Bart Truyen

Hierarchical contour matching in medical images

A hierarchical finite difference method to match analogous contours is presented. Our approach has been inspired by the method due to Duncan, who proposed a scheme for matching two contours based on the minimization of a quadratic fitting criterion. This criterion consists of a curvature dependent bending energy term and a smoothness term. Cohen improved this method by ensuring that the resulting displacement vectors actually map points belonging to the two contours. Building on this method, the innovation of our work is in the introduction of a number of modifications and extensions, which promise to considerably improve its already proven performance. First, a new smoothness term in the matching cost function has been derived, supported by a revealing analysis of the discretization process. As a result, the computational complexity is reduced and the equation corresponding to the minimization of the fitting criterion has a simple interpretation. To solve the resulting nonlinear system of equations, a new method is derived based on a two-step predictor-corrector scheme, for which we present a detailed analytical convergence analysis. Unlike previous algorithms, which relied on (semi-)implicit problem formulations, this explicit scheme has a clear advantage in terms of convergence rate. Finally, the algorithm is extended with a new multi-smoothing scheme which not only increases the convergence speed, but even more importantly, makes the method more robust and less dependent on a good initialization value to guarantee convergence to a global optimum. Experimental validation is carried out on three medical applications: (i) Matching of left ventricular contours in successive images of a time sequence of spin echo cardiac magnetic resonance (MR) images; (ii) matching of brain object contours in consecutive slices of a digital brain atlas; (iii) matching of brain object contours in segmented MR images to the outlines of the corresponding brain objects in a digital anatomical atlas.

2D image registration using focused mutual information for application in dentistry

Spatial alignment of image data is a common task in computer vision and medical imaging. This should preferentially be done with minimal intervention of an operator. Similarity measures with origin in the information theory such as mutual information (MI) have proven to be robust registration criteria for this purpose. Intra-oral radiographs can be considered images of piecewise rigid objects. Teeth and jaws are rigid but can be displaced with respect to each other. Therefore MI criteria combined with affine deformations tend to fail, when teeth and jaws move with respect to each other between image acquisitions. In this paper, we consider a focused weighing of pixels in the reference image. The resulting criterion, focused mutual information (FMI) is an adequate tool for the registration of rigid parts of a scene. We also show that the use of FMI is more robust for the subtraction of lateral radiographs of teeth, than MI confined to a region of interest. Furthermore, the criterion allows the follow-up of small carious lesions when upper and lower jaw moved between the acquisition of test and reference image.

Adiabatic layering: a new concept of hierarchical multi-scale optimization

Abstract Recurrent neural networks (RNNs) with linearized dynamics have shown great promise in solving continuous valued optimization problems subject to bound constraints. Building on this progress, a novel method of constrained hierarchical multi-scale optimization is developed that applies to a wide range of optimization problems and signal decomposition tasks. Central to the underlying concept is the definition of adiabatic layering. Analytic justification of this model can be regarded as a natural development of the mean-field theory. What emerges is an alternative hierarchical optimization method that promises to improve upon existing hierarchical schemes in combining the accuracy of global optimization with the compact representation of hierarchical optimization. Whereas conventional hierarchical optimization techniques typically tend to average over fine-scale detail when applied to bound-constrained problems, such behavior is avoided by the modified dynamics of the proposed method. Applied to the signal decomposition problem of RBF approximation, the behaviour of the adiabatic layering model is shown to be in close correspondence with the theoretical expectations.

Weakly convex discontinuity adaptive regularization for 3D quantitative microwave tomography

We present an analysis of weakly convex discontinuity adaptive (WCDA) models for regularizing three-dimensional (3D) quantitative microwave imaging. In particular, we are concerned with complex permittivity reconstructions from sparse measurements such that the reconstruction process is significantly accelerated. When dealing with such a highly underdetermined problem, it is crucial to employ regularization, relying in this case on prior knowledge about the structural properties of the underlying permittivity profile: we consider piecewise homogeneous objects. We present a numerical study on the choice of the potential function parameter for the Huber function and for two selected WCDA functions, one of which (the Leclerc‐CauchyLorentzian function) is designed to be more edge-preserving than the other (the Leclerc‐Huber function). We evaluate the effect of reducing the number of (simulated) scatteredfield data on the reconstruction quality. Furthermore, reconstructions from subsampled single-frequency experimental data from the 3D Fresnel database illustrate the effectiveness of WCDA regularization.

Applicability of an effective conductivity approach in modeling thoracic impedance changes

This paper describes numerical simulations of the influence of conductivity changes inside a volume conductor on impedance changes measured on its surface. A simple model based on the finite element method has been developed to estimate an applicability of the effective conductivity theory in human chest modeling. The model consisted of a cylinder with two concentric spheres inside. Simulations were performed for two cases: first the geometry was changing and material properties were constant within each subdomain, next, the geometry was constant but conductivity values were changing for each phase of cardiac cycle. In the considered range of geometry changes dependence between impedance changes calculated for two models was linear. Performed simulations showed that effective conductivity approach can be utilized when studying dynamic processes involved by volume changes of internal organs.

An adiabatic neural network for RBF approximation

Numerous studies have addressed nonlinear functional approximation by multilayer perceptrons (MLPs) and RBF networks as a special case of the more general mapping problem. The performance of both these supervised network models intimately depends on the efficiency of their learning process. This paper presents an unsupervised recurrent neural network, based on the recurrent Mean Field Theory (MFT) network model, that finds a least-squares approximation to an arbitrary L2 function, given a set of Gaussian radially symmetric basis functions (RBFs). Essential is the reformulation of RBF approximation as a problem of constrained optimisation. A new concept of adiabatic network organisation is introduced. Together with an adaptive mechanism of temperature control this allows the network to build a hierarchical multiresolution approximation with preservation of the global optimisation characteristics. A revised problem mapping results in a position invariant local interconnectivity pattern, which makes the network attractive for electronic implementation. The dynamics and performance of the network are illustrated by numerical simulation.

Energy Minimisation Methods for Static and Dynamic Curve Matching

Curve matching is an important problem in pattern recognition with a variety of applications including model based recognition. In these applications the two matched curves are usually very similar. An application of curve matching to model based recognition involves typically a decision whether a model curve and an image curve are the same, up to some scaling or a transformation and some permitted level of noise. Most of the work on curve matching relates directly to contour matching, where one should further make a distinction between dense matching and feature matching. The latter approach is based on a set of features, calculated for both contours. In that case, the distance of the contours in feature space is used as matching criterion. Dense matching is usually formulated as a parameterisation problem, with some cost function to be minimised. The cost might be defined as the elastic energy needed to transform one curve to the other [1, 2, 3], but other alternatives exist [4, 5, 6].

Piecewise Multi-linear PDF Modelling, Using an ML Approach

This paper addresses the problem of estimating the model parameters of a piecewise multi-linear (PML) approximation to a probability density function (PDF). In an earlier paper, we already introduced the PML model and discussed its use for the purpose of designing Bayesian pattern classifiers. The estimation of the unknown model parameters was based on a least squares minimisation of the difference between the estimated PDF and the estimating PML function. Here, we show how a Maximum Likelihood (ML) approach can be used to estimate the unknown parameters and discuss the advantages of this approach. Subsequently, we briefly introduce its application in a new approach to histogram matching in digital subtraction radiography.