@phdthesis{Ambellan, author = {Ambellan, Felix}, title = {Efficient Riemannian Statistical Shape Analysis with Applications in Disease Assessment}, doi = {10.17169/refubium-36729}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:188-refubium-37016-3}, abstract = {In this work, we address the challenge of developing statistical shape models that account for the non-Euclidean nature inherent to (anatomical) shape variation and at the same time offer fast, numerically robust processing and as much invariance as possible regarding translation and rotation, i.e. Euclidean motion. With the aim of doing that we formulate a continuous and physically motivated notion of shape space based on deformation gradients. We follow two different tracks endowing this differential representation with a Riemannian structure to establish a statistical shape model. (1) We derive a model based on differential coordinates as elements in GL(3)+. To this end, we adapt the notion of bi-invariant means employing an affine connection structure on GL(3)+. Furthermore, we perform second-order statistics based on a family of Riemannian metrics providing the most possible invariance, viz. GL(3)+-left-invariance and O(3)-right-invariance. (2) We endow the differential coordinates with a non-Euclidean structure, that stems from a product Lie group of stretches and rotations. This structure admits a bi-invariant metric and thus allows for a consistent analysis via manifold-valued Riemannian statistics. This work further presents a novel shape representation based on discrete fundamental forms that is naturally invariant under Euclidean motion, namely the fundamental coordinates. We endow this representation with a Lie group structure that admits bi-invariant metrics and therefore allows for consistent analysis using manifold-valued statistics based on the Riemannian framework. Furthermore, we derive a simple, efficient, robust, yet accurate (i.e. without resorting to model approximations) solver for the inverse problem that allows for interactive applications. Beyond statistical shape modeling the proposed framework is amenable for surface processing such as quasi-isometric flattening. Additionally, the last part of the thesis aims on shape-based, continuous disease stratification to provide means that objectify disease assessment over the current clinical practice of ordinal grading systems. Therefore, we derive the geodesic B-score, a generalization of the of the Euclidean B-score, in order to assess knee osteoarthritis. In this context we present a Newton-type fixed point iteration for projection onto geodesics in shape space. On the application side, we show that the derived geodesic B-score features, in comparison to its Euclidean counterpart, an improved predictive performance on assessing the risk of total knee replacement surgery.}, language = {en} } @misc{AmbellanHanikvonTycowicz, author = {Ambellan, Felix and Hanik, Martin and von Tycowicz, Christoph}, title = {Morphomatics: Geometric morphometrics in non-Euclidean shape spaces}, doi = {10.12752/8544}, abstract = {Morphomatics is an open-source Python library for (statistical) shape analysis developed within the geometric data analysis and processing research group at Zuse Institute Berlin. It contains prototype implementations of intrinsic manifold-based methods that are highly consistent and avoid the influence of unwanted effects such as bias due to arbitrary choices of coordinates.}, language = {en} } @misc{AmbellanLameckervonTycowiczetal., author = {Ambellan, Felix and Lamecker, Hans and von Tycowicz, Christoph and Zachow, Stefan}, title = {Statistical Shape Models - Understanding and Mastering Variation in Anatomy}, issn = {1438-0064}, doi = {10.1007/978-3-030-19385-0_5}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72699}, abstract = {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.}, language = {en} } @incollection{AmbellanLameckervonTycowiczetal., author = {Ambellan, Felix and Lamecker, Hans and von Tycowicz, Christoph and Zachow, Stefan}, title = {Statistical Shape Models - Understanding and Mastering Variation in Anatomy}, series = {Biomedical Visualisation}, volume = {3}, booktitle = {Biomedical Visualisation}, number = {1156}, editor = {Rea, Paul M.}, edition = {1}, publisher = {Springer Nature Switzerland AG}, isbn = {978-3-030-19384-3}, doi = {10.1007/978-3-030-19385-0_5}, pages = {67 -- 84}, abstract = {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.}, language = {en} } @inproceedings{AmbellanTackEhlkeetal., author = {Ambellan, Felix and Tack, Alexander and Ehlke, Moritz and Zachow, Stefan}, title = {Automated Segmentation of Knee Bone and Cartilage combining Statistical Shape Knowledge and Convolutional Neural Networks: Data from the Osteoarthritis Initiative}, series = {Medical Imaging with Deep Learning}, booktitle = {Medical Imaging with Deep Learning}, abstract = {We present a method for the automated segmentation of knee bones and cartilage from magnetic resonance imaging, that combines a priori knowledge of anatomical shape with Convolutional Neural Networks (CNNs). The proposed approach incorporates 3D Statistical Shape Models (SSMs) as well as 2D and 3D CNNs to achieve a robust and accurate segmentation of even highly pathological knee structures. The method is evaluated on data of the MICCAI grand challenge "Segmentation of Knee Images 2010". For the first time an accuracy equivalent to the inter-observer variability of human readers has been achieved in this challenge. Moreover, the quality of the proposed method is thoroughly assessed using various measures for 507 manual segmentations of bone and cartilage, and 88 additional manual segmentations of cartilage. Our method yields sub-voxel accuracy. In conclusion, combining of anatomical knowledge using SSMs with localized classification via CNNs results in a state-of-the-art segmentation method.}, language = {en} } @misc{AmbellanTackEhlkeetal., author = {Ambellan, Felix and Tack, Alexander and Ehlke, Moritz and Zachow, Stefan}, title = {Automated Segmentation of Knee Bone and Cartilage combining Statistical Shape Knowledge and Convolutional Neural Networks: Data from the Osteoarthritis Initiative}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-72704}, abstract = {We present a method for the automated segmentation of knee bones and cartilage from magnetic resonance imaging (MRI) that combines a priori knowledge of anatomical shape with Convolutional Neural Networks (CNNs).The proposed approach incorporates 3D Statistical Shape Models (SSMs) as well as 2D and 3D CNNs to achieve a robust and accurate segmentation of even highly pathological knee structures.The shape models and neural networks employed are trained using data from the Osteoarthritis Initiative (OAI) and the MICCAI grand challenge "Segmentation of Knee Images 2010" (SKI10), respectively. We evaluate our method on 40 validation and 50 submission datasets from the SKI10 challenge.For the first time, an accuracy equivalent to the inter-observer variability of human readers is achieved in this challenge.Moreover, the quality of the proposed method is thoroughly assessed using various measures for data from the OAI, i.e. 507 manual segmentations of bone and cartilage, and 88 additional manual segmentations of cartilage. Our method yields sub-voxel accuracy for both OAI datasets. We make the 507 manual segmentations as well as our experimental setup publicly available to further aid research in the field of medical image segmentation.In conclusion, combining localized classification via CNNs with statistical anatomical knowledge via SSMs results in a state-of-the-art segmentation method for knee bones and cartilage from MRI data.}, language = {en} } @misc{AmbellanTackEhlkeetal., author = {Ambellan, Felix and Tack, Alexander and Ehlke, Moritz and Zachow, Stefan}, title = {Automated Segmentation of Knee Bone and Cartilage combining Statistical Shape Knowledge and Convolutional Neural Networks: Data from the Osteoarthritis Initiative (Supplementary Material)}, series = {Medical Image Analysis}, volume = {52}, journal = {Medical Image Analysis}, number = {2}, doi = {10.12752/4.ATEZ.1.0}, pages = {109 -- 118}, abstract = {We present a method for the automated segmentation of knee bones and cartilage from magnetic resonance imaging that combines a priori knowledge of anatomical shape with Convolutional Neural Networks (CNNs). The proposed approach incorporates 3D Statistical Shape Models (SSMs) as well as 2D and 3D CNNs to achieve a robust and accurate segmentation of even highly pathological knee structures. The shape models and neural networks employed are trained using data of the Osteoarthritis Initiative (OAI) and the MICCAI grand challenge "Segmentation of Knee Images 2010" (SKI10), respectively. We evaluate our method on 40 validation and 50 submission datasets of the SKI10 challenge. For the first time, an accuracy equivalent to the inter-observer variability of human readers has been achieved in this challenge. Moreover, the quality of the proposed method is thoroughly assessed using various measures for data from the OAI, i.e. 507 manual segmentations of bone and cartilage, and 88 additional manual segmentations of cartilage. Our method yields sub-voxel accuracy for both OAI datasets. We made the 507 manual segmentations as well as our experimental setup publicly available to further aid research in the field of medical image segmentation. In conclusion, combining statistical anatomical knowledge via SSMs with the localized classification via CNNs results in a state-of-the-art segmentation method for knee bones and cartilage from MRI data.}, language = {en} } @article{AmbellanTackEhlkeetal., author = {Ambellan, Felix and Tack, Alexander and Ehlke, Moritz and Zachow, Stefan}, title = {Automated Segmentation of Knee Bone and Cartilage combining Statistical Shape Knowledge and Convolutional Neural Networks: Data from the Osteoarthritis Initiative}, series = {Medical Image Analysis}, volume = {52}, journal = {Medical Image Analysis}, number = {2}, doi = {10.1016/j.media.2018.11.009}, pages = {109 -- 118}, abstract = {We present a method for the automated segmentation of knee bones and cartilage from magnetic resonance imaging that combines a priori knowledge of anatomical shape with Convolutional Neural Networks (CNNs). The proposed approach incorporates 3D Statistical Shape Models (SSMs) as well as 2D and 3D CNNs to achieve a robust and accurate segmentation of even highly pathological knee structures. The shape models and neural networks employed are trained using data of the Osteoarthritis Initiative (OAI) and the MICCAI grand challenge "Segmentation of Knee Images 2010" (SKI10), respectively. We evaluate our method on 40 validation and 50 submission datasets of the SKI10 challenge. For the first time, an accuracy equivalent to the inter-observer variability of human readers has been achieved in this challenge. Moreover, the quality of the proposed method is thoroughly assessed using various measures for data from the OAI, i.e. 507 manual segmentations of bone and cartilage, and 88 additional manual segmentations of cartilage. Our method yields sub-voxel accuracy for both OAI datasets. We made the 507 manual segmentations as well as our experimental setup publicly available to further aid research in the field of medical image segmentation. In conclusion, combining statistical anatomical knowledge via SSMs with the localized classification via CNNs results in a state-of-the-art segmentation method for knee bones and cartilage from MRI data.}, language = {en} } @inproceedings{AmbellanTackWilsonetal., author = {Ambellan, Felix and Tack, Alexander and Wilson, Dave and Anglin, Carolyn and Lamecker, Hans and Zachow, Stefan}, title = {Evaluating two methods for Geometry Reconstruction from Sparse Surgical Navigation Data}, series = {Proceedings of the Jahrestagung der Deutschen Gesellschaft f{\"u}r Computer- und Roboterassistierte Chirurgie (CURAC)}, volume = {16}, booktitle = {Proceedings of the Jahrestagung der Deutschen Gesellschaft f{\"u}r Computer- und Roboterassistierte Chirurgie (CURAC)}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-65339}, pages = {24 -- 30}, abstract = {In this study we investigate methods for fitting a Statistical Shape Model (SSM) to intraoperatively acquired point cloud data from a surgical navigation system. We validate the fitted models against the pre-operatively acquired Magnetic Resonance Imaging (MRI) data from the same patients. We consider a cohort of 10 patients who underwent navigated total knee arthroplasty. As part of the surgical protocol the patients' distal femurs were partially digitized. All patients had an MRI scan two months pre-operatively. The MRI data were manually segmented and the reconstructed bone surfaces used as ground truth against which the fit was compared. Two methods were used to fit the SSM to the data, based on (1) Iterative Closest Points (ICP) and (2) Gaussian Mixture Models (GMM). For both approaches, the difference between model fit and ground truth surface averaged less than 1.7 mm and excellent correspondence with the distal femoral morphology can be demonstrated.}, language = {en} } @misc{AmbellanTackWilsonetal., author = {Ambellan, Felix and Tack, Alexander and Wilson, Dave and Anglin, Carolyn and Lamecker, Hans and Zachow, Stefan}, title = {Evaluating two methods for Geometry Reconstruction from Sparse Surgical Navigation Data}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-66052}, abstract = {In this study we investigate methods for fitting a Statistical Shape Model (SSM) to intraoperatively acquired point cloud data from a surgical navigation system. We validate the fitted models against the pre-operatively acquired Magnetic Resonance Imaging (MRI) data from the same patients. We consider a cohort of 10 patients who underwent navigated total knee arthroplasty. As part of the surgical protocol the patients' distal femurs were partially digitized. All patients had an MRI scan two months pre-operatively. The MRI data were manually segmented and the reconstructed bone surfaces used as ground truth against which the fit was compared. Two methods were used to fit the SSM to the data, based on (1) Iterative Closest Points (ICP) and (2) Gaussian Mixture Models (GMM). For both approaches, the difference between model fit and ground truth surface averaged less than 1.7 mm and excellent correspondence with the distal femoral morphology can be demonstrated.}, language = {en} }