The goal of this paper is to increase the statistical power of crossing-fiber statistics in voxelwise analyses of diffusion-weighted magnetic resonance imaging (DW-MRI) data. In the proposed framework, a fiber orientation atlas and a model complexity atlas were used to fit the ball-and-sticks model to diffusion-weighted images of subjects in a prospective population-based cohort study. Reproducibility and sensitivity of the partial volume fractions in the ball-and-sticks model were analyzed using TBSS (tract-based spatial statistics) and compared to a reference framework. The reproducibility was investigated on two scans of 30 subjects acquired with an interval of approximately three weeks by studying the intraclass correlation coefficient (ICC). The sensitivity to true biological effects was evaluated by studying the regression with age on 500 subjects from 65 to 90 years old. Compared to the reference framework, the ICC improved significantly when using the proposed framework. Higher t-statistics indicated that regression coefficients with age could be determined more precisely with the proposed framework and more voxels correlated significantly with age. The application of a fiber orientation atlas and a model complexity atlas can significantly improve the reproducibility and sensitivity of crossing-fiber statistics in TBSS.

Quantitative MRI methods that estimate multiple physical parameters simultaneously often require the fitting of a computational complex signal model defined through the Bloch equations. Repeated Bloch simulations can be avoided by matching the measured signal with a precomputed signal dictionary on a discrete parameter grid (i.e. lookup table) as used in MR Fingerprinting. However, accurate estimation requires discretizing each parameter with a high resolution and consequently high computational and memory costs for dictionary generation, storage, and matching. Here, we reduce the required parameter resolution by approximating the signal between grid points through B-spline interpolation. The interpolant and its gradient are evaluated efficiently which enables a least-squares fitting method for parameter mapping. The resolution of each parameter was minimized while obtaining a user-specified interpolation accuracy. The method was evaluated by phantom and in-vivo experiments using fully-sampled and undersampled unbalanced (FISP) MR fingerprinting acquisitions. Bloch simulations incorporated relaxation effects (T1, T2), proton density (PD), receiver phase (φ0), transmit field inhomogeneity (B1+), and slice profile. Parameter maps were compared with those obtained from dictionary matching, where the parameter resolution was chosen to obtain similar signal (interpolation) accuracy. For both the phantom and the in-vivo acquisition, the proposed method approximated the parameter maps obtained through dictionary matching while reducing the parameter resolution in each dimension (T1, T2, B1+) by - on average - an order of magnitude. In effect, the applied dictionary was reduced from 1.47GB to 464KB. Furthermore, the proposed method was equally robust against undersampling artifacts as dictionary matching. Dictionary fitting with B-spline interpolation reduces the computational and memory costs of dictionary-based methods and is therefore a promising method for multi-parametric mapping.

Corneal endothelium images obtained by in vivo specular microscopy provide important information to assess the health status of the cornea. Estimation of clinical parameters, such as cell density, polymegethism, and pleomorphism, requires accurate cell segmentation. State-of-the-art techniques to automatically segment the endothelium are error-prone when applied to images with low contrast and/or large variation in cell size. Here, we propose an automatic method to segment the endothelium. Starting with an oversegmented image comprised of superpixels obtained from a stochastic watershed segmentation, the proposed method uses intensity and shape information of the superpixels to identify and merge those that constitute a cell, using support vector machines. We evaluated the automatic segmentation on a data set of in vivo specular microscopy images (Topcon SP-1P), obtaining 95.8% correctly merged cells and 2.0% undersegmented cells. We also evaluated the parameter estimation against the results of the vendor's built-in software, obtaining a statistically significant better precision in all parameters and a similar or better accuracy. The parameter estimation was also evaluated on three other data sets from different imaging modalities (confocal microscopy, phase-contrast microscopy, and fluorescence confocal microscopy) and tissue types (ex vivo corneal endothelium and retinal pigment epithelium). In comparison with the estimates of the data sets' authors, we achieved statistically significant better accuracy and precision in all parameters except pleomorphism, where a similar accuracy and precision were obtained.

Accurate quantification of retinal structures in 3-D optical coherence tomography data of eyes with pathologies provides clinically relevant information. We present an approach to jointly segment retinal layers and lesions in eyes with topology-disrupting retinal diseases by a loosely coupled level set framework. In the new approach, lesions are modeled as an additional space-variant layer delineated by auxiliary interfaces. Furthermore, the segmentation of interfaces is steered by local differences in the signal between adjacent retinal layers, thereby allowing the approach to handle local intensity variations. The accuracy of the proposed method of both layer and lesion segmentation has been evaluated on eyes affected by central serous retinopathy and age-related macular degeneration. In addition, layer segmentation of the proposed approach was evaluated on eyes without topology-disrupting retinal diseases. Good agreement between the segmentation performed manually by a medical doctor and results obtained from the automatic segmentation was found for all data types. The mean unsigned error for all interfaces varied between 2.3 and 11.9 μm (0.6-3.1 pixels). Furthermore, lesion segmentation showed a Dice coefficient of 0.68 for drusen and 0.89 for fluid pockets. Overall, the method provides a flexible and accurate solution to jointly segment lesions and retinal layers.

Extraction of image-based biomarkers, such as the presence, visibility, or thickness of a certain layer, from 3-D optical coherence tomography data provides relevant clinical information. We present a method to simultaneously determine the number of visible layers in the outer retina and segment them. The method is based on a model selection approach with special attention given to the balance between the quality of a fit and model complexity. This will ensure that a more complex model is selected only if this is sufficiently supported by the data. The performance of the method was evaluated on healthy and retinitis pigmentosa (RP) affected eyes. In addition, the reproducibility of automatic method and manual annotations was evaluated on healthy eyes. Good agreement between the segmentation performed manually by a medical doctor and results obtained from the automatic segmentation was found. The mean unsigned deviation for all outer retinal layers in healthy and RP affected eyes varied between 2.6 and 4.9 μm. The reproducibility of the automatic method was similar to the reproducibility of the manual segmentation. Overall, the method provides a flexible and accurate solution for determining the visibility and location of outer retinal layers and could be used as an aid for the disease diagnosis and monitoring.

Registration of images in the presence of intra-image signal fluctuations is a challenging task. The definition of an appropriate objective function measuring the similarity between the images is crucial for accurate registration. This paper introduces an objective function that embeds local phase features derived from the monogenic signal in the modality independent neighborhood descriptor (MIND). The image similarity relies on the autocorrelation of local structure (ALOST) which has two important properties: 1) low sensitivity to space-variant intensity distortions (e.g., differences in contrast enhancement in MRI); 2) high distinctiveness for 'salient' image features such as edges. The ALOST method is quantitatively compared to the MIND approach based on three different datasets: thoracic CT images, synthetic and real abdominal MR images. The proposed method outperformed the NMI and MIND similarity measures on these three datasets. The registration of dynamic contrast enhanced and post-contrast MR images of patients with Crohn's disease led to relative contrast enhancement measures with the highest correlation (r=0.56) to the Crohn's disease endoscopic index of severity.

Direct imaging of ligament damage in the wrist remains a challenge. Still, such damage can be assessed indirectly through the analysis of changes in wrist pose and motion pattern. For this purpose we built a statistical reference model that describes healthy motion patterns. We show that such a model can also be used to detect and quantify pathologies. A model that only describes the global translations and rotations of the carpal bones is insufficiently accurate due to size and shape variations of the bones. We present a local statistical motion model that minimizes the influence of size and shape differences by analyzing the coordinate differences of pairs of points on adjacent bone surfaces. These differences are determined in a set of 14 healthy example wrists imaged in a range of poses by means of 4D-RX imaging. The distribution of the differences as a function of the pose form the local statistical motion model (LSMM). Translations of 2 mm and rotations of 20° with respect to the healthy example wrists are detected as outliers in the point pair distributions. An evaluation involving wrists with a damaged ligament between scaphoid and lunate shows that not only joint space widenings can be detected, but also shifts of congruent bone surfaces. The LSMM is also used to perform a virtual reconstruction of the most likely healthy wrist after a simulated perturbation of bones. The reconstruction precision is shown to be about 1 mm. Therefore, the presented 4D statistical model of wrist bone movement may become a valuable clinical tool for diagnosis and surgical planning.

Diffusion Tensor MRI (DTI) is a rather recent image acquisition modality that can help identify disease processes in nerve bundles in the brain. Due to the large and complex nature of such data, its analysis requires new and sophisticated pipelines that are more efficiently executed within a grid environment. We present our progress over the past four years in the development and porting of the DTI analysis pipeline to grids. Starting with simple jobs submitted from the command-line, we moved towards a workflow-based implementation and finally into a web service that can be accessed via web browsers by end-users. The analysis algorithms evolved from basic to state-of-the-art, currently enabling the automatic calculation of a population-specific `atlas' where even complex brain regions are described in an anatomically correct way. Performance statistics show a clear improvement over the years, representing a mutual benefit from both a technology push and application pull.

Multiframe super-resolution (SR) reconstruction of small moving objects against a cluttered background is difficult for two reasons: a small object consists completely of “mixed” boundary pixels and the background contribution changes from frame-to-frame. We present a solution to this problem that greatly improves recognition of small moving objects under the assumption of a simple linear motion model in the real-world. The presented method not only explicitly models the image acquisition system, but also the space-time variant fore- and background contributions to the “mixed” pixels. The latter is due to a changing local background as a result of the apparent motion. The method simultaneously estimates a subpixel precise polygon boundary as well as a high-resolution (HR) intensity description of a small moving object subject to a modified total variation constraint. Experiments on simulated and real-world data show excellent performance of the proposed multiframe SR reconstruction method.

There is an ongoing debate on how to model diffusivity in fiber crossings. We propose an optimization framework for the selection of a dual tensor model and the set of diffusion weighting parameters b, such that both the diffusion shape and orientation parameters can be precisely as well as accurately estimated. For that, we have adopted the Cramér-Rao lower bound (CRLB) on the variance of the model parameters, and performed Monte Carlo simulations. We have found that the axial diffusion lambda(parallel) needs to be constrained, while an isotropic fraction can be modeled by a single parameter f(iso). Under these circumstances, the Fractional Anisotropy (FA) of both tensors can theoretically be independently estimated with a precision of 9% (at SNR = 25). Levenberg-Marquardt optimization of the Maximum Likelihood function with a Rician noise model approached this precision while the bias was insignificant. A two-element b-vector b = [1.0 3.5] x 10(3) mm(-2)s was found to be sufficient for estimating parameters of heterogeneous tissue with low error. This has allowed us to estimate consistent FA-profiles along crossing tracts. This work defines fundamental limits for comparative studies to correctly analyze crossing white matter structures.

We present a computer-aided detection (CAD) system for computed tomography colonography that orders the polyps according to clinical relevance. The CAD system consists of two steps: candidate detection and supervised classification. The characteristics of the detection step lead to specific choices for the classification system. The candidates are ordered by a linear logistic classifier (logistic regression) based on only three features: the protrusion of the colon wall, the mean internal intensity, and a feature to discard detections on the rectal enema tube. This classifier can cope with a small number of polyps available for training, a large imbalance between polyps and non-polyp candidates, a truncated feature space, unbalanced and unknown misclassification costs, and an exponential distribution with respect to candidate size in feature space. Our CAD system was evaluated with data sets from four different medical centers. For polyps larger than or equal to 6 mm we achieved sensitivities of respectively 95%, 85%, 85%, and 100% with 5, 4, 5, and 6 false positives per scan over 86, 48, 141, and 32 patients. A cross-center evaluation in which the system is trained and tested with data from different sources showed that the trained CAD system generalizes to data from different medical centers and with different patient preparations. This is essential to application in large-scale screening for colorectal polyps.

Today's computer aided detection systems for computed tomography colonography (CTC) enable automated detection and segmentation of colorectal polyps. We present a paradigm shift by proposing a method that measures the amount of protrudedness of a candidate object in a scale adaptive fashion. One of the main results is that the performance of the candidate detection depends only on one parameter, the amount of protrusion. Additionally the method yields correct polyp segmentation without the need of an additional segmentation step. The supervised pattern recognition involves a clear distinction between size related features and features related to shape or intensity. A Mahalanobis transformation of the latter facilitates ranking of the objects using a logistic classifier. We evaluate two implementations of the method on 84 patients with a total of 57 polyps larger than or equal to 6 mm. We obtained a performance of 95% sensitivity at four false positives per scan for polyps larger than or equal to 6 mm.

Comparing wrist shapes of different individuals requires alignment of these wrists into the same pose. Unconstrained registration of the carpal bones results in anatomically nonfeasible wrists. In this paper, we propose to constrain the registration using the shapes of adjacent bones, by keeping the width of the gap between adjacent bones constant. The registration is formulated as an optimization involving two terms. One term aligns the wrist bones by minimizing the distances between corresponding bone surfaces. The second term constrains the registration by minimizing the distances between adjacent sliding surfaces. The registration is based on the Iterative Closest Point algorithm. All bones are registered concurrently so that no bias is introduced towards any of the bones. The proposed registration method delivers anatomically correct configurations of the bones. The registration errors are in the order of the voxel size of the acquired CT data (0.3 x 0.3 x 0.3 mm(3)). The standard deviation in the widths of gaps between adjacent bones is in the order of 10% with an insignificant bias. This is a large improvement over the standard deviations of 30%-80% encountered in unconstrained registration. The value of this method is its capability of accurately registering joints in varying poses resulting in physiological joint configurations.

Moving objects are often the most interesting parts in image sequences. When images from a camera are undersampled and the moving object is depicted small on the image plane, processing afterwards may help to improve the visibility as well as automatic recognition of the object. This paper presents an approach which performs Super-Resolution (SR) specifically on small moving objects. The presented approach estimates simultaneously a sub-pixel accurate boundary and an intensity description of the small moving object. This approach has the advantage that it permits explicit modeling of the partial volume effect for pixels which are influenced by both the moving object and the background of the scene. This paper describes the setup of the proposed SR algorithm for small moving objects and shows its superior performance in comparison with a standard SR approach.

CT colonography (CTC) is a rapidly evolving technique to screen for colorectal polyps. Fecal residue may occlude or, reversely, mimic polyps. Electronic cleansing aims at removing contrast-enhanced fecal residue from the image. However, thin layers of soft tissue (the colon wall or a fold) or residue are easily misclassified by current electronic cleansing methods, thereby causing holes in the colon wall or other artefacts that hamper visualization and automated detection. We present a thin layer model to detect and characterize such layers to support electronic cleansing. It is demonstrated that the model sustains robust estimation of the location and thickness of such a layer. Such thicknesses of thin layers were measured in real data sets. A lower bound on the thickness of such layers exists and was found to be 1.0 mm for our data.

A fully automated method is presented to classify 3-D CT data into material fractions. An analytical scale-invariant description relating the data value to derivatives around Gaussian blurred step edges--arch model--is applied to uniquely combine robustness to noise, global signal fluctuations, anisotropic scale, noncubic voxels, and ease of use via a straightforward segmentation of 3-D CT images through material fractions. Projection of noisy data value and derivatives onto the arch yields a robust alternative to the standard computed Gaussian derivatives. This results in a superior precision of the method. The arch-model parameters are derived from a small, but over-determined, set of measurements (data values and derivatives) along a path following the gradient uphill and downhill starting at an edge voxel. The model is first used to identify the expected values of the two pure materials (named L and H) and thereby classify the boundary. Second, the model is used to approximate the underlying noise-free material fractions for each noisy measurement. An iso-surface of constant material fraction accurately delineates the material boundary in the presence of noise and global signal fluctuations. This approach enables straightforward segmentation of 3-D CT images into objects of interest for computer-aided diagnosis and offers an easy tool for the design of otherwise complicated transfer functions in high-quality visualizations. The method is applied to segment a tooth volume for visualization and digital cleansing for virtual colonoscopy.

Unlike most Super-Resolution (SR) methods described in literature, which perform only SR reconstruction on the background of an image scene, we propose a framework that performs SR reconstruction simultaneously on the background and on moving objects. After registration of the background, moving objects are detected and to each moving object registration is applied. The fusion and deblurring tasks of the framework are performed by the well-known method of Hardie. To evaluate the performance of the framework the Triangle Orientation Discrimination (TOD) method is used. The TOD method quantitatively measures the SR performance on the image background and on moving objects. From experiments it can be concluded that under proper conditions, the SR performance on moving objects is similar as the SR performance on the background.

The development of methods to detect slowly progressing diseases is often hampered by the time-consuming acquisition of a sufficiently large data set. In this paper, a method is presented to model the change in images acquired by scanning laser polarimetry, for the detection of glaucomatous progression. The model is based on image series of 23 healthy eyes and incorporates colored noise, incomplete cornea compensation and masking by the retinal blood vessels. Additionally, two methods for detecting progression, taking either one or two follow-up visits into account, are discussed and tested on these simulated images. Both methods are based on Student's t-tests, morphological operations and anisotropic filtering. The images simulated by the model are visually pleasing, show corresponding statistical properties to the real images and are used to optimize the detection methods. The results show that detecting progression based on two follow-up visits greatly improves the sensitivity without adversely affecting the specificity.

Bilateral filtering is an edge-preserving filtering technique that employs both geometric closeness and photometric similarity of neighboring pixels to construct its filter kernel. Multi-dimensional bilateral filtering is computationally expensive because the adaptive kernel has to be recomputed at every pixel. In this paper, we present a separable implementation of the bilateral filter. The separable implementation offers equivalent adaptive filtering capability at a fraction of execution time compared to the traditional filter. Because of this efficiency, the separable bilateral filter can be used for fast preprocessing of images and videos. Experiments show that better image quality and higher compression efficiency is achievable if the original video is preprocessed with the separable bilateral filter.

Conventional edge-detection methods suffer from the dislocation of curved surfaces due to the PSF. We propose a new method that uses the isophote curvature to circumvent this. It is accurate for objects with locally constant curvature, even for small objects (like blood vessels) and in the presence of noise.

When performing measurements in digitized images, the pixel pitch does not necessarily limit the attainable accuracy. Proper sampling of a band-limited continuous-domain image preserves all information present in the image prior to digitization. It is therefore (theoretically) possible to obtain measurements from the digitized image that are identical to measurements made in the continuous domain. Such measurements are sampling invariant, since they are independent of the chosen sampling grid. It is impossible to attain strict sampling invariance for filters in mathematical morphology due to their nonlinearity, but it is possible to approximate sampling invariance with arbitrary accuracy at the expense of additional computational cost. In this paper, we study morphological filters with line segments as structuring elements. We present a comparison of three known and three new methods to implement these filters. The method that yields a good compromise between accuracy and computational cost employs a (subpixel) skew to the image, followed by filtering along the grid axes using a discrete line segment, followed by an inverse skew. The staircase approximations to line segments under random orientations can be modeled by skewing a horizontal or vertical line segment. Rather than skewing the binary line segment we skew the image data, which substantially reduces quantization error. We proceed to determine the optimal number of orientations to use when measuring the length of line segments with unknown orientation.

In this paper, we present a novel method to estimate curvature of iso gray-level surfaces in gray-value images. Our method succeeds where standard isophote curvature estimation methods fail. There is neither a segmentation of the surface needed nor a parametric model assumed. Our estimator works on the orientation field of the surface. This orientation field and a description of local structure is obtained by the Gradient Structure Tensor. The estimated orientation field has discontinuities mod pi. It is mapped via the Knutsson mapping to a continuous representation. The principal curvatures of the surface, a coordinate invariant property, are computed in this mapped representation. From these curvatures, locally the bending energy is computed to describe the surface shape. An extensive evaluation shows that our curvature estimation is robust even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.

Local curvature represents an important shape parameter of space curves which are well described by differential geometry. We have developed an estimator for local curvature of space curves embedded in n-dimensional (n-D) grey-value images. There is neither a segmentation of the curve needed nor a parametric model assumed. Our estimator works on the orientation field of the space curve. This orientation field and a description of local structure is obtained by the gradient structure tensor. The orientation field has discontinuities; walking around a closed contour yields two such discontinuities in orientation. This field is mapped via the Knutsson mapping to a continuous representation; from a n-D vector to a symmetric n2-D tensor field. The curvature of a space curve, a coordinate invariant property, is computed in this tensor field representation. An extensive evaluation shows that our curvature estimation is unbiased even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.

In this paper we present a new method for estimating confidence and curvature of 3-D curvilinear structures. The gradient structure tensor (GST) models shift-invariance. The eigenstructure of the tensor allows estimation of local dimensionality, orientation, and the corresponding confidence value. Local rotational invariance, which occurs often in images, causes a lower confidence estimate. This underestimation can be corrected for by a parabolic deformation of the data, in such a way that it becomes translational invariant. We show that the optimal deformation can be found analytically and yields a local curvature estimate as a valuable by-product. We tested our new method on synthetic images and applied it to the detection of channels in 3-D seismic delta.

Curved oriented patterns are dominated by high frequencies and exhibit zero gradients on ridges and valleys. Existing curvature estimators fail here. The characterization of curved oriented patterns based on translation invariance lacks an estimation of local curvature and yields a biased curvature-dependent confidence measure. Using parameterized curvilinear models we measure the amount of local gradient energy along the model gradient as a function of model curvature. Minimizing the residual energy yields a closed-form solution for the local curvature estimate and the corresponding confidence measure. We show that simple curvilinear models are applicable in the analysis of a wide variety of curved oriented patterns.

Micromachined picoliter vials in silicon dioxide with a typical depth of 6.0 /spl mu/m are filled with a liquid sample. Epi-illuminated microscopic imaging during evaporation of the liquid shows dynamic fringe patterns. These fringe patterns are caused by interference between the direct part and the reflected part of an incident plane wave (reflected from the bottom of the vial). The optical path difference (OPD) between the direct and the reflected wave is proportional to the distance to the reflecting bottom of the vial. Evaporation decreases the OPD at the meniscus level and causes alternating constructive and destructive interference of the incident light resulting in an interferogram. Imaging of the space-varying OPD yields a fringe pattern in which the isophotes correspond to isoheight curves of the meniscus. When the bottom is flat, the interference pattern allows monitoring of the liquid meniscus as a function of time during evaporation. On the other hand, when there are objects on the bottom of the vial, the height of these objects are observed as phase jumps in the fringes proportional to their height. First, this paper presents the underlying optical model. Secondly, an image processing method is described to retrieve the meniscus profile from the interference pattern. This algorithm is based on estimating the wrapped (relative) phase of the fringe pattern in the recorded images. Finally, this algorithm is applied to measure height differences on the bottom in other micromachined vials with a precision of about five nanometer.

We present a recursive algorithm for the Gabor filter that achieves, to within a multiplicative constant, the fastest possible implementation. For a signal consisting of N samples, our implementation requires O(N) multiply-and-add operations. Further, the complexity is and coefficients of the recursive equation have a simple independent of the values of /spl sigma/ and /spl omega/ in the Gabor kernel closed-form solution given /spl sigma/ and /spl omega/. Our implementation admits not only a forward Gabor transform from t/spl rarr//spl omega/ but an inverse transform from /spl omega//spl rarr/t that is also O(N) complexity.

In this paper we describe a new stragegy for combining orientation adaptive filtering and edge preserving filtering. The filter adapts to the local orientation and avoids filtering across borders. The local orientation for steering the filter will be estimated in a fixed sized window which never contains two orientation fields. This can be achieved using generalized Kuwahara filtering. This filter selects from a set of fixed sized windows that contain the current pixel, the orientation of the window with the highest anisotropy. We compare out filter strategy with a multi-scale approach. We found that our filter strategy has a lower complexity and yields a constant improvement of the SNR.

The gradient-square tensor describes the orientation dependence of the squared directional derivative in images. The ratio of eigenvalues is a measure of local anisotropy. For an area showing shift invariance along some orientation (think of a piece of straight rail track) one of the tensor eigenvalues is zero. In practical situations (think of a piece of curved rail track) rotation invariance (perhaps around a remote center) occurs more often than shift invariance. Then curvature contributes to the smallest eigenvalue. In order to avoid this we deform a local area in such a way that the rotational symmetry becomes a translational one. Next the gradient square tensor defined on the transformed area, is expressed in derivatives of the original area. A curvature corrected anisotropy measure is defined. The correction turns out to be simple and straightforward. An average-curvature estimate for the area results as a valuable by product.

We propose a strategy to design recursive implementations of the Gaussian filter and Gaussian regularized derivative filters. Each recursive filter consists of a cascade of two stable Nth-order subsystems (causal and anti-causal). The computational complexity is 2N multiplications per pixel per dimension independent of the size (/spl sigma/) of the Gaussian kernel. The filter coefficients have a closed-form solution as a function of scale (/spl sigma/) and recursion order N (N=3, 4, 5). The recursive filters yield a high accuracy and excellent isotropy in n-D space.

We have developed a completely automated fluorescence microscope system that can examine 500 cells in approximately 20 minutes to determine the number of labeled chromosomes (seen as dots) in each cell nucleus. This system works with two fluorescent dyes-one for the DNA hybridization dots (e.g. FITC) and one for the cell nucleus (e.g. DAPI). After the stage has moved to a new field the image is automatically focused, acquired by a Photometrics KAF 1400 camera, and then analyzed on a Macintosh Quadra 840AV computer. After the required number of cells has been analyzed, the user may interact to correct the computer by working with a gallery of the cell images. The machine accuracies are equal to panels of human experts (manual) and limited by the overlapping of dots in the 3D cell as seen through the 2D projection.

The authors study the location error of curved edges in two- and three-dimensional images after analog and digital low-pass filtering. The zero crossing of a second derivative filter is a well-known edge localization criterion. The second derivative in gradient direction (SDGD) produces a predictable bias in edge location towards the centers of curvature while the linear Laplace filter produces a shift in the opposite direction. Their sum called PLUS (PLUS=Laplace+SDGD) leads to an edge detector that finds curved edges one order more accurately than its constituents. This argument holds irrespective of the dimension. The influence of commonly used low-pass filters (such as the PSF originating from diffraction limited optics using incoherent light (2-D), the Gaussian filter with variable cutoff point (D-D), and the isotropic uniform filter (D-D)) is studied.>

A metric defines the distance between any two points. The “natural” metrics of the digital world do not approximate the Euclidean metric of the continuous world well. Skeletonization (sometimes named topology preserving shrinking or homotopic thinning) is one example in which this leads to unacceptable results. In the present work we propose and demonstrate skeletonization using path-based metrics which are a better approximation of the Euclidean metric. Moreover, we achieve a good performance on sequential processors by processing each pixel only once in the calculations of binary (Hilditch) and grey-value (upper) skeletons.

Existing estimators for edge length in 2D and surface area in 3D are applied to a binary representation of the object. The authors estimate length and area through volume measurements. Volume is measured without thresholding and does not introduce a sampling error. Edges are transformed into volumes by giving them a constant height after which they can be shifted perpendicular to the edge over a small distance. Subtraction of two images shifted in opposite direction produces a volume that is proportional to the edge length. To guarantee a constant edge height along the edge or across the surface to be measured the authors apply a 'soft' clipping operation to the linear region of the edge. For accurate and isotropic displacement of edges the authors introduce a continuous space equivalent to the discrete local minimum and maximum filters. These filters are sampling invariant and allow shifts in the subpixel region.>

Sequential (search) methods for edge and line detection and parallel (filter) methods for edge detection are well-known. Filter methods for line detection are generally based on direction-by-direction filtering: each filter is parallel, but only special hardware architectures allow filtering in different directions simultaneously. The authors present a class of isotropic edge and line detection filters that work in arbitrary dimension: symmetry filters. The principle of the method is correlation of the filter window content with a mapped version. The mapping may be point inversion, blow or rotation, all relative to the window center. Covariance is used as correlation measure. In the paper only point inversion is considered. Moreover, the filter may contain weighting coefficients e.g. to emphasize contributions from the central part. For point inversion, lines give a positive correlation and edges a negative correlation (twofold symmetry and antisymmetry).>