Zachow, Stefan
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We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent Riemannian setting, we construct a framework that reliably handles large deformations. Due to the explicit character of Lie group operations, our non-Euclidean method is very efficient allowing for fast and numerically robust processing. This facilitates Riemannian analysis of large shape populations accessible through longitudinal and multi-site imaging studies providing increased statistical power. We evaluate the performance of our model w.r.t. shape-based classification of pathological malformations of the human knee and show that it outperforms the standard Euclidean as well as a recent nonlinear approach especially in presence of sparse training data. To provide insight into the model’s ability of capturing natural biological shape variability, we carry out an analysis of specificity and generalization ability.
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.
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.
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.
Functional surgery on the nasal framework requires referential criteria to objectively assess nasal breathing for indication and follow-up. Thismotivated us to generate amean geometry of the nasal cavity based on a statistical shape model. In this study, the authors could demonstrate that the introduced nasal cavity’s mean geometry features characteristics of the inner shape and airflow, which are commonly observed in symptom-free subjects. Therefore, the mean geometry might serve as a reference-like model when one considers qualitative aspects. However, to facilitate quantitative considerations and statistical inference, further research is necessary. Additionally, the authorswere able to obtain details about the importance of the isthmus nasi and the inferior turbinate for the intranasal airstream.
Successful functional surgery on the nasal framework requires reliable and comprehensive diagnosis. In this regard, the authors introduce a new methodology: Digital Analysis of Nasal Airflow (diANA). It is based on computational fluid dynamics, a statistical shape model of the healthy nasal cavity and rhinologic expertise. diANA necessitates an anonymized tomographic dataset of the paranasal sinuses including the complete nasal cavity and, when available, clinical information. The principle of diANA is to compare the morphology and the respective airflow of an individual nose with those of a reference. This enablesmorphometric aberrations and consecutive flow field anomalies to localize and quantify within a patient’s nasal cavity. Finally, an elaborated expert opinion with instructive visualizations is provided. Using diANA might support surgeons in decision-making, avoiding unnecessary surgery, gaining more precision, and target-orientation for indicated operations.
Volumetry of the cartilage of the knee, as needed for the assessment of knee osteoarthritis (KOA), is typically performed in a tedious and subjective process. We present an automated segmentation-based method for the quantification of cartilage volume by employing 3D Convolutional Neural Networks
(CNNs). CNNs were trained in a supervised manner using magnetic resonance imaging data as well as cartilage volumetry readings given by clinical experts for 1378 subjects. It was shown that 3D CNNs can be employed for cartilage volumetry with an accuracy similar to expert volumetry readings. In future, accurate automated cartilage volumetry might support both, diagnosis of KOA as well as assessment of KOA progression via longitudinal analysis.
Advanced osteoarthritis is a leading cause of knee replacement and loss of functionality. Early detection of risk factors plays an important role in the application of preventive measures. One of the risk factors is the leg alignment which influences the speed of
knee cartilage degradation. The ’gold standard’ measurement of leg alignment is done by determining the Hip Knee Ankle (HKA) angle from full lower limb radiographs. Convolutional Neural Networks (CNNs) have gained popularity recently in computer vision. In this thesis we developed methods using CNNs to determine HKA angles from full lower limb radiographs. We trained the CNNs using data from the Osteoarthritis Initiative (OAI). We evaluated our method’s performance by evaluating its agreement to experts measurement and its reliability. Our best performing method shows excellent agreement and reliability levels.
Volumetry of cartilage of the knee is needed for knee osteoarthritis (KOA) assessment. It is typically performed manually in a tedious and subjective process. We developed a method for an automated, segmentation-based quantification of cartilage volume by employing 3D Convolutional Neural Networks (CNNs). CNNs were trained in a supervised manner using magnetic resonance imaging data and cartilage volumetry readings performed by clinical experts for 1378 subjects provided by the Osteoarthritis Initiative. It was shown that 3D CNNs are able to achieve volume measures comparable to the magnitude of variation between expert readings and
the real in vivo situation. In the future, accurate automated cartilage volumetry might support both, diagnosis of KOA as well as longitudinal analysis of KOA progression.