TY - CHAP A1 - Dachsel, Robert A1 - Breuß, Michael A1 - Hoeltgen, Laurent ED - Felsberg, Michael ED - Heyden, Andreas ED - Krüger, Norbert T1 - The Classic Wave Equation Can Do Shape Correspondence T2 - Computer Analysis of Images and Patterns, CAIP International Conference on Computer Analysis of Images and Patterns, Ystad,Sweden, 2017 N2 - 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 Schrödinger 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. KW - Feature descriptor KW - Shape analysis KW - Wave equation Y1 - 2017 SN - 978-3-319-64688-6 U6 - https://doi.org/10.1007/978-3-319-64689-3_22 SP - 264 EP - 275 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Dachsel, Robert A1 - Breuß, Michael A1 - Hoeltgen, Laurent T1 - Shape Matching by Time Integration of Partial Differential Equations T2 - 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 N2 - 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. KW - Shape matching Point descriptor Shape analysis Heat equation Schrödinger equation Y1 - 2017 SN - 978-3-319-58770-7 U6 - https://doi.org/10.1007/978-3-319-58771-4_53 SP - 669 EP - 680 PB - Springer International Publishing CY - Cham ER - TY - CHAP A1 - Bähr, Martin A1 - Dachsel, Robert A1 - Breuß, Michael ED - Welk, Martin ED - Urschler, Martin ED - Roth, Peter M. T1 - Fast Solvers for Solving Shape Matching by Time Integration T2 - Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria N2 - 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. Y1 - 2018 SN - 978-3-85125-603-1 U6 - https://doi.org/10.3217/978-3-85125-603-1-14 SP - 65 EP - 72 PB - Verlag der TU Graz CY - Graz ER - TY - CHAP A1 - Dachsel, Robert A1 - Breuß, Michael A1 - Hoeltgen, Laurent ED - Welk, Martin ED - Urschler, Martin ED - Roth, Peter M. T1 - A Study of Spectral Expansion for Shape Correspondence T2 - Proceedings of the OAGM Workshop 2018 Medical Image Analysis, May 15 - 16, 2018, Hall/Tyrol, Austria N2 - 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 Schrödinger 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. Y1 - 2018 SN - 978-3-85125-603-1 U6 - https://doi.org/10.3217/978-3-85125-603-1-15 SP - 73 EP - 79 PB - Verlag der TU Graz CY - Graz ER - TY - GEN A1 - Dachsel, Robert A1 - Jöster, Annika A1 - Breuß, Michael ED - Lee, Chilwoo ED - Su, Zhixun ED - Sugimoto, Akihiro T1 - Real-Time Retinal Vessel Segmentation on High-Resolution Fundus Images Using Laplacian Pyramids T2 - Image and Video Technology, 9th Pacific-Rim Symposium, PSIVT 2019, Sydney, NSW, Australia, November 18–22, 2019, Proceedings N2 - In ophthalmology, fundus images are commonly used to examine the human eye. The image data shows among others the capillary system of the retina. Recognising alternations in the retinal blood vessels is pivotal to diagnosing certain diseases. The visual inspection of those fundus images is a time-consuming process and a challenging task which has to be done by medical experts. Furthermore, rapid advances in medical imaging allow for generating fundus images of increased quality and resolution. Therefore, the support by computers for the analysis and evaluation of complex fundus image information is growing in importance and there is a corresponding need for fast and efficient algorithms. In this paper, we present a well-engineered, robust real-time segmentation algorithm which is adapted to the recent and upcoming challenges of high resolution fundus images. Thereby we make use of the multiscale representation of the Laplacian pyramid which is fast to compute and useful for detecting coarse as well as finely branched blood vessels. It is possible to process images of size 3504×2336 pixels in 0.8 s on a standard desktop computer and 0.3 on a Nvidia Titan XP GPU. By a detailed evaluation at hand of an accessible high-resolution data set we demonstrate that our approach is competitive in quality to state of the art methods for segmenting blood vessels but much faster. KW - Laplacian pyramids Vessel segmentation High-resolution fundus images Real-time retinal imaging Y1 - 2019 SN - 978-3-030-34878-6 SN - 978-3-030-34879-3 U6 - https://doi.org/10.1007/978-3-030-34879-3_26 SN - 0302-9743 SN - 1611-3349 SP - 337 EP - 350 PB - Springer CY - Cham ER -