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

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.Comment: Please cite CVPR 2016 versio

A Solution for Multi-Alignment by Transformation Synchronisation

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 can be retrieved from 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 transitively consistent. Simulations demonstrate that for noisy transformations, a large proportion of missing data and even for wrong correspondence assignments the method delivers encouraging results.Comment: Accepted for CVPR 2015 (please cite CVPR version

Integration of sparse electrophysiological measurements with preoperative MRI using 3D surface estimation in deep brain stimulation surgery

Intraoperative microelectrode recordings (MER) have been used for several decades to guide neurosurgeons during the implantation of Deep Brain Stimulation (DBS) electrodes, especially when targeting the subthalamic nucleus (STN) to suppress the symptoms of Parkinson’s Disease. The standard approach is to use an array of up to five MER electrodes in a fixed configuration. Interpretation of the recorded signals yields a spatiallyvery sparse set of information about the morphology of the respective brain structures in the targeted area. However, no aid is currently available for surgeons to intraoperatively integrate this information with other data available on the patient’s individual morphology (e.g. MR imaging data used for surgical planning). This integration might allow surgeons to better determine the most probable position of the electrodes within the target structure during surgery. This paper suggests a method for reconstructing a surface patch from the sparse MER dataset utilizing additional a-priori knowledge about the geometrical configuration of the measurement electrodes. The conventional representation of MER measurements as intervals of target region/non-target region is therefore transformed into an equivalent boundary set representation, allowing efficient point-based calculations. Subsequently, the problem is to integrate the resulting patch with a preoperative model of the target structure, which can be formulated as registration problem minimizing a distance measure between the two surfaces. When restricting this registration procedure to translations, which is reasonable given certain geometric considerations, the problem can be solved globally by employing an exhaustive search with arbitrary precision in polynomial time. The proposed method is demonstrated using bilateral STN/Substantia Nigra segmentation data from preoperative MRIs of 17 Patients with simulated MER electrode placement. When using simulated data of heavily perturbed electrodes and subsequent MER measureme

Assessment of Electrode Displacement and Deformation with Respect to Pre-Operative Planning in Deep Brain Stimulation

The post-operative validation of deep brain stimulation electrode displacement and deformation is an important task towards improved DBS targeting. In this paper a method is proposed to align models of deep brain stimulation electrodes that are automatically extracted from post-operative CT imaging in a common coordinate system utilizing the planning data as reference. This enables the assessment of electrode displacement and deformation over the whole length of the trajectory with respect to the pre-operative planning. Accordingly, it enables the estimation of plan deviations in the surgical process as well as cross-patient statistics on electrode deformation, e.g. the bending induced by brain-shift

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

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

Control of miniature proton exchange fuel cells based on fuzzy logic

A control strategy is presented in this paper which is suitable for miniature hydrogen/air proton-exchange membrane (PEM) fuel cells. The control approach is based on process modelling using fuzzy logic and tested using a PEM stack consisting of 15 cells with parallel channels on the cathode side and a meander-shaped flow-field on the anode side. The active area per cell is 8 cm^2. Commercially available materials are used for the bipolar plates,gas diffusion layers and the membrane-electrode assembly. It is concluded from basic thermodynamic principles that water management at different temperatures can be achieved by controlling the air stoichiometry. This is achieved by varying the fan voltage for the air supply of the PEM stack. A control strategy of the Takagi Sugeno Kang (TSK) type, based on fuzzy logic, is presented. The TSK-type controller offers the advantage that the system output can be computed in an efficient way: the rule consequents of the controller combine the system variables in linear equations. It is shown experimentally that drying out of the membrane at high temperatures can be monitored by measuring the AC impedance of the fuel cell stack at a frequency of 1kHz. Flooding of single cells leads to an abrupt drop of the corresponding single-cell voltage. Therefore, the fuzzy rule base consists of the AC impedance at 1kHz and all single-cell voltages. The parameters of the fuzzy rule base are determined by plotting characteristic diagrams of the fuel cell stack at constant temperatures. Stable system operation is achieved at T=60°C for a power level of 7.5 W. The fuel cell stack is controlled successfully even when the external electric load changes. The maximum power level for stable system operation was found to be 8 W at T=65°C. A decrease of the maximum power level is observed for higher temperatures