Articulated Statistical Shape Modelling of the Shoulder Joint

The shoulder joint is the most mobile and unstable joint in the human body. This makes it vulnerable to soft tissue pathologies and dislocation. Insight into the kinematics of the joint may enable improved diagnosis and treatment of different shoulder pathologies. Shoulder joint kinematics can be influenced by the articular geometry of the joint. The aim of this project was to develop an analysis framework for shoulder joint kinematics via the use of articulated statistical shape models (ASSMs). Articulated statistical shape models extend conventional statistical shape models by combining the shape variability of anatomical objects collected from different subjects (statistical shape models), with the physical variation of pose between the same objects (articulation). The developed pipeline involved manual annotation of anatomical landmarks selected on 3D surface meshes of scapulae and humeri and establishing dense surface correspondence across these data through a registration process. The registration was performed using a Gaussian process morphable model fitting approach. In order to register two objects separately, while keeping their shape and kinematics relationship intact, one of the objects (scapula) was fixed leaving the other (humerus) to be mobile. All the pairs of registered humeri and scapulae were brought back to their native imaged position using the inverse of the associated registration transformation. The glenohumeral rotational center and local anatomic coordinate system of the humeri and scapulae were determined using the definitions suggested by the International Society of Biomechanics. Three motions (flexion, abduction, and internal rotation) were generated using Euler angle sequences. The ASSM of the model was built using principal component analysis and validated. The validation results show that the model adequately estimated the shape and pose encoded in the training data. Developing ASSM of the shoulder joint helps to define the statistical shape and pose parameters of the gleno humeral articulating surfaces. An ASSM of the shoulder joint has potential applications in the analysis and investigation of population-wide joint posture variation and kinematics. Such analyses may include determining and quantifying abnormal articulation of the joint based on the range of motion; understanding of detailed glenohumeral joint function and internal joint measurement; and diagnosis of shoulder pathologies. Future work will involve developing a protocol for encoding the shoulder ASSM with real, rather than handcrafted, pose variation

Computational Anatomy for Multi-Organ Analysis in Medical Imaging: A Review

The medical image analysis field has traditionally been focused on the development of organ-, and disease-specific methods. Recently, the interest in the development of more 20 comprehensive computational anatomical models has grown, leading to the creation of multi-organ models. Multi-organ approaches, unlike traditional organ-specific strategies, incorporate inter-organ relations into the model, thus leading to a more accurate representation of the complex human anatomy. Inter-organ relations are not only spatial, but also functional and physiological. Over the years, the strategies 25 proposed to efficiently model multi-organ structures have evolved from the simple global modeling, to more sophisticated approaches such as sequential, hierarchical, or machine learning-based models. In this paper, we present a review of the state of the art on multi-organ analysis and associated computation anatomy methodology. The manuscript follows a methodology-based classification of the different techniques 30 available for the analysis of multi-organs and multi-anatomical structures, from techniques using point distribution models to the most recent deep learning-based approaches. With more than 300 papers included in this review, we reflect on the trends and challenges of the field of computational anatomy, the particularities of each anatomical region, and the potential of multi-organ analysis to increase the impact of 35 medical imaging applications on the future of healthcare.Comment: Paper under revie

Proper shape representation of single figure and multi-figure anatomical objects

Extracting anatomic objects from medical images is an important process in various medical applications. This extraction, called image segmentation, is often realized by deformable models. Among deformable model methods, medial deformable models have the unique advantage of representing not only the object boundary surfaces but also the object interior volume. Based on one medial deformable model called the m-rep, the main goal of this dissertation is to provide proper shape representations of simple anatomical objects of one part and complex anatomical objects of multiple parts in a population. This dissertation focuses on several challenges in the existing medially based deformable model method: 1. how to derive a proper continuous form by interpolating a discrete medial shape representation; 2. how to represent complex objects with several parts and do statistical analysis on them; 3. how to avoid local shape defects, such as folding or creasing, in shapes represented by the deformable model. The proposed methods in this dissertation address these challenges in more detail: 1. An interpolation method for a discrete medial shape model is proposed to guarantee the legality of the interpolated shape. This method is based on the integration of medial shape operators. 2. A medially based representation with hierarchy is proposed to represent complex objects with multiple parts by explicitly modeling interrelations between object parts and modeling smooth transitions between each pair of connected parts. A hierarchical statistical analysis is also proposed for these complex objects. 3. A method to fit a medial model to binary images is proposed to use an explicit legality penalty derived from the medial shape operators. Probability distributions learned from the fitted shape models by the proposed fitting method have proven to yield better image segmentation results

The Blum medial linking structure for multi-region analysis

The Blum medial axis of a region with smooth boundary in Rsuperscript{n+1} is a skeleton-like topological structure that captures shape and geometric properties of the region and its boundary. We introduce a structure, called the Blum medial linking structure, which extends the advantages of the medial axis to configurations of multiple disjoint regions in order to capture both their individual and positional or relative geometry. We use singularity theory to classify the generic local normal forms of the medial linking structure for generic configurations of regions in dimensions n is less than or equal to 6, which requires proving a transversality theorem for families of multi--distance functions. We show how invariants of the geometry of the regions and their complement may be computed directly from the linking structure. We conclude with applications of the linking structure to the analysis of multiple objects in medical images

Clustering and Shifting of Regional Appearance for Deformable Model Segmentation

Automated medical image segmentation is a challenging task that benefits from the use of effective image appearance models. An appearance model describes the grey-level intensity information relative to the object being segmented. Previous models that compare the target against a single template image or that assume a very small-scale correspondence fail to capture the variability seen in the target cases. In this dissertation I present novel appearance models to address these deficiencies, and I show their efficacy in segmentation via deformable models. The models developed here use clustering and shifting of the object-relative appearance to capture the true variability in appearance. They all learn their parameters from training sets of previously-segmented images. The first model uses clustering on cross-boundary intensity profiles in the training set to determine profile types, and then it builds a template of optimal types that reflects the various edge characteristics seen around the boundary. The second model uses clustering on local regional image descriptors to determine large-scale regions relative to the boundary. The method then partitions the object boundary according to region type and captures the intensity variability per region type. The third and fourth models allow shifting of the image model on the boundary to reflect knowledge of the variable regional conformations seen in training. I evaluate the appearance models by considering their efficacy in segmentation of the kidney, bladder, and prostate in abdominal and male pelvis CT. I compare the automatically generated segmentations using these models against expert manual segmentations of the target cases and against automatically generated segmentations using previous models

Estimation of probability distribution on multiple anatomical objects and evaluation of statistical shape models

The estimation of shape probability distributions of anatomic structures is a major research area in medical image analysis. The statistical shape descriptions estimated from training samples provide means and the geometric shape variations of such structures. These are key components in many applications. This dissertation presents two approaches to the estimation of a shape probability distribution of a multi-object complex. Both approaches are applied to objects in the male pelvis, and show improvement in the estimated shape distributions of the objects. The first approach is to estimate the shape variation of each object in the complex in terms of two components: the object's variation independent of the effect of its neighboring objects; and the neighbors' effect on the object. The neighbors' effect on the target object is interpreted using the idea on which linear mixed models are based. The second approach is to estimate a conditional shape probability distribution of a target object given its neighboring objects. The estimation of the conditional probability is based on principal component regression. This dissertation also presents a measure to evaluate the estimated shape probability distribution regarding its predictive power, that is, the ability of a statistical shape model to describe unseen members of the population. This aspect of statistical shape models is of key importance to any application that uses shape models. The measure can be applied to PCA-based shape models and can be interpreted as a ratio of the variation of new data explained by the retained principal directions estimated from training data. This measure was applied to shape models of synthetic warped ellipsoids and right hippocampi. According to two surface distance measures and a volume overlap measure it was empirically verified that the predictive measure reflects what happens in the ambient space where the model lies

Refinement of object-based segmentation

Automated object-based segmentation methods calculate the shape and pose of anatomical structures of interest. These methods require modeling both the geometry and object-relative image intensity patterns of target structures. Many object-based segmentation methods minimize a non-convex function and risk failure due to convergence to a local minimum. This dissertation presents three refinements to existing object-based segmentation methods. The first refinement mitigates the risk of local minima by initializing the segmentation closely to the correct answer. The initialization searches pose- and shape-spaces for the object that best matches user specified points on three designated image slices. Thus-initialized m-rep based segmentations of the bladder from CT are frequently better than segmentations reported elsewhere. The second refinement is a statistical test on object-relative intensity patterns that allows estimation of the local credibility of a segmentation. This test effectively identifies regions with local segmentation errors in m-rep based segmentations of the bladder and prostate from CT. The third refinement is a method for shape interpolation that is based on changes in the position and orientation of samples and that tends to be more shape-preserving than a competing linear method. This interpolation can be used with dynamic structures and to understand changes between segmentations of an object in atlas and target images. Together, these refinements aid in the segmentation of a dense collection of targets via a hybrid of object-based and atlas-based methods. The first refinement increases the probability of successful object-based segmentations of the subset of targets for which such methods are appropriate, the second increases the user's confidence that those object-based segmentations are correct, and the third is used to transfer the object-based segmentations to an atlas-based method that will be used to segment the remainder of the targets