Retrospective correction of MR intensity inhomogeneity by information minimization

Exponential Entropy Driven HUM on Knee MR Images

A very important artifact corrupting Magnetic Resonance Images is the RF inhomogeneity. This kind of artifact generates variations of illumination which trouble both direct examination by the doctor and segmentation algorithms. Even if homomorphic filtering approaches have been presented in literature, none of them has developed a measure to determine the cut-off frequency. In this work we present a measure based on information theory with a large experimental setup aimed to demonstrate the validity of our approach.

Entropy based method to correct intensity inhomogeneity in MR images

We are involved in a comprehensive program to characterize atherosclerotic disease using multiple MR images having different contrast mechanisms (T1W, T2W, PDW, magnetization transfer, etc.) of human carotid and animal model arteries. We use specially designed intravascular and surface array coils that give high signal-to-noise but suffer from sensitivity inhomogeneity and significant noise. We present here a new non-parametric method for correcting the images without assumption of the number of different tissues. Intensity inhomogeneity is modeled with cubic spline and is locally optimized using an entropy criterion. Validation has been performed on a specially design neck phantom as well as actual MR scans on patient neck. The steep bias is corrected sufficiently to aid human interpretation of gray scales. It should also make possible computerized tissue classification.

A Gabor-based technique for bias removal in MR images

Magnetic Resonance images are often characterized by irregularly displaced luminance fluctuations that are called bias artifact. This disturb is due to a drop in signal intensity caused by the distance between imaged sample and receiver coil. An original approach to bias removal in Magnetic Resonance images is presented, which is based on the use of Gabor filter to extract the artifact. The proposed technique restores the image using a correction model, which is derived from the attenuation of signal diffusion across the tissues. No hypotheses are made about the structure of the tissues under investigation and the used MR spectrum. The approach is presented in detail, and extensive experimental results are reported along with a comparison with other popular techniques for bias removal.

De-enhancing the dynamic contrast-enhanced breast MRI for robust registration

Dynamic enhancement causes serious problems for registration of contrast enhanced breast MRI, due to variable uptakes of agent on different tissues or even same tissues in the breast. We present an iterative optimization algorithm to de-enhance the dynamic contrast-enhanced breast MRI and then register them for avoiding the effects of enhancement on image registration. In particular, the spatially varying enhancements are modeled by a Markov Random Field, and estimated by a locally smooth function with boundaries using a graph cut algorithm. The de-enhanced images are then registered by conventional B-spline based registration algorithm. These two steps benefit from each other and are repeated until the results converge. Experimental results show that our two-step registration algorithm performs much better than conventional mutual information based registration algorithm. Also, the effects of tumor shrinking in the conventional registration algorithms can be effectively avoided by our registration algorithm.

A novel, fast entropy-minimization algorithm for bias field correction in MR images

A novel, fast entropy-minimization algorithm for bias field correction in magnetic resonance (MR) images is suggested to correct the intensity inhomogeneity degradation of MR images that has become an increasing problem with the use of phased-array coils. Four important modifications were made to the conventional algorithm: (a) implementation of a modified two-step sampling strategy for stacked 2D image data sets, which included reducing the size of the measured image on each slice with a simple averaging method without changing the number of slices and then using a binary mask generated by a histogram threshold method to define the sampled voxels in the reduced image; (b) improvement of the efficiency of the correction function by using a Legendre polynomial as an orthogonal base function polynomial; (c) use of a nonparametric Parzen window estimator with a Gaussian kernel to calculate the probability density function and Shannon entropy directly from the image data; and (d) performing entropy minimization with a conjugate gradient method. Results showed that this algorithm could correct different types of MR images from different types of coils acquired at different field strengths very efficiently and with decreased computational load.

The fast automatic algorithm for correction of MR bias field

PURPOSE

To develop a method for efficient automatic correction of slow-varying nonuniformity in MR images.

MATERIALS AND METHODS

The original MR image is represented by a piecewise constant function, and the bias (nonuniformity) field of an MR image is modeled as multiplicative and slow varying, which permits to approximate it with a low-order polynomial basis in a "log-domain." The basis coefficients are determined by comparing partial derivatives of the modeled bias field with the original image.

RESULTS

We tested the resulting algorithm named derivative surface fitting (dsf) on simulated images and phantom and real data. A single iteration was sufficient in most cases to produce a significant improvement to the MR image's visual quality. dsf does not require prior knowledge of intensity distribution and was successfully used on brain and chest images. Due to its design, dsf can be applied to images of any modality that can be approximated as piecewise constant with a multiplicative bias field.

CONCLUSION

The resulting algorithm appears to be an efficient method for fast correction of slow varying nonuniformity in MR images.

Illumination Correction on MR Images

OBJECTIVE

An important artifact corrupting Magnetic Resonance Images is the rf inhomogeneity, also called bias artifact. This anomaly produces an abnormal illumination fluctuation on the image, due to variations of the device magnetic field. This artifact is particularly strong on images acquired with a device specialized on upper and lower limbs due to their coil configuration. A method based on homomorphic filtering aimed to suppress this artifact was proposed by Guillemaud. This filter has two faults: it doesn't provide an indication about the cutoff frequency (cf) and introduces another illumination artifact on the edges of the foreground. This work is an improvement to this method because it resolves both problems.

METHODS

The experimental setup has been performed on knee images obtained by 5 volunteers and acquired through an Artoscan device using the following parameters: Spin Echo sequence, Repetition time: 980 ms, Echo time: 26 ms, Slice thickness: 4 mm, Flip Angle: 90 degrees .

RESULTS

Two specialists in orthoptics evaluated the results of the proposed approach by examining the restored images and validating the results produced by the filter. A quantitative evaluation has been performed on a manually segmented restored image using the coefficient of variation (cv) measure.

CONCLUSIONS

Following the specialists qualitative evaluation, the illuminance of upper and lower peripheral zones results to be enhanced; a loose of contrast can be noted only in few cases. The Bias image exhibits an artifact focused usually on the central part of the foreground. The quantitative evaluation based on cv shows that this index is lowered for all the segmented regions with respect to the original value. The method is automatic and doesn't require any hypothesis on the tissues. A manual version of the algorithm can be also implemented allowing the physician to choose the preferred cf. In this case the value selected by the method can be considered as a default value.

A Review on MR Image Intensity Inhomogeneity Correction

Intensity inhomogeneity (IIH) is often encountered in MR imaging, and a number of techniques have been devised to correct this artifact. This paper attempts to review some of the recent developments in the mathematical modeling of IIH field. Low-frequency models are widely used, but they tend to corrupt the low-frequency components of the tissue. Hypersurface models and statistical models can be adaptive to the image and generally more stable, but they are also generally more complex and consume more computer memory and CPU time. They are often formulated together with image segmentation within one framework and the overall performance is highly dependent on the segmentation process. Beside these three popular models, this paper also summarizes other techniques based on different principles. In addition, the issue of quantitative evaluation and comparative study are discussed.

Intensity inhomogeneity correction of multispectral MR images

Intensity inhomogeneity in MR images is an undesired phenomenon, which often hampers different steps of quantitative image analysis such as segmentation or registration. In this paper, we propose a novel fully automated method for retrospective correction of intensity inhomogeneity. The basic assumption is that inhomogeneity correction could be improved by integrating spatial and intensity information from multiple MR channels, i.e., T1, T2, and PD weighted images. Intensity inhomogeneities of such multispectral images are removed simultaneously in a four-step iterative procedure. First, the probability distribution of image intensities and corresponding spatial features is calculated. In the second step, intensity correction forces that tend to minimize joint entropy of multispectral image are estimated for all image voxels. Third, independent inhomogeneity correction fields are obtained for each channel by regularization and normalization of voxel forces, and last, corresponding partial inhomogeneity corrections are performed separately for each channel. The method was quantitatively evaluated on simulated and real MR brain images and compared to three other methods.

Method to correct intensity inhomogeneity in MR images for atherosclerosis characterization

We are developing methods to characterize atherosclerotic disease in human carotid arteries using multiple MR images having different contrast mechanisms (T1W, T2W, PDW). To enable the use of voxel gray values for interpretation of disease, we created a new method, local entropy minimization with a bicubic spline model (LEMS), to correct the severe (approximately 80%) intensity inhomogeneity that arises from the surface coil array. This entropy-based method does not require classification and robustly addresses some problems that are more severe than those found in brain imaging, including noise, steep bias field, sensitivity of artery wall voxels to edge artifacts, and signal voids near the artery wall. Validation studies were performed on a synthetic digital phantom with realistic intensity inhomogeneity, a physical phantom roughly mimicking the neck, and patient carotid artery images. We compared LEMS to a modified fuzzy c-means segmentation based method (mAFCM), and a linear filtering method (LINF). Following LEMS correction, skeletal muscles in patient images were relatively isointense across the field of view. In the physical phantom, LEMS reduced the variation in the image to 1.9% and across the vessel wall region to 2.5%, a value which should be sufficient to distinguish plaque tissue types, based on literature measurements. In conclusion, we believe that the correction method shows promise for aiding human and computerized tissue classification from MR signal intensities.

Deformation-based mapping of volume change from serial brain MRI in the presence of local tissue contrast change

This paper is motivated by the analysis of serial structural magnetic resonance imaging (MRI) data of the brain to map patterns of local tissue volume loss or gain over time, using registration-based deformation tensor morphometry. Specifically, we address the important confound of local tissue contrast changes which can be induced by neurodegenerative or neurodevelopmental processes. These not only modify apparent tissue volume, but also modify tissue integrity and its resulting MRI contrast parameters. In order to address this confound we derive an approach to the voxel-wise optimization of regional mutual information (RMI) and use this to drive a viscous fluid deformation model between images in a symmetric registration process. A quantitative evaluation of the method when compared to earlier approaches is included using both synthetic data and clinical imaging data. Results show a significant reduction in errors when tissue contrast changes locally between acquisitions. Finally, examples of applying the technique to map different patterns of atrophy rate in different neurodegenerative conditions is included.

3-D reconstruction of tissue components for atherosclerotic human arteries using ex vivo high-resolution MRI

Automatic computer-based methods are well suited for the image analysis of the different components in atherosclerotic plaques. Although several groups work on such analysis some of the methods used are oversimplified and require improvements when used within a computational framework for predicting meaningful stress and strain distributions in the heterogeneous arterial wall under various loading conditions. Based on high-resolution magnetic resonance imaging of excised atherosclerotic human arteries and a series of two-dimensional (2-D) contours we present a segmentation tool that permits a three-dimensional (3-D) reconstruction of the most important tissue components of atherosclerotic arteries. The underlying principle of the proposed approach is a model-based snake algorithm for identifying 2-D contours, which uses information about the plaque composition and geometric data of the tissue layers. Validation of the computer-generated tissue boundaries is performed with 100 MR images, which are compared with the results of a manual segmentation performed by four experts. Based on the Hausdorff distance and the average distance for computer-to-expert differences and the interexpert differences for the outer boundary of the adventitia, the adventitia-media, media-intima, intima-lumen and calcification boundaries are less than 1 pixel (0.234 mm). The percentage statistic shows similar results to the modified Williams index in terms of accuracy. Except for the identification of lipid-rich regions the proposed algorithm is automatic. The nonuniform rational B-spline-based computer-generated 3-D models of the individual tissue components provide a basis for clinical and computational analysis.

3-D/2-D registration by integrating 2-D information in 3-D

In image-guided therapy, high-quality preoperative images serve for planning and simulation, and intraoperatively as "background", onto which models of surgical instruments or radiation beams are projected. The link between a preoperative image and intraoperative physical space of the patient is established by image-to-patient registration. In this paper, we present a novel 3-D/2-D registration method. First, a 3-D image is reconstructed from a few 2-D X-ray images and next, the preoperative 3-D image is brought into the best possible spatial correspondence with the reconstructed image by optimizing a similarity measure (SM). Because the quality of the reconstructed image is generally low, we introduce a novel SM, which is able to cope with low image quality as well as with different imaging modalities. The novel 3-D/2-D registration method has been evaluated and compared to the gradient-based method (GBM) using standardized evaluation methodology and publicly available 3-D computed tomography (CT), 3-D rotational X-ray (3DRX), and magnetic resonance (MR) and 2-D X-ray images of two spine phantoms, for which gold standard registrations were known. For each of the 3DRX, CT, or MR images and each set of X-ray images, 1600 registrations were performed from starting positions, defined as the mean target registration error (mTRE), randomly generated and uniformly distributed in the interval of 0-20 mm around the gold standard. The capture range was defined as the distance from gold standard for which the final TRE was less than 2 mm in at least 95% of all cases. In terms of success rate, as the function of initial misalignment and capture range the proposed method outperformed the GBM. TREs of the novel method and the GBM were approximately the same. For the registration of 3DRX and CT images to X-ray images as few as 2-3 X-ray views were sufficient to obtain approximately 0.4 mm TREs, 7-9 mm capture range, and 80%-90% of successful registrations. To obtain similar results for MR to X-ray registrations, an image, reconstructed from at least 11 X-ray images was required. Reconstructions from more than 11 images had no effect on the registration results.

A Fast and Automatic Method to Correct Intensity Inhomogeneity in MR Brain Images

This paper presents a method to improve the semi-automatic method for intensity inhomogeneity correction by Dawant et al. through introducing a fully automatic approach to reference points generation, which is based on order statistics and integrates information from the fine to coarse scale representations of the input image. The method has been validated and compared with two popular methods, N3 and BFC. Advantages of the proposed method are demonstrated.

Morphological exponential entropy driven-HUM

This paper presents an improvement to the exponential entropy driven-homomorphic unsharp masking (E(2)D-HUM) algorithm devoted to illumination artifact suppression on magnetic resonance images. E(2)D-HUM requires a segmentation step to remove dark regions in the foreground whose intensity is comparable with background, because strong edges produce streak artifacts on the tissues. This new version of the algorithm keeps the same good properties of E(2)D-HUM without a segmentation phase, whose parameters should be chosen in relation to the image.

Intensity non-uniformity correction in MRI: existing methods and their validation

Magnetic resonance imaging is a popular and powerful non-invasive imaging technique. Automated analysis has become mandatory to efficiently cope with the large amount of data generated using this modality. However, several artifacts, such as intensity non-uniformity, can degrade the quality of acquired data. Intensity non-uniformity consists in anatomically irrelevant intensity variation throughout data. It can be induced by the choice of the radio-frequency coil, the acquisition pulse sequence and by the nature and geometry of the sample itself. Numerous methods have been proposed to correct this artifact. In this paper, we propose an overview of existing methods. We first sort them according to their location in the acquisition/processing pipeline. Sorting is then refined based on the assumptions those methods rely on. Next, we present the validation protocols used to evaluate these different correction schemes both from a qualitative and a quantitative point of view. Finally, availability and usability of the presented methods is discussed.

Inhomogeneity correction for brain magnetic resonance images by rank leveling

OBJECTIVE

A postprocessing method of rank filtering inhomogeneity correction using nonlinear rank filtering of magnetic resonance imaging (MRI) scans is described. The method addresses some of the problems of homomorphic unsharp masking (HUM) using mean or median filtering.

METHODS

Maximum rank filtering was used to estimate the bias image, which was then smoothed and used to normalize the original image. The coefficient of variation within and between tissue classes before and after inhomogeneity correction was calculated in simulated brain phantom images and clinical T1-weighted MRI images. Comparison was made with mean filter-based and median filter-based HUM.

RESULTS

Maximum rank filtering reduced within and between class coefficients of variation. Performance of median filtering was inferior to that of mean filtering, and both were inferior to performance of maximum rank filtering.

CONCLUSION

The method is easy to implement and is effective against different bias types. It is less prone to edge effects than mean and median filtering.

A soft-segmentation visualization scheme for magnetic resonance images

Prevalent visualization tools exploit gray value distribution in images through modified histogram equalization and matching technique, referred to as the window width/window level-based method, to improve visibility and enhance diagnostic value. The window width/window level tool is extensively used in magnetic resonance (MR) images to highlight tissue boundaries during image interpretation. However, the identification of different regions and distinct boundaries between them based on gray-level distribution and displayed intensity levels is extremely difficult because of the large dynamic range of tissue intensities inherent in MR images. We propose a soft-segmentation visualization scheme to generate pixel partitions from the histogram of MR image data using a connectionist approach and then generate selective visual depictions of pixel partitions using pseudo color based on an appropriate fuzzy membership function. By applying the display scheme in clinical examples in this study, we could demonstrate additional overlapping regions between distinct tissue types in healthy and diseased areas (in the brain) that could help improve the tissue characterization ability of MR images.

Normalized mutual information based registration using k-means clustering and shading correction

In this paper the influence of intensity clustering and shading correction on mutual information based image registration is studied. Instead of the generally used equidistant re-binning, we use k-means clustering in order to achieve a more natural binning of the intensity distribution. Secondly, image inhomogeneities occurring notably in MR images can have adverse effects on the registration. We use a shading correction method in order to reduce these effects. The method is validated on clinical MR, CT and PET images, as well as synthetic MR images. It is shown that by employing clustering with inhomogeneity correction the number of misregistrations is reduced without loss of accuracy thus increasing robustness as compared to the standard non-inhomogeneity corrected and equidistant binning based registration.

Correction of bias field in MR images using singularity function analysis

A new approach for correcting bias field in magnetic resonance (MR) images is proposed using the mathematical model of singularity function analysis (SFA), which represents a discrete signal or its spectrum as a weighted sum of singularity functions. Through this model, an MR image's low spatial frequency components corrupted by a smoothly varying bias field are first removed, and then reconstructed from its higher spatial frequency components not polluted by bias field. The thus reconstructed image is then used to estimate bias field for final image correction. The approach does not rely on the assumption that anatomical information in MR images occurs at higher spatial frequencies than bias field. The performance of this approach is evaluated using both simulated and real clinical MR images.

Interplay between intensity standardization and inhomogeneity correction in MR image processing

Image intensity standardization is a postprocessing method designed for correcting acquisition-to-acquisition signal intensity variations (nonstandardness) inherent in magnetic resonance (MR) images. Inhomogeneity correction is a process used to suppress the low frequency background nonuniformities (inhomogeneities) of the image domain that exist in MR images. Both these procedures have important implications in MR image analysis. The effects of these postprocessing operations on improvement of image quality in isolation has been well documented. However, the combined effects of these two processes on MR images and how the processes influence each other have not been studied thus far. In this paper, we evaluate the effect of inhomogeneity correction followed by standardization and vice-versa on MR images in order to determine the best sequence to follow for enhancing image quality. We conducted experiments on several clinical and phantom data sets (nearly 4000 three-dimensional MR images were analyzed) corresponding to four different MRI protocols. Different levels of artificial nonstandardness, and different models and levels of artificial background inhomogeneity were used in these experiments. Our results indicate that improved standardization can be achieved by preceding it with inhomogeneity correction. There is no statistically significant difference in image quality obtained between the results of standardization followed by correction and that of correction followed by standardization from the perspective of inhomogeneity correction. The correction operation is found to bias the effect of standardization. We demonstrate this bias both qualitatively and quantitatively by using two different methods of inhomogeneity correction. We also show that this bias in standardization is independent of the specific inhomogeneity correction method used. The effect of this bias due to correction was also seen in magnetization transfer ratio (MTR) images, which are naturally endowed with the standardness property. Standardization, on the other hand, does not seem to influence the correction operation. It is also found that longer sequences of repeated correction and standardization operations do not considerably improve image quality. These results were found to hold for the clinical and the phantom data sets, for different MRI protocols, for different levels of artificial nonstandardness, for different models and levels of artificial inhomogeneity, for different correction methods, and for images that were endowed with inherent standardness as well as for those that were standardized by using the intensity standardization method. Overall, we conclude that inhomogeneity correction followed by intensity standardization is the best sequence to follow from the perspective of both image quality and computational efficiency.

Unified segmentation

A probabilistic framework is presented that enables image registration, tissue classification, and bias correction to be combined within the same generative model. A derivation of a log-likelihood objective function for the unified model is provided. The model is based on a mixture of Gaussians and is extended to incorporate a smooth intensity variation and nonlinear registration with tissue probability maps. A strategy for optimising the model parameters is described, along with the requisite partial derivatives of the objective function.

MRI intensity inhomogeneity correction by combining intensity and spatial information

We propose a novel fully automated method for retrospective correction of intensity inhomogeneity, which is an undesired phenomenon in many automatic image analysis tasks, especially if quantitative analysis is the final goal. Besides most commonly used intensity features, additional spatial image features are incorporated to improve inhomogeneity correction and to make it more dynamic, so that local intensity variations can be corrected more efficiently. The proposed method is a four-step iterative procedure in which a non-parametric inhomogeneity correction is conducted. First, the probability distribution of image intensities and corresponding second derivatives is obtained. Second, intensity correction forces, condensing the probability distribution along the intensity feature, are computed for each voxel. Third, the inhomogeneity correction field is estimated by regularization of all voxel forces, and fourth, the corresponding partial inhomogeneity correction is performed. The degree of inhomogeneity correction dynamics is determined by the size of regularization kernel. The method was qualitatively and quantitatively evaluated on simulated and real MR brain images. The obtained results show that the proposed method does not corrupt inhomogeneity-free images and successfully corrects intensity inhomogeneity artefacts even if these are more dynamic.

Method for bias field correction of brain T1-weighted magnetic resonance images minimizing segmentation error

This work presents a new algorithm (nonuniform intensity correction; NIC) for correction of intensity inhomogeneities in T1-weighted magnetic resonance (MR) images. The bias field and a bias-free image are obtained through an iterative process that uses brain tissue segmentation. The algorithm was validated by means of realistic phantom images and a set of 24 real images. The first evaluation phase was based on a public domain phantom dataset, used previously to assess bias field correction algorithms. NIC performed similar to previously described methods in removing the bias field from phantom images, without introduction of degradation in the absence of intensity inhomogeneity. The real image dataset was used to compare the performance of this new algorithm to that of other widely used methods (N3, SPM'99, and SPM2). This dataset included both low and high bias field images from two different MR scanners of low (0.5 T) and medium (1.5 T) static fields. Using standard quality criteria for determining the goodness of the different methods, NIC achieved the best results, correcting the images of the real MR dataset, enabling its systematic use in images from both low and medium static field MR scanners. A limitation of our method is that it might fail if the bias field is so high that the initial histogram does not show bimodal distribution for white and gray matter.

Automated segmentation of human brain MR images using a multi-agent approach

Image interpretation consists in finding a correspondence between radiometric information and symbolic labeling with respect to specific spatial constraints. It is intrinsically a distributed process in terms of goals to be reached, zones in the image to be processed and methods to be applied. To cope the the difficulty inherent in this process, several information processing steps are required to gradually extract information. In this paper we advocate the use of situated cooperative agents as a framework for managing such steps. Dedicated agent behaviors are dynamically adapted depending on their position in the image, of their topographic relationships and of the radiometric information available. The information collected by the agents is gathered, shared via qualitative maps, or used as soon as available by acquaintances. Incremental refinement of interpretation is obtained through a coarse to fine strategy. Our work is essentially focused on radiometry-based tissue interpretation where knowledge is introduced or extracted at several levels to estimate models for tissue-intensity distribution and to cope with noise, intensity non-uniformity and partial volume effect. Several experiments on phantom and real images were performed. A complete volume can be segmented in less than 5 min with about 0.84% accuracy of the segmented reference. Comparison with other techniques demonstrates the potential interest of our approach for magnetic resonance imaging (MRI) brain scan interpretation.

Noise-adaptive nonlinear diffusion filtering of MR images with spatially varying noise levels

Anisotropic diffusion filtering is widely used for MR image enhancement. However, the anisotropic filter is nonoptimal for MR images with spatially varying noise levels, such as images reconstructed from sensitivity-encoded data and intensity inhomogeneity-corrected images. In this work, a new method for filtering MR images with spatially varying noise levels is presented. In the new method, a priori information regarding the image noise level spatial distribution is utilized for the local adjustment of the anisotropic diffusion filter. Our new method was validated and compared with the standard filter on simulated and real MRI data. The noise-adaptive method was demonstrated to outperform the standard anisotropic diffusion filter in both image error reduction and image signal-to-noise ratio (SNR) improvement. The method was also applied to inhomogeneity-corrected and sensitivity encoding (SENSE) images. The new filter was shown to improve segmentation of MR brain images with spatially varying noise levels.

3-D/2-D registration of CT and MR to X-ray images

A crucial part of image-guided therapy is registration of preoperative and intraoperative images, by which the precise position and orientation of the patient's anatomy is determined in three dimensions. This paper presents a novel approach to register three-dimensional (3-D) computed tomography (CT) or magnetic resonance (MR) images to one or more two-dimensional (2-D) X-ray images. The registration is based solely on the information present in 2-D and 3-D images. It does not require fiducial markers, intraoperative X-ray image segmentation, or timely construction of digitally reconstructed radiographs. The originality of the approach is in using normals to bone surfaces, preoperatively defined in 3-D MR or CT data, and gradients of intraoperative X-ray images at locations defined by the X-ray source and 3-D surface points. The registration is concerned with finding the rigid transformation of a CT or MR volume, which provides the best match between surface normals and back projected gradients, considering their amplitudes and orientations. We have thoroughly validated our registration method by using MR, CT, and X-ray images of a cadaveric lumbar spine phantom for which "gold standard" registration was established by means of fiducial markers, and its accuracy assessed by target registration error. Volumes of interest, containing single vertebrae L1-L5, were registered to different pairs of X-ray images from different starting positions, chosen randomly and uniformly around the "gold standard" position. CT/X-ray (MR/ X-ray) registration, which is fast, was successful in more than 91% (82% except for L1) of trials if started from the "gold standard" translated or rotated for less than 6 mm or 17 degrees (3 mm or 8.6 degrees), respectively. Root-mean-square target registration errors were below 0.5 mm for the CT to X-ray registration and below 1.4 mm for MR to X-ray registration.