Shape-aware surface reconstruction from sparse 3D point-clouds

in Medical Image Analysis (2017), 38

The reconstruction of an object’s shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process ... [more ▼]

The reconstruction of an object’s shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal with sparse data, which significantly aggravates the problem of reconstruction. However, medical applications often provide contextual information about the 3D point data that allow to incorporate prior knowledge about the shape that is to be reconstructed. To this end, we propose the use of a statistical shape model (SSM) as a prior for surface reconstruction. The SSM is represented by a point distribution model (PDM), which is associated with a surface mesh. Using the shape distribution that is modelled by the PDM, we formulate the problem of surface reconstruction from a probabilistic perspective based on a Gaussian Mixture Model (GMM). In order to do so, the given points are interpreted as samples of the GMM. By using mixture components with anisotropic covariances that are “oriented” according to the surface normals at the PDM points, a surface-based fitting is accomplished. Estimating the parameters of the GMM in a maximum a posteriori manner yields the reconstruction of the surface from the given data points. We compare our method to the extensively used Iterative Closest Points method on several different anatomical datasets/SSMs (brain, femur, tibia, hip, liver) and demonstrate superior accuracy and robustness on sparse data. [less ▲]

Novel Methods for Multi-Shape Analysis

Doctoral thesis (2016)

Multi-shape analysis has the objective to recognise, classify, or quantify morphological patterns or regularities within a set of shapes of a particular object class in order to better understand the ... [more ▼]

Multi-shape analysis has the objective to recognise, classify, or quantify morphological patterns or regularities within a set of shapes of a particular object class in order to better understand the object class of interest. One important aspect of multi-shape analysis are Statistical Shape Models (SSMs), where a collection of shapes is analysed and modelled within a statistical framework. SSMs can be used as (statistical) prior that describes which shapes are more likely and which shapes are less likely to be plausible instances of the object class of interest. Assuming that the object class of interest is known, such a prior can for example be used in order to reconstruct a three-dimensional surface from only a few known surface points. One relevant application of this surface reconstruction is 3D image segmentation in medical imaging, where the anatomical structure of interest is known a-priori and the surface points are obtained (either automatically or manually) from images. Frequently, Point Distribution Models (PDMs) are used to represent the distribution of shapes, where each shape is discretised and represented as labelled point set. With that, a shape can be interpreted as an element of a vector space, the so-called shape space, and the shape distribution in shape space can be estimated from a collection of given shape samples. One crucial aspect for the creation of PDMs that is tackled in this thesis is how to establish (bijective) correspondences across the collection of training shapes. Evaluated on brain shapes, the proposed method results in an improved model quality compared to existing approaches whilst at the same time being superior with respect to runtime. The second aspect considered in this work is how to learn a low-dimensional subspace of the shape space that is close to the training shapes, where all factors spanning this subspace have local support. Compared to previous work, the proposed method models the local support regions implicitly, such that no initialisation of the size and location of these regions is necessary, which is advantageous in scenarios where this information is not available. The third topic covered in this thesis is how to use an SSM in order to reconstruct a surface from only few surface points. By using a Gaussian Mixture Model (GMM) with anisotropic covariance matrices, which are oriented according to the surface normals, a more surface-oriented fitting is achieved compared to a purely point-based fitting when using the common Iterative Closest Point (ICP) algorithm. In comparison to ICP we find that the GMM-based approach gives superior accuracy and robustness on sparse data. Furthermore, this work covers the transformation synchronisation method, which is a procedure for removing noise that accounts for transitive inconsistency in the set of pairwise linear transformations. One interesting application of this methodology that is relevant in the context of multi-shape analysis is to solve the multi-alignment problem in an unbiased/reference-free manner. Moreover, by introducing an improvement of the numerical stability, the methodology can be used to solve the (affine) multi-image registration problem from pairwise registrations. Compared to reference-based multi-image registration, the proposed approach leads to an improved registration accuracy and is unbiased/reference-free, which makes it ideal for statistical analyses. [less ▲]

Linear Shape Deformation Models with Local Support using Graph-based Structured Matrix Factorisation

in Linear Shape Deformation Models with Local Support using Graph-based Structured Matrix Factorisation (2016)

Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly ... [more ▼]

Representing 3D shape deformations by linear models in high-dimensional space has many applications in computer vision and medical imaging, such as shape-based interpolation or segmentation. Commonly, using Principal Components Analysis a low-dimensional (affine) subspace of the high-dimensional shape space is determined. However, the resulting factors (the most dominant eigenvectors of the covariance matrix) have global support, i.e. changing the coefficient of a single factor deforms the entire shape. In this paper, a method to obtain deformation factors with local support is presented. The benefits of such models include better flexibility and interpretability as well as the possibility of interactively deforming shapes locally. For that, based on a well-grounded theoretical motivation, we formulate a matrix factorisation problem employing sparsity and graph-based regularisation terms. We demonstrate that for brain shapes our method outperforms the state of the art in local support models with respect to generalisation ability and sparse shape reconstruction, whereas for human body shapes our method gives more realistic deformations. [less ▲]

Shape-aware 3D Interpolation using Statistical Shape Models

in Symposium on Statistical Shape Models and Applications (2015, October)

Susceptibility-Weighted MRI for Deep Brain Stimulation: Potentials in Trajectory Planning

in Stereotactic and Functional Neurosurgery (2015), 93(5), 303-308

Background: Deep brain stimulation (DBS) trajectory plan- ning is mostly based on standard 3-D T1-weighted gado- linium-enhanced MRI sequences (T1-Gd). Susceptibility- weighted MRI sequences (SWI) show ... [more ▼]

Background: Deep brain stimulation (DBS) trajectory plan- ning is mostly based on standard 3-D T1-weighted gado- linium-enhanced MRI sequences (T1-Gd). Susceptibility- weighted MRI sequences (SWI) show neurovascular struc- tures without the use of contrast agents. The aim of this study was to investigate whether SWI might be useful in DBS trajectory planning. Methods: We performed bilateral DBS planning using conventional T1-Gd images of 10 patients with different kinds of movement disorders. Afterwards, we matched SWI sequences and compared the visibility of vas- cular structures in both imaging modalities. Results: By ana- lyzing 100 possible trajectories, we found a potential vascu- lar conflict in 13 trajectories based on T1-Gd in contrast to 53 in SWI. Remarkably, all vessels visible in T1-Gd were also de- picted in SWI, whereas SWI showed many additional vascular structures which could not be identified in T1-Gd. Conclu- sion/Discussion: The sensitivity for detecting neurovascular structures for DBS planning seems to be significantly higher in SWI. As SWI does not require a contrast agent, we suggest that SWI may be a valuable alternative to T1-Gd MRI for DBS trajectory planning. Furthermore, the data analysis suggests that vascular interactions of DBS trajectories might be more frequent than expected from the very low incidence of symptomatic bleedings. The explanation for this is currently the subject of debate and merits further studies. [less ▲]

A solution for Multi-Alignment by Transformation Synchronisation

in The proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2015)

The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered ... [more ▼]

The alignment of a set of objects by means of transformations plays an important role in computer vision. Whilst the case for only two objects can be solved globally, when multiple objects are considered usually iterative methods are used. In practice the iterative methods perform well if the relative transformations between any pair of objects are free of noise. However, if only noisy relative transformations are available (e.g. due to missing data or wrong correspondences) the iterative methods may fail. Based on the observation that the underlying noise-free transformations lie in the null space of a matrix that can directly be obtained from pairwise alignments, this paper presents a novel method for the synchronisation of pairwise transformations such that they are globally consistent. Simulations demonstrate that for a high amount of noise, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results. [less ▲]

Improving the Consistency of Manual Deep Brain Structure Segmentations by Combining Variational Interpolation, Simultaneous Multi-Modality Visualisation and Histogram Equilisation

in Biomedizinische Technik. Biomedical Engineering (2014), 59(1), 131-134