A two-dimensional model for the cochlea

Summary An alternative is given for the approach of the two-dimensional problem presented in [12]. Because of the mathematical simplicity of this alternative, several extensions of the model are possible. In this work the compressibility of the perilymph and variations of the scalaheight are considered; other extensions are briefly discussed.The numerical calculations lead to the following conclusions: (1) the results of the one- and two-dimensional models show large quantitative but hardly any qualitative differences; (2) Von Békésy's [1] conclusions concerning the influence of the scalaheight upon the motion of the partition are incorrect; (3) the quantitative discrepancies between the model's results and the experiments of Rhode [6] can be eliminated by a large reduction of the scalaheight; (4) the phase difference as a function of frequency and the phase velocity show no qualitative disparities with the experimental data; (5) models with few sections, such as the hybrid computer model of Hubbard and Geisler [4] are inaccurate.     

A quantitative analysis of 3-D coronary modeling from two or more projection images

A method is introduced to examine the geometrical accuracy of the three-dimensional (3-D) representation of coronary arteries from multiple (two and more) calibrated two-dimensional (2-D) angiographic projections. When involving more then two projections, (multiprojection modeling) a novel procedure is presented that consists of fully automated centerline and width determination in all available projections based on the information provided by the semi-automated centerline detection in two initial calibrated projections. The accuracy of the 3-D coronary modeling approach is determined by a quantitative examination of the 3-D centerline point position and the 3-D cross sectional area of the reconstructed objects. The measurements are based on the analysis of calibrated phantom and calibrated coronary 2-D projection data. From this analysis a confidence region (alpha degrees approximately equal to [35 degrees - 145 degrees]) for the angular distance of two initial projection images is determined for which the modeling procedure is sufficiently accurate for the applied system. Within this angular border range the centerline position error is less then 0.8 mm, in terms of the Euclidean distance to a predefined ground truth. When involving more projections using our new procedure, experiments show that when the initial pair of projection images has an angular distance in the range alpha degrees approximately equal to [35 degrees - 145 degrees], the centerlines in all other projections (gamma = 0 degrees - 180 degrees) were indicated very precisely without any additional centering procedure. When involving additional projection images in the modeling procedure a more realistic shape of the structure can be provided. In case of the concave segment, however, the involvement of multiple projections does not necessarily provide a more realistic shape of the reconstructed structure.     

F-information measures in medical image registration

A measure for registration of medical images that currently draws much attention is mutual information. The measure originates from information theory, but has been shown to be successful for image registration as well. Information theory, however, offers many more measures that may be suitable for image registration. These all measure the divergence of the joint distribution of the images' grey values from the joint distribution that would have been found had the images been completely independent. This paper compares the performance of mutual information as a registration measure with that of other F-information measures. The measures are applied to rigid registration of positron emission tomography (PET)/magnetic resonance (MR) and MR/computed tomography (CT) images, for 35 and 41 image pairs, respectively. An accurate gold standard transformation is available for the images, based on implanted markers. The registration performance, robustness and accuracy of the measures are studied. Some of the measures are shown to perform poorly on all aspects. The majority of measures produces results similar to those of mutual information. An important finding, however, is that several measures, although slightly more difficult to optimize, can potentially yield significantly more accurate results than mutual information.     

Image registration by maximization of combined mutual information and gradient information

Mutual information has developed into an accurate measure for rigid and affine monomodality and multimodality image registration. The robustness of the measure is questionable, however. A possible reason for this is the absence of spatial information in the measure. The present paper proposes to include spatial information by combining mutual information with a term based on the image gradient of the images to be registered. The gradient term not only seeks to align locations of high gradient magnitude, but also aims for a similar orientation of the gradients at these locations. Results of combining both standard mutual information as well as a normalized measure are presented for rigid registration of three-dimensional clinical images [magnetic resonance (MR), computed tomography (CT), and positron emission tomography (PET)]. The results indicate that the combined measures yield a better registration function does mutual information or normalized mutual information per se. The registration functions are less sensitive to low sampling resolution, do not contain incorrect global maxima that are sometimes found in the mutual information function, and interpolation-induced local minima can be reduced. These characteristics yield the promise of more robust registration measures. The accuracy of the combined measures is similar to that of mutual information-based methods.     

Fast delineation and visualization of vessels in 3-D angiographic images

A method is presented which aids the clinician in obtaining quantitative measures and a three-dimensional (3-D) representation of vessels from 3-D angiographic data with a minimum of user interaction. Based on two user defined starting points, an iterative procedure tracks the central vessel axis. During the tracking process, the minimum diameter and a surface rendering of the vessels are computed, allowing for interactive inspection of the vasculature. Applications of the method to CTA, contrast enhanced (CE)-MRA and phase contrast (PC)-MRA images of the abdomen are shown. In all applications, a long stretch of vessels with varying width is tracked, delineated, and visualized, in less than 10 s on a standard clinical workstation.     

Vessel axis tracking using topology constrained surface evolution

An approach to 3-D vessel axis tracking based on surface evolution is presented. The main idea is to guide the evolution of the surface by analyzing its skeleton topology during evolution, and imposing shape constraints on the topology. For example, the intermediate topology can be processed such that it represents a single vessel segment, a bifurcation, or a more complex vascular topology. The evolving surface is then reinitialized with the newly found topology. Reinitialization is a crucial step since it creates probing behavior of the evolving front, encourages the segmentation process to extract the vascular structure of interest and reduces the risk on leaking of the curve into the background. The method was evaluated in two computed tomography angiography applications: 1) extracting the internal carotid arteries including the region in which they traverse through the skull base, which is challenging due to the proximity of bone structures and overlap in intensity values; 2) extracting the carotid bifurcations including many cases in which they are severely stenosed and contain calcifications. The vessel axis was found in 90% (18/20 internal carotids in ten patients) and 70% (14/20 carotid bifurcations in a different set of ten patients) of the cases.     

Image Registration for Digital Subtraction Angiography

In clinical practice, Digital Subtraction Angiography (DSA) is a powerful technique for the visualization of blood vessels in the human body. The diagnostic relevance of the images is often reduced by artifacts which arise from the misalignment of successive images in the sequence, due to patient motion. In order to improve the quality of the subtraction images, several registration techniques have been proposed. However, because of the required computation times, it has never led to algorithms that are fast enough so as to be acceptable for integration in clinical applications. In this paper, a new approach to the registration of digital angiographic images is proposed. It involves an edge-based selection of control points for which the displacement is computed by means of template matching, and from which the complete displacement vector field is constructed by means of interpolation. The final warping of the images according to the calculated displacement vector field is performed real-time by graphics hardware. Experimental results with several clinical data sets show that the proposed algorithm is both effective and very fast.     

Retrospective shading correction based on entropy minimization

Shading is a prominent phenomenon in microscopy, manifesting itself via spurious intensity variations not present in the original scene. The elimination of shading effects is frequently necessary for subsequent image processing tasks, especially if quantitative analysis is the final goal. While most of the shading effects may be minimized by setting up the image acquisition conditions carefully and capturing additional calibration images, object-dependent shading calls for retrospective correction. In this paper a novel method for retrospective shading correction is proposed. Firstly, the image formation process and the corresponding shading effects are described by a linear image formation model, which consists of an additive and a multiplicative parametric component. Secondly, shading correction is performed by the inverse of the image formation model, whose shading components are estimated retrospectively by minimizing the entropy of the acquired images. A number of tests, performed on artificial and real microscopical images, show that this approach is efficient for a variety of differently structured images and as such may have applications in and beyond the field of microscopical imaging.     

Reversible 3-D decorrelation of medical images

Two methods, namely, differential pulse code modulation (DPCM) and hierarchical interpolation (HINT), are considered. It is shown that HINT cannot be extended straightforwardly to 3-D images as contrasted with DPCM. A 3-D HINT is therefore proposed which is based on a combination of 2-D and 3-D filters. Both decorrelation methods were applied to three-dimensional computed tomography (CT), magnetic resonance (MR), and single-photon-emission CT (SPECT) images. It was found that a 3-D approach is optimal for some studies, while for other studies 2-D or even 1-D decorrelation performs better. The optimal dimensionality of DPCM is related to the magnitudes of the local correlation coefficients (CCs). However, the nonlocal nature of HINT makes the local correlation coefficients useless as indicators of the dimensionality; a better candidate is the image voxel size. For images with cubic or nearly cubic voxels 3-D HINT is generally optimal. For images in which the slice thickness is large compared to the pixel size a 2-D (intraslice) HINT is best. In general, the increase in efficiency obtained by extending 2-D decorrelation method to 3-D is small.