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Statistical shape models (SSM) are used to introduce shape priors in the segmentation of medical images. However, such models require large training datasets in the case of multi-object structures, since it is required to obtain not only the individual shape variations but also the relative position and orientation among objects. A solution to overcome this limitation is to model each individual shape independently. However, this approach does not take into account the relative position, orientations and shapes among the parts of an articulated object, which may result in unrealistic geometries, such as with object overlaps. In this article, we propose a new Statistical Model, the Statistical Interspace Model (SIM), which provides information about the interaction of all the individual structures by modeling the interspace between them. The SIM is described using relative position vectors between pair of points that belong to different objects that are facing each other. These vectors are divided into their magnitude and direction, each of these groups modeled as independent manifolds. The SIM was included in a segmentation framework that contains an SSM per individual object. This framework was tested using three distinct types of datasets of CT images of the spine. Results show that the SIM completely eliminated the inter-process overlap while improving the segmentation accuracy.

Detailed segmentation of the vertebrae is an important pre-requisite in various applications of image-based spine assessment, surgery and biomechanical modeling. In particular, accurate segmentation of the processes is required for image-guided interventions, for example for optimal placement of bone grafts between the transverse processes. Furthermore, the geometry of the processes is now required in musculoskeletal models due to their interaction with the muscles and ligaments. In this paper, we present a new method for detailed segmentation of both the vertebral bodies and processes based on statistical shape decomposition and conditional models. The proposed technique is specifically developed with the aim to handle the complex geometry of the processes and the large variability between individuals. The key technical novelty in this work is the introduction of a part-based statistical decomposition of the vertebrae, such that the complexity of the subparts is effectively reduced, and model specificity is increased. Subsequently, in order to maintain the statistical and anatomic coherence of the ensemble, conditional models are used to model the statistical inter-relationships between the different subparts. For shape reconstruction and segmentation, a robust model fitting procedure is used to exclude improbable inter-part relationships in the estimation of the shape parameters. Segmentation results based on a dataset of 30 healthy CT scans and a dataset of 10 pathological scans show a point-to-surface error improvement of 20% and 17% respectively, and the potential of the proposed technique for detailed vertebral modeling.

The construction of statistical shape models (SSMs) that are rich, i.e., that represent well the natural and complex variability of anatomical structures, is an important research topic in medical imaging. To this end, existing works have addressed the limited availability of training data by decomposing the shape variability hierarchically or by combining statistical and synthetic models built using artificially created modes of variation. In this paper, we present instead a method that merges multiple statistical models of 3D shapes into a single integrated model, thus effectively encoding extra variability that is anatomically meaningful, without the need for the original or new real datasets. The proposed framework has great flexibility due to its ability to merge multiple statistical models with unknown point correspondences. The approach is beneficial in order to re-use and complement pre-existing SSMs when the original raw data cannot be exchanged due to ethical, legal, or practical reasons. To this end, this paper describes two main stages, i.e., (1) statistical model normalization and (2) statistical model integration. The normalization algorithm uses surface-based registration to bring the input models into a common shape parameterization with point correspondence established across eigenspaces. This allows the model fusion algorithm to be applied in a coherent manner across models, with the aim to obtain a single unified statistical model of shape with improved generalization ability. The framework is validated with statistical models of the left and right cardiac ventricles, the L1 vertebra, and the caudate nucleus, constructed at distinct research centers based on different imaging modalities (CT and MRI) and point correspondences. The results demonstrate that the model integration is statistically and anatomically meaningful, with potential value for merging pre-existing multi-modality statistical models of 3D shapes., (Copyright © 2014 Elsevier B.V. All rights reserved.)

This paper presents a framework for the fusion of multiple point distribution models (PDMs) with unknown point correspondences. With this work, models built from distinct patient groups and imaging modalities can be merged, with the aim to obtain a PDM that encodes a wider range of anatomical variability. To achieve this, two technical challenges are addressed in this work. Firstly, the model fusion must be carried out directly on the corresponding means and eigenvectors as the original data is not always available and cannot be freely exchanged across centers for various legal and practical reasons. Secondly, the PDMs need to be normalized before fusion as the point correspondence is unknown. The proposed framework is validated by integrating statistical models of the left and right ventricles of the heart constructed from different imaging modalities (MRI and CT) and with different landmark representations of the data. The results show that the integration is statistically and anatomically meaningful and that the quality of the resulting model is significantly improved.