Pmj Peter Rongen

An efficient method for tensor voting using steerable filters

In many image analysis applications there is a need to extract curves in noisy images. To achieve a more robust extraction, one can exploit correlations of oriented features over a spatial context in the image. Tensor voting is an existing technique to extract features in this way. In this paper, we present a new computational scheme for tensor voting on a dense field of rank-2 tensors. Using steerable filter theory, it is possible to rewrite the tensor voting operation as a linear combination of complex-valued convolutions. This approach has computational advantages since convolutions can be implemented efficiently. We provide speed measurements to indicate the gain in speed, and illustrate the use of steerable tensor voting on medical applications.

A model for arterial adaptation combining microstructural collagen remodeling and 3D tissue growth

Long-term adaptation of soft tissues is realized through growth and remodeling (G&R). Mathematical models are powerful tools in testing hypotheses on G&R and supporting the design and interpretation of experiments. Most theoretical G&R studies concentrate on description of either growth or remodeling. Our model combines concepts of remodeling of collagen recruitment stretch and orientation suggested by other authors with a novel model of general 3D growth. We translate a growth-induced volume change into a change in shape due to the interaction of the growing tissue with its environment. Our G&R model is implemented in a finite element package in 3D, but applied to two rotationally symmetric cases, i.e., the adaptation towards the homeostatic state of the human aorta and the development of a fusiform aneurysm. Starting from a guessed non-homeostatic state, the model is able to reproduce a homeostatic state of an artery with realistic parameters. We investigate the sensitivity of this state to settings of initial parameters. In addition, we simulate G&R of a fusiform aneurysm, initiated by a localized degradation of the matrix of the healthy artery. The aneurysm stabilizes in size soon after the degradation stops.

The influence of contrast agent injection on physiological flow in the circle of Willis

X-ray videodensitometry allows in vivo flow measurements from gradients in contrast agent concentration. However, the injection of contrast agent alters the flow to be measured. Here, the temporal, spatial, and inter-patient variability of the response to injection are examined. To this purpose, an injection is prescribed in the internal carotid in a 1D wave propagation model of the arterial circulation. Although the resulting effect of injection is constant over a cardiac cycle, the response does vary with the location within the cerebral circulation and the geometry of the circle of Willis. At the injection site, the injection partly suppresses the incoming blood flow, such that the distal flow is increased by approximately 10%. This corresponds to approximately 20% of the injection rate added to the blood flow during injection, depending on the vascular geometry. In the communicating arteries, the flow direction is reversed during injection. Since the measured flow is not equal to the physiological blood flow, the effect of injection should be taken into account when deriving the flow from travelling contrast agent.

A variational principle for magneto-elastic buckling

A variational principle that can serve as the basis for a magneto-elastic stability (or buckling) problem is constructed. For the two cases of soft ferromagnetic media and superconductors, respectively, it is shown how the variational principle directly yields an explicit expression for the buckling value. The formulation starts from a specific choice for a magneto-elastic Lagrangian L (associated with the so-called Maxwell-Minkowski model for magneto-elastic interactions). For the evaluation of the principle the first and second variations of L are calculated both inside and outside the solid magneto-elastic body. Thus, a general buckling criterion, consisting of an expression for the critical field value, together with a set of constraints for the field variables occurring in the right-hand side of this expression, is constructed. Finally, more detailed formulations are given for, successively, soft ferromagnetic bodies and superconductors. Applications to specific structures, yielding explicit numerical values for the magneto-elastic buckling fields, will be given in a forthcoming paper.

Cardiac left atrium CT image segmentation for ablation guidance

Catheter ablation is an increasingly important curative procedure for atrial fibrillation. Knowledge of the local wall thickness is essential to determine the proper ablation energy. This paper presents the first semi-automatic atrial wall thickness measurement method for ablation guidance. It includes both endocardial and epicardial atrial wall segmentation on CT image data. Segmentation is based on active contours, Otsus multiple threshold method and hysteresis thresholding. Segmentation results were compared to contours manually drawn by two experts, using repeated measures analysis of variance. The root mean square differences between the semi-automatic and the manually drawn contours were comparable to intra-observer variation (endocardium: p = 0.23, epicardium: p = 0.18). Mean wall thickness difference is significant between one of the experts on one side, and the presented method and the other expert on the other side (p ≪ 0.001). Wall thicknesses found were in the range of 0.5–5.5mm, corresponding to values presented in literature.

Surgical needle reconstruction using small-angle multi-view X-ray

In biopsies, drainages, vertebroplasty, and other needle-based procedures, insight on the 3D position of a needle is crucial for correct navigation by the clinician. In this paper, we present a method for the reconstruction of surgical needles using multi-view X-ray imaging with a small motion of the C-arm. It is required that the extent of the motion is limited (< 30 degrees) to allow use of this method during an intervention. This small motion provides sufficient multi-view information, which is used in combination with a needle model for the 3D reconstruction of the needle. To this end, we describe a system comprising the steps of (a) needle detection in a novel, RANSAC-based framework, (b) tracking of needles in subsequent views using geometric constraints and (c) needle reconstruction. Results are presented in comparison to a volume reconstruction using a full rotation of the C-arm (≈ 207 degrees), showing good accuracy of the proposed method.

Sparse-plus-dense-RANSAC for estimation of multiple complex curvilinear models in 2D and 3D

The detection of multiple complex structures in noisy, outlier-rich two- and three-dimensional data is a challenging model estimation problem. In this paper, we build on the RANSAC method to select multiple model instances, focusing especially on curve estimation. Estimation of complex curves such as splines has so far received little attention in the context of model estimation, but has primarily been considered as a segmentation problem. Our proposed curve estimation is based on Sparse-Plus-Dense RANSAC, a framework in which estimation is performed on sparse points, guided by dense image data. This approach is extended to complex curvilinear models, in two- and three-dimensional data. The estimation is hierarchical, based on a merging step that uses an intuitive cost function. Results are presented on synthetic and real X-ray data, showing that the proposed approach performs comparably to state-of-the-art multiple model estimation in the synthetic data, while it significantly outperforms state-of-the-art in the real X-ray sequences. It also achieves correct localization of the model endpoints, which is a crucial aspect in the context of the clinical application.

Multiple Model Estimation for the Detection of Curvilinear Segments in Medical X-ray Images Using Sparse-plus-dense-RANSAC

In this paper, we build on the RANSAC method to detect multiple instances of objects in an image, where the objects are modeled as curvilinear segments with distinct endpoints. Our approach differs from previously presented work in that it incorporates soft constraints, based on a dense image representation, that guide the estimation process in every step. This enables (1) better correspondence with image content, (2) explicit endpoint detection and (3) a reduction in the number of iterations required for accurate estimation. In the case of curvilinear objects examined in this paper, these constraints are formulated as binary image labels, where the estimation proved to be robust to mislabeling, e.g. in case of intersections. Results for both synthetic and real data from medical X-ray images show the improvement from incorporating soft image-based constraints.

A variational approach to magneto-elastic buckling problems for systems of ferromagnetic or superconducting beams

Based upon a variational principle derived in a preceding paper, expressions for the magneto-elastic buckling values for ferromagnetic or superconducting systems are given. These relations are evaluated for systems of slender beams. Explicit buckling values are calculated for a single ferromagnetic or superconducting beam of arbitrary cross-section, and for systems of two parallel ferromagnetic or superconducting rods. In the analysis needed for the calculation of the intermediate (i.e., rigid-body) and the perturbed magnetic fields, an intensive use of methods inherent in the theory of complex functions is made. In conclusion our results for a set of two superconducting rods are compared with the results of a mathematically less complicated, but also less rigorous, theory.

Toward a full-reference information-theoretic quality assessment method for x-ray images

This work aims at defining an information-theoretic quality assessment technique for cardiovascular X-ray images, using a full-reference scheme (relying on averaging a sequence to obtain a noiseless reference). With the growth of advanced signal processing in medical imaging, such an approach will enable objective comparisons of the quality of processed images. A concept for describing the quality of an image is to express it in terms of its information capacity. Shannon has derived this capacity for noisy channel coding. However, for X-ray images, the noise is signal-dependent and non-additive, so that Shannons theorem is not directly applicable. To overcome this complication, we exploit the fact that any invertible mapping on a signal does not change its information content. We show that it is possible to transform the images in such a way that the Shannon theorem can be applied. A general method for calculating such a transformation is used, given a known relation between signal mean and noise standard deviation. After making the noise signal-independent, it is possible to assess the information content of an image and to calculate an overall quality metric (e.g. information capacity) which includes the effects of sharpness, contrast and noise. We have applied this method on phantom images under different acquisition conditions and computed the information capacity for those images. We aim to show that the results of this assessment are consistent with variations in noise, contrast and sharpness, introduced by system settings and image processing.