Peter Burger

Structure adaptive anisotropic image filtering

Noise filtering of images is essentially a smoothing process, and it is an issue that has been addressed for many years. The most commonly used low-pass filtering methods blur important image structures such as edges and lines, and thus reduce image contrast and damage image fidelity. This paper presents a structure adaptive anisotropic filtering technique with its application to processing magnetic resonance images. It differs from other techniques in that, instead of using local gradients as a means of controlling the anisotropism of filters, it uses both a local intensity orientation and an anisotropic measure of level contours to control the shape and extent of the filter kernel. This ensures that corners and junctions are well preserved throughout the filtering process. The following two aspects of the proposed technique demonstrate the advantage of using this filtering method. Firstly, the use of local orientation detection provides a robust and convenient way for shaping the filter kernel. Secondly, the structural adaptiveness of the filtering process ensures that salient image features are non-symmetrically enhanced.

Automatic tracking of the aorta in cardiovascular MR images using deformable models

Presents a new algorithm for the robust and accurate tracking of the aorta in cardiovascular magnetic resonance (MR) images. First, a rough estimate of the location and diameter of the aorta is obtained by applying a multiscale medial-response function using the available a priori knowledge. Then, this estimate is refined using an energy-minimizing deformable model which the authors define in a Markov-random-field (MRF) framework. In this context, the authors propose a global minimization technique based on stochastic relaxation. Simulated annealing (SA), which is shown to be superior to other minimization techniques, for minimizing the energy of the deformable model. The authors have evaluated the performance and robustness of the algorithm on clinical compliance studies in cardiovascular MR images. The segmentation and tracking has been successfully tested in spin-echo MR images of the aorta. The results show the ability of the algorithm to produce not only accurate, but also very reliable results in clinical routine applications.

Depth and shape from shading using the photometric stereo method

The independent calculation of local position and orientation of the Lambertian surface of an opaque object is proposed using the photometric stereo method. A number of shaded video images are taken using different positions of an ideal point light source which is placed close to the object. Normally, three images are required for a uniform and four for a textured Lambertian surface. By restricting three light sources to lie in a straight line, the depth calculations for an arbitrary surface with textured Lambertian reflection characteristics can be also determined; however, in this case the orientation of the surface cannot be calculated independently. It is shown that for both uniform and textured Lambertian surfaces the equations which are functions of three independent variables, namely, depth (D) and surface normal direction vector (n = [p, q, − 1]), can be reduced to a single nonlinear equation of depth, i.e., the distance between the camera and the point on the surface. Both convergence and a unique solution are ensured because of the simple behavior of the nonlinear equation within a practical range of depth and gradient values. The robustness of the algorithm is demonstrated by synthetic as well as experimental data. The calculation of the approximate positions and orientations of discontinuous surfaces is demonstrated when random noise is added to the synthetically calculated image intensities. Two parallel planes with a gap, two sloped planes, and a spherical surface are used to demonstrate that the algorithms work well. An important feature of calculating both depth and orientation independently is that for smooth surfaces they must obey the partial differential expressions p = δDδxand q = δDδy. If we are certain that the experimental errors are within a known limit then the numerical approximation to these partial derivative expressions can be used to determine discontinuities within the image. On the other hand, if we know that the surfaces are smooth then errors in the numerical evaluation of these differential expressions allow the estimation of experimental errors.

Motion and deformation tracking for short-axis echo-planar myocardial perfusion imaging

The assessment of regional myocardial perfusion during the first-pass of a contrast agent bolus requires tracking of the signal time course for each myocardial segment so that a detailed perfusion map can be derived. To obtain such a map in practice, however, is not trivial because deformation of the shape of the myocardium and respiratory-induced motion render a major difficulty in this process. This study describes an automated approach for motion and deformation tracking of functional myocardial perfusion images. The effectiveness of the described method has been evaluated using a numerical phantom and results are compared with those from existing techniques which use deformable models. Preliminary results from applying our approach to 20 patients are discussed and compared with those from SPECT studies.

Differential algorithm for the determination of shape from shading using a point light source

Abstract This paper presents a linear algorithm for recovering shape information of Lambertian surfaces from the shading information inherent in a single 2D image. The local orientation of a planar Lambertian surface patch is determined from a single video image when both camera and a light source are near to the surface. A simple linear relationship is derived between the ratios of the measured image intensities and their first partial derivatives and the components of the surface normal vector. An advantage of the formulation is that the resulting equations are independent of the intensity strength of the illuminating source as well as the surface reflection coefficient (albedo). Results for noisy synthetic images as well as real images are presented.

Geometrically Deformable Templates for Shape-Based Segmentation and Tracking in Cardiac MR Images

We present a new approach to shape-based segmentation and tracking of multiple, deformable anatomical structures in cardiac MR images. We propose to use an energy-minimizing geometrically deformable template (GDT) which can deform into similar shapes under the influence of image forces. The degree of deformation of the template from its equilibrium shape is measured by a penalty function associated with mapping between the two shapes. In 2D, this term corresponds to the bending energy of an idealized thin-plate of metal. By minimizing this term along with the image energy terms of the classic deformable model, the deformable template is attracted towards objects in the image whose shape is similar to its equilibrium shape. This framework allows for the simultaneous segmentation of multiple deformable objects using intra-as well as inter-shape information. The energy minimization problem of the deformable template is formulated in a Bayesian framework and solved using relaxation techniques: Simulated Annealing (SA), a stochastic relaxation technique is used for segmentation while Iterated Conditional Modes (ICM), a deterministic relaxation technique is used for tracking. We present results of the algorithm applied to the reconstruction of the left and right ventricle of the human heart in 4D MR images.

Knowledge-based tensor anisotropic diffusion of cardiac magnetic resonance images

We present a general formulation for a new knowledge-based approach to anisotropic diffusion of multi-valued and multi-dimensional images, with an illustrative application for the enhancement and segmentation of cardiac magnetic resonance (MR) images. In the proposed method all available information is incorporated through a new definition of the conductance function which differs from previous approaches in two aspects. First, we model the conductance as an explicit function of time and position, and not only of the differential structure of the image data. Inherent properties of the system (such as geometrical features or non-homogeneous data sampling) can therefore be taken into account by allowing the conductance function to vary depending on the location in the spatial and temporal coordinate space. Secondly, by defining the conductance as a second-rank tensor, the non-homogeneous diffusion equation gains a truly anisotropic character which is essential to emulate and handle certain aspects of complex data systems. The method presented is suitable for image enhancement and segmentation of single- or multi-valued images. We demonstrate the efficiency of the proposed framework by applying it to anatomical and velocity-encoded cine volumetric (4-D) MR images of the left ventricle. Spatial and temporal a priori knowledge about the shape and dynamics of the heart is incorporated into the diffusion process. We compare our results to those obtained with other diffusion schemes and exhibit the improvement in regions of the image with low contrast and low signal-to-noise ratio.

Contour fitting using an adaptive spline model

This paper presents a new segmentation algorithm by fitting active contour models (or snakes) to objects using adaptive splines. The adaptive spline model describes the contour of an object by a set of piecewisely interpolating C polynomial spline patches which are locally controlled. Thus the resulting description of the object contour is continuous and smooth. Polynomial splines provide a fast and efficient way for interpolating the object contour and allow us to compute its internal energy due to bending and elasticity deformations analytically. The adaptive spline model can be represented by its spline control points. The accuracy of the model is gradually increased during the segmentation process by inserting new control points. For estimating the optimal position of the control points, two different relaxation techniques based on Markov-Random-Fields (MRFs) have been combined and evaluated: Simulated Annealing (SA), which is a stochastic relaxation technique, and Iterated Conditional Modes (ICM), which is a probabilistic relaxation technique. We have studied convergence behavior and performance on artificial and medical images. The results show that the combination of both relaxation techniques provides very robust and initialization independent segmentation results.

Shape-based segmentation and tracking in 4D cardiac MR images

We present a new approach to shape-based segmentation and tracking of multiple, deformable anatomical structures in cardiac MR images. We propose to use an energy-minimizing geometrically deformable template (GDT) which can deform into similar shapes under the influence of image forces. The degree of deformation of the template from its equilibrium shape is measured by a penalty function associated with mapping between the two shapes. In 2D, this term corresponds to the bending energy of an idealized thin-plate of metal. By minimizing this term along with the image energy terms of the classic deformable model, the deformable template is attracted towards objects in the image whose shape is similar to its equilibrium shape. This framework allows the simultaneous segmentation of multiple deformable objects using intra- as well as inter-shape information. The energy minimization problem of the deformable template is formulated in a Bayesian framework and solved using relaxation techniques: Simulated Annealing (SA), a stochastic relaxation technique is used for segmentation while Iterated Conditional Modes (ICM), a deterministic relaxation technique is used for tracking. We present results of the algorithm applied to the reconstruction of the left and right ventricle of the human heart in 4D MR images.

In vivo blood flow visualization with magnetic resonance imaging

Blood movement investigated by magnetic resonance (MR) velocity mapping is generally presented in the form of velocity components in one or more chosen velocity encoding directions. By viewing these components separately, it is difficult for MR practitioners to conceptualize and comprehend the underlying flow structures, especially when the image data have strong background noise. A flow visualization technique that adapts the idea of particle tracing used in classical fluid dynamics for visualizing flow is presented. The flow image processing relies on the strong correlation between the principal flow direction estimated from the distribution of the modulus of the velocity field and the direction derived from the raw image data. By correlation calculation, severe background noise can be eliminated. Flow pattern rendering and animation provide an efficient way for representing internal flow structures.<<ETX>>