TY - JOUR A1 - Kofler, Andreas A1 - Wald, Christian A1 - Kolbitsch, Christoph A1 - von Tycowicz, Christoph A1 - Ambellan, Felix T1 - Joint Reconstruction and Segmentation in Undersampled 3D Knee MRI combining Shape Knowledge and Deep Learning JF - Physics in Medicine and Biology N2 - Task-adapted image reconstruction methods using end-to-end trainable neural networks (NNs) have been proposed to optimize reconstruction for subsequent processing tasks, such as segmentation. However, their training typically requires considerable hardware resources and thus, only relatively simple building blocks, e.g. U-Nets, are typically used, which, albeit powerful, do not integrate model-specific knowledge. In this work, we extend an end-to-end trainable task-adapted image reconstruction method for a clinically realistic reconstruction and segmentation problem of bone and cartilage in 3D knee MRI by incorporating statistical shape models (SSMs). The SSMs model the prior information and help to regularize the segmentation maps as a final post-processing step. We compare the proposed method to a state-of-the-art (SOTA) simultaneous multitask learning approach for image reconstruction and segmentation (MTL) and to a complex SSMs-informed segmentation pipeline (SIS). Our experiments show that the combination of joint end-to-end training and SSMs to further regularize the segmentation maps obtained by MTL highly improves the results, especially in terms of mean and maximal surface errors. In particular, we achieve the segmentation quality of SIS and, at the same time, a substantial model reduction that yields a five-fold decimation in model parameters and a computational speedup of an order of magnitude. Remarkably, even for undersampling factors of up to R=8, the obtained segmentation maps are of comparable quality to those obtained by SIS from ground-truth images. Y1 - 2024 U6 - https://doi.org/10.1088/1361-6560/ad3797 VL - 69 IS - 9 ER - TY - GEN A1 - Ambellan, Felix A1 - Lamecker, Hans A1 - von Tycowicz, Christoph A1 - Zachow, Stefan T1 - Statistical Shape Models - Understanding and Mastering Variation in Anatomy N2 - In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression. Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated. We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) statistical shape models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods ormachine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring. T3 - ZIB-Report - 19-13 Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-72699 SN - 1438-0064 ER - TY - CHAP A1 - Ambellan, Felix A1 - Lamecker, Hans A1 - von Tycowicz, Christoph A1 - Zachow, Stefan ED - Rea, Paul M. T1 - Statistical Shape Models - Understanding and Mastering Variation in Anatomy T2 - Biomedical Visualisation N2 - In our chapter we are describing how to reconstruct three-dimensional anatomy from medical image data and how to build Statistical 3D Shape Models out of many such reconstructions yielding a new kind of anatomy that not only allows quantitative analysis of anatomical variation but also a visual exploration and educational visualization. Future digital anatomy atlases will not only show a static (average) anatomy but also its normal or pathological variation in three or even four dimensions, hence, illustrating growth and/or disease progression. Statistical Shape Models (SSMs) are geometric models that describe a collection of semantically similar objects in a very compact way. SSMs represent an average shape of many three-dimensional objects as well as their variation in shape. The creation of SSMs requires a correspondence mapping, which can be achieved e.g. by parameterization with a respective sampling. If a corresponding parameterization over all shapes can be established, variation between individual shape characteristics can be mathematically investigated. We will explain what Statistical Shape Models are and how they are constructed. Extensions of Statistical Shape Models will be motivated for articulated coupled structures. In addition to shape also the appearance of objects will be integrated into the concept. Appearance is a visual feature independent of shape that depends on observers or imaging techniques. Typical appearances are for instance the color and intensity of a visual surface of an object under particular lighting conditions, or measurements of material properties with computed tomography (CT) or magnetic resonance imaging (MRI). A combination of (articulated) statistical shape models with statistical models of appearance lead to articulated Statistical Shape and Appearance Models (a-SSAMs).After giving various examples of SSMs for human organs, skeletal structures, faces, and bodies, we will shortly describe clinical applications where such models have been successfully employed. Statistical Shape Models are the foundation for the analysis of anatomical cohort data, where characteristic shapes are correlated to demographic or epidemiologic data. SSMs consisting of several thousands of objects offer, in combination with statistical methods ormachine learning techniques, the possibility to identify characteristic clusters, thus being the foundation for advanced diagnostic disease scoring. Y1 - 2019 SN - 978-3-030-19384-3 SN - 978-3-030-19385-0 U6 - https://doi.org/10.1007/978-3-030-19385-0_5 VL - 3 IS - 1156 SP - 67 EP - 84 PB - Springer Nature Switzerland AG ET - 1 ER - TY - GEN A1 - Götschel, Sebastian A1 - von Tycowicz, Christoph A1 - Polthier, Konrad A1 - Weiser, Martin T1 - Reducing Memory Requirements in Scientific Computing and Optimal Control N2 - In high accuracy numerical simulations and optimal control of time-dependent processes, often both many time steps and fine spatial discretizations are needed. Adjoint gradient computation, or post-processing of simulation results, requires the storage of the solution trajectories over the whole time, if necessary together with the adaptively refined spatial grids. In this paper we discuss various techniques to reduce the memory requirements, focusing first on the storage of the solution data, which typically are double precision floating point values. We highlight advantages and disadvantages of the different approaches. Moreover, we present an algorithm for the efficient storage of adaptively refined, hierarchic grids, and the integration with the compressed storage of solution data. T3 - ZIB-Report - 13-64 KW - optimal control KW - trajectory storage KW - mesh compression KW - compression Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42695 SN - 1438-0064 ER - TY - GEN A1 - Tycowicz, Christoph von A1 - Ambellan, Felix A1 - Mukhopadhyay, Anirban A1 - Zachow, Stefan T1 - A Riemannian Statistical Shape Model using Differential Coordinates N2 - We propose a novel Riemannian framework for statistical analysis of shapes that is able to account for the nonlinearity in shape variation. By adopting a physical perspective, we introduce a differential representation that puts the local geometric variability into focus. We model these differential coordinates as elements of a Lie group thereby endowing our shape space with a non-Euclidian structure. A key advantage of our framework is that statistics in a manifold shape space become numerically tractable improving performance by several orders of magnitude over state-of-the-art. We show that our Riemannian model is well suited for the identification of intra-population variability as well as inter-population differences. In particular, we demonstrate the superiority of the proposed model in experiments on specificity and generalization ability. We further derive a statistical shape descriptor that outperforms the standard Euclidian approach in terms of shape-based classification of morphological disorders. T3 - ZIB-Report - 16-69 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-61175 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/6485 SN - 1438-0064 ER - TY - CHAP A1 - Götschel, Sebastian A1 - Tycowicz, Christoph von A1 - Polthier, Konrad A1 - Weiser, Martin ED - Carraro, T. ED - Geiger, M. ED - Koerkel, S. ED - Rannacher, R. T1 - Reducing Memory Requirements in Scientific Computing and Optimal Control T2 - Multiple Shooting and Time Domain Decomposition Methods Y1 - 2015 SP - 263 EP - 287 PB - Springer ER - TY - GEN A1 - Brandt, Christopher A1 - Tycowicz, Christoph von A1 - Hildebrandt, Klaus T1 - Geometric Flows of Curves in Shape Space for Processing Motion of Deformable Objects N2 - We introduce techniques for the processing of motion and animations of non-rigid shapes. The idea is to regard animations of deformable objects as curves in shape space. Then, we use the geometric structure on shape space to transfer concepts from curve processing in R^n to the processing of motion of non-rigid shapes. Following this principle, we introduce a discrete geometric flow for curves in shape space. The flow iteratively replaces every shape with a weighted average shape of a local neighborhood and thereby globally decreases an energy whose minimizers are discrete geodesics in shape space. Based on the flow, we devise a novel smoothing filter for motions and animations of deformable shapes. By shortening the length in shape space of an animation, it systematically regularizes the deformations between consecutive frames of the animation. The scheme can be used for smoothing and noise removal, e.g., for reducing jittering artifacts in motion capture data. We introduce a reduced-order method for the computation of the flow. In addition to being efficient for the smoothing of curves, it is a novel scheme for computing geodesics in shape space. We use the scheme to construct non-linear “Bézier curves” by executing de Casteljau’s algorithm in shape space. T3 - ZIB-Report - 16-29 Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-59504 SN - 1438-0064 ER - TY - GEN A1 - Nava-Yazdani, Esfandiar A1 - Hege, Hans-Christian A1 - von Tycowicz, Christoph A1 - Sullivan, T. J. T1 - A Shape Trajectories Approach to Longitudinal Statistical Analysis N2 - For Kendall’s shape space we determine analytically Jacobi fields and parallel transport, and compute geodesic regression. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As application example we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative. Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data only. T3 - ZIB-Report - 18-42 KW - shape space, shape trajectories, geodesic regression, longitudinal analysis, osteoarthritis Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69759 SN - 1438-0064 ER - TY - CHAP A1 - Krämer, Martin A1 - Maggioni, Marta A1 - Tycowicz, Christoph von A1 - Brisson, Nick A1 - Zachow, Stefan A1 - Duda, Georg A1 - Reichenbach, Jürgen T1 - Ultra-short echo-time (UTE) imaging of the knee with curved surface reconstruction-based extraction of the patellar tendon T2 - ISMRM (International Society for Magnetic Resonance in Medicine), 26th Annual Meeting 2018, Paris, France N2 - Due to very short T2 relaxation times, imaging of tendons is typically performed using ultra-short echo-time (UTE) acquisition techniques. In this work, we combined an echo-train shifted multi-echo 3D UTE imaging sequence with a 3D curved surface reconstruction to virtually extract the patellar tendon from an acquired 3D UTE dataset. Based on the analysis of the acquired multi-echo data, a T2* relaxation time parameter map was calculated and interpolated to the curved surface of the patellar tendon. Y1 - 2018 ER - TY - CHAP A1 - von Tycowicz, Christoph T1 - Towards Shape-based Knee Osteoarthritis Classification using Graph Convolutional Networks T2 - 2020 IEEE 17th International Symposium on Biomedical Imaging (ISBI 2020) N2 - We present a transductive learning approach for morphometric osteophyte grading based on geometric deep learning. We formulate the grading task as semi-supervised node classification problem on a graph embedded in shape space. To account for the high-dimensionality and non-Euclidean structure of shape space we employ a combination of an intrinsic dimension reduction together with a graph convolutional neural network. We demonstrate the performance of our derived classifier in comparisons to an alternative extrinsic approach. Y1 - 2020 U6 - https://doi.org/10.1109/ISBI45749.2020.9098687 ER -