Groupwise surface correspondence by optimization: Representation and regularization

Fast automated segmentation of multiple objects via spatially weighted shape learning

Active shape models (ASMs) have proved successful in automatic segmentation by using shape and appearance priors in a number of areas such as prostate segmentation, where accurate contouring is important in treatment planning for prostate cancer. The ASM approach however, is heavily reliant on a good initialisation for achieving high segmentation quality. This initialisation often requires algorithms with high computational complexity, such as three dimensional (3D) image registration. In this work, we present a fast, self-initialised ASM approach that simultaneously fits multiple objects hierarchically controlled by spatially weighted shape learning. Prominent objects are targeted initially and spatial weights are progressively adjusted so that the next (more difficult, less visible) object is simultaneously initialised using a series of weighted shape models. The scheme was validated and compared to a multi-atlas approach on 3D magnetic resonance (MR) images of 38 cancer patients and had the same (mean, median, inter-rater) Dice's similarity coefficients of (0.79, 0.81, 0.85), while having no registration error and a computational time of 12-15 min, nearly an order of magnitude faster than the multi-atlas approach.

Statistical shape model reconstruction with sparse anomalous deformations: Application to intervertebral disc herniation

Many medical image processing techniques rely on accurate shape modeling of anatomical features. The presence of shape abnormalities challenges traditional processing algorithms based on strong morphological priors. In this work, a sparse shape reconstruction from a statistical shape model is presented. It combines the advantages of traditional statistical shape models (defining a 'normal' shape space) and previously presented sparse shape composition (providing localized descriptors of anomalies). The algorithm was incorporated into our image segmentation and classification software. Evaluation was performed on simulated and clinical MRI data from 22 sciatica patients with intervertebral disc herniation, containing 35 herniated and 97 normal discs. Moderate to high correlation (R=0.73) was achieved between simulated and detected herniations. The sparse reconstruction provided novel quantitative features describing the herniation morphology and MRI signal appearance in three dimensions (3D). The proposed descriptors of local disc morphology resulted to the 3D segmentation accuracy of 1.07±1.00mm (mean absolute vertex-to-vertex mesh distance over the posterior disc region), and improved the intervertebral disc classification from 0.888 to 0.931 (area under receiver operating curve). The results show that the sparse shape reconstruction may improve computer-aided diagnosis of pathological conditions presenting local morphological alterations, as seen in intervertebral disc herniation.

Automated detection, 3D segmentation and analysis of high resolution spine MR images using statistical shape models

Recent advances in high resolution magnetic resonance (MR) imaging of the spine provide a basis for the automated assessment of intervertebral disc (IVD) and vertebral body (VB) anatomy. High resolution three-dimensional (3D) morphological information contained in these images may be useful for early detection and monitoring of common spine disorders, such as disc degeneration. This work proposes an automated approach to extract the 3D segmentations of lumbar and thoracic IVDs and VBs from MR images using statistical shape analysis and registration of grey level intensity profiles. The algorithm was validated on a dataset of volumetric scans of the thoracolumbar spine of asymptomatic volunteers obtained on a 3T scanner using the relatively new 3D T2-weighted SPACE pulse sequence. Manual segmentations and expert radiological findings of early signs of disc degeneration were used in the validation. There was good agreement between manual and automated segmentation of the IVD and VB volumes with the mean Dice scores of 0.89 ± 0.04 and 0.91 ± 0.02 and mean absolute surface distances of 0.55 ± 0.18 mm and 0.67 ± 0.17 mm respectively. The method compares favourably to existing 3D MR segmentation techniques for VBs. This is the first time IVDs have been automatically segmented from 3D volumetric scans and shape parameters obtained were used in preliminary analyses to accurately classify (100% sensitivity, 98.3% specificity) disc abnormalities associated with early degenerative changes.

Patient specific prostate segmentation in 3-d magnetic resonance images

Accurate localization of the prostate and its surrounding tissue is essential in the treatment of prostate cancer. This paper presents a novel approach to fully automatically segment the prostate, including its seminal vesicles, within a few minutes of a magnetic resonance (MR) scan acquired without an endorectal coil. Such MR images are important in external beam radiation therapy, where using an endorectal coil is highly undesirable. The segmentation is obtained using a deformable model that is trained on-the-fly so that it is specific to the patient's scan. This case specific deformable model consists of a patient specific initialized triangulated surface and image feature model that are trained during its initialization. The image feature model is used to deform the initialized surface by template matching image features (via normalized cross-correlation) to the features of the scan. The resulting deformations are regularized over the surface via well established simple surface smoothing algorithms, which is then made anatomically valid via an optimized shape model. Mean and median Dice's similarity coefficients (DSCs) of 0.85 and 0.87 were achieved when segmenting 3T MR clinical scans of 50 patients. The median DSC result was equal to the inter-rater DSC and had a mean absolute surface error of 1.85 mm. The approach is showed to perform well near the apex and seminal vesicles of the prostate.

Discrete differential geometry: the nonplanar quadrilateral mesh

We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.

4-D cardiac MR image analysis: left and right ventricular morphology and function

In this study, a combination of active shape model (ASM) and active appearance model (AAM) was used to segment the left and right ventricles of normal and Tetralogy of Fallot (TOF) hearts on 4-D (3-D+time) MR images. For each ventricle, a 4-D model was first used to achieve robust preliminary segmentation on all cardiac phases simultaneously and a 3-D model was then applied to each phase to improve local accuracy while maintaining the overall robustness of the 4-D segmentation. On 25 normal and 25 TOF hearts, in comparison to the expert traced independent standard, our comprehensive performance assessment showed subvoxel segmentation accuracy, high overlap ratios, good ventricular volume correlations, and small percent volume differences. Following 4-D segmentation, novel quantitative shape and motion features were extracted using shape information, volume-time and dV/dt curves, analyzed and used for disease status classification. Automated discrimination between normal/TOF subjects achieved 90%-100% sensitivity and specificity. The features obtained from TOF hearts show higher variability compared to normal subjects, suggesting their potential use as disease progression indicators. The abnormal shape and motion variations of the TOF hearts were accurately captured by both the segmentation and feature characterization.