A probabilistic framework for robust, group-wise rigid alignment of point-sets using a mixture of Students t-distribution especially when the point sets are of varying lengths, are corrupted by an unknown degree of outliers or in the presence of missing data. Medical images (in particular magnetic resonance (MR) images), their segmentations and consequently point-sets generated from these are highly susceptible to corruption by outliers. This poses a problem for robust correspondence estimation and accurate alignment of shapes, necessary for training statistical shape models (SSMs). To address these issues, this study proposes to use a t-mixture model (TMM), to approximate the underlying joint probability density of a group of similar shapes and align them to a common reference frame. The heavy-tailed nature of t-distributions provides a more robust registration framework in comparison to state of the art algorithms. Significant reduction in alignment errors is achieved in the presence of outliers, using the proposed TMM-based group-wise rigid registration method, in comparison to its Gaussian mixture model (GMM) counterparts. The proposed TMM-framework is compared with a group-wise variant of the well-known Coherent Point Drift (CPD) algorithm and two other group-wise methods using GMMs, using both synthetic and real data sets. Rigid alignment errors for groups of shapes are quantified using the Hausdorff distance (HD) and quadratic surface distance (QSD) metrics.
Digital photoelasticity offers enormous potential for the validation of computational models of biomedical soft tissue applications. The challenges of creating suitable birefringent surrogate materials are outlined. The recent progress made in the development of photoelastic materials and full-field, quantitative methods for biomechanics applications is illustrated with two complementary case studies: needle insertion and shaken baby syndrome. Initial experiments are described and the future exciting possibilities of using digital photoelasticity are discussed.
This paper presents a novel method to treat discontinuities in a 3D piece-wise non-rigid registration framework, coined as EXtended Free-Form Deformation (XFFD). Existing discontinuities in the image, such as sliding motion of the lungs or the cardiac boundary adjacent to the blood pool, should be handled to obtain physically plausible deformation fields for motion analysis. However, conventional Free-form deformations (FFDs) impose continuity over the whole image, introducing inaccuracy near discontinuity boundaries. The proposed method incorporates enrichment functions into the FFD formalism, inspired by the linear interpolation method in the EXtended Finite Element Method (XFEM). Enrichment functions enable B-splines to handle discontinuities with minimal increase of computational complexity, while avoiding boundary-matching problem. It retains all properties of the framework of FFDs yet seamlessly handles general discontinuities and can also coexist with other proposed improvements of the FFD formalism. The proposed method showed high performance on synthetic and 3D lung CT images. The target registration error on the CT images is comparable to the previous methods, while being a generic method without assuming any type of motion constraint. Therefore, it does not include any penalty term. However, any of these terms could be included to achieve higher accuracy for specific applications.
The use of biomechanics-based numerical simulations has attracted growing interest in recent years for computer-aided diagnosis and treatment planning. With this in mind, a method for automatic mesh generation of brain structures of interest, using statistical models of shape (SSM) and appearance (SAM), for personalised computational modelling is presented. SSMs are constructed as point distribution models (PDMs) while SAMs are trained using intensity profiles sampled from a training set of T1-weighted magnetic resonance images. The brain structures of interest are, the cortical surface (cerebrum, cerebellum & brainstem), lateral ventricles and falx-cerebri membrane. Two methods for establishing correspondences across the training set of shapes are investigated and compared (based on SSM quality): the Coherent Point Drift (CPD) point-set registration method and B-spline mesh-to-mesh registration method. The MNI-305 (Montreal Neurological Institute) average brain atlas is used to generate the template mesh, which is deformed and registered to each training case, to establish correspondence over the training set of shapes. 18 healthy patients’ T1-weightedMRimages form the training set used to generate the SSM and SAM. Both model-training and model-fitting are performed over multiple brain structures simultaneously. Compactness and generalisation errors of the BSpline-SSM and CPD-SSM are evaluated and used to quantitatively compare the SSMs. Leave-one-out cross validation is used to evaluate SSM quality in terms of these measures. The mesh-based SSM is found to generalise better and is more compact, relative to the CPD-based SSM. Quality of the best-fit model instance from the trained SSMs, to test cases are evaluated using the Hausdorff distance (HD) and mean absolute surface distance (MASD) metrics.
Realistic modelling of mechanical interactions between tissues is an important part of surgical simulation, and
may become a valuable asset in surgical computer guidance. Unfortunately, it is also computationally very
demanding. Explicit matrix-free FEM solvers have been shown to be a good choice for fast tissue simulation,
however little work has been done on contact algorithms for such FEM solvers.
This work introduces such an algorithm that is capable of handling both deformable-deformable (soft-tissue interacting
with soft-tissue) and deformable-rigid (e.g. soft-tissue interacting with surgical instruments) contacts.
The proposed algorithm employs responses computed with a fully matrix-free, virtual node-based version of
the model first used by Taylor and Flanagan in PRONTO3D. For contact detection, a bounding-volume hierarchy
(BVH) capable of identifying self collisions is introduced. The proposed BVH generation and update
strategies comprise novel heuristics to minimise the number of bounding volumes visited in hierarchy update
and collision detection.
Aside from speed, stability was a major objective in the development of the algorithm, hence a novel method for
computation of response forces from C0-continuous normals, and a gradual application of response forces from
rate constraints has been devised and incorporated in the scheme. The continuity of the surface normals has
advantages particularly in applications such as sliding over irregular surfaces, which occurs, e.g., in simulated
The effectiveness of the scheme is demonstrated on a number of meshes derived from medical image data and
artificial test cases.
Non-rigid registration techniques are commonly used in medical image analysis. However these techniques are
often time consuming. Graphics Processing Unit (GPU) execution appears to be a good way to decrease computation
time significantly. However for an efficient implementation on GPU, an algorithm must be data parallel.
In this paper we compare the analytical calculation of the gradient of Normalised Mutual Information with
an approximation better suited to parallel implementation. Both gradient approaches have been implemented
using a Free-Form Deformation framework based on cubic B-Splines and including a smoothness constraint. We
applied this technique to recover realistic deformation fields generated from 65 3D-T1 images. The recovered
fields using both gradients and the ground truth were compared. We demonstrated that the approximated gradient
performed similarly to the analytical gradient but with a greatly reduced computation time when both
approaches are implemented on the CPU. The implementation of the approximated gradient on the GPU leads
to a computation time of 3 to 4 minutes when registering 190 × 200 × 124 voxel images with a grid including
57 × 61 × 61 control points.