterns 18th International Conference, CAIP 2019, Salerno, Italy, September 3-5, 2019, Proceedings, Part I}, editor = {Vento, Mario and Percannella, Gennaro}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-29887-6}, issn = {978-3-030-29888-3}, doi = {/10.1007/978-3-030-29888-3_33}, pages = {409 -- 420}, abstract = {One of the fundamental problems in computer vision is to attain the apparent motion in image sequences, the optical flow. As evaluations at hand of recent benchmarks show, this field is highly competitive. High ranking variational methods often consist of a combination of techniques, where frequently the presentation in the literature focuses on novel contributions in modelling. In this paper we investigate the warping technique and related algorithmic design choices that are fundamental for practical implementation. At hand of a detailed yet straightforward derivation we discuss different warping variations. These are evaluated in numerical experiments, and furthermore we investigate the impact of a variety of interpolation methods that can be used.}, language = {en} } @misc{BaehrRadowBreussetal., author = {B{\"a}hr, Martin and Radow, Georg and Breuß, Michael and F{\"u}genschuh, Armin}, title = {Computation of Stable Honeycomb Structures for Additive Manufacturing}, series = {Operations Research Proceedings 2018, Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Brussels, Belgium, September 12-14, 2018}, journal = {Operations Research Proceedings 2018, Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), Brussels, Belgium, September 12-14, 2018}, editor = {Fortz, Bernard and Labb{\´e}, Martine}, publisher = {Springer}, address = {Cham}, isbn = {978-3-030-18499-5}, issn = {978-3-030-18500-8}, doi = {10.1007/978-3-030-18500-8_45}, pages = {363 -- 369}, abstract = {In certain additive manufacturing processes of industrial interest, the task arises to build up structures layer-wise in a purely vertical manner. The question arises how to construct such a structure in a convenient way so that it is structurally as stable as possible. In this paper, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this we employ Lloyd's algorithm in two different realisations. For computing the incorporated Voronoi tessellation we consider the use of a Delaunay triangulation or the Eikonal equation. As a main point of our paper, we give a comparison of these two methods. We show that one can make use of the arising graph of the honeycomb structure as input for a specific routing scheme that enhances printability when the printing material stays soft for some time during the printing process.}, language = {en} }