Steerable filter pairs that are near quadrature have many image processing applications. This paper proposes a new methodology for designing such filters. The key idea is to design steerable filters by minimizing a departure-from-quadrature function. These minimizing filter pairs are almost exactly in quadrature. The polar part of the filters is nonnegative, monotonic, and highly focused around an axis, and asymptotically the filters achieve exact quadrature. These results are established by exploiting a relation between the filters and generalized Hilbert matrices. These near-quadrature filters closely approximate three dimensional Gabor filters. We experimentally verify the asymptotic mathematical results and further demonstrate the use of these filter pairs by efficient calculation of local Fourier shell correlation of cryogenic electron microscopy.

Clinical scores (disease rating scales) are ordinal in nature. Longitudinal studies which use clinical scores produce ordinal time series. These time series tend to be noisy and often have a short-duration. This paper proposes a denoising method for such time series. The method uses a hierarchical approach to draw statistical power from the entire population of a study's patients to give reliable, subject-specific results. The denoising method is applied to MDS-UPDRS motor scores for Parkinson's disease.

Classifying SPECT images requires a preprocessing step which normalizes the images using a normalization region. The choice of the normalization region is not standard, and using different normalization regions introduces normalization region-dependent variability. This paper mathematically analyzes the effect of the normalization region to show that normalized-classification is exactly equivalent to a subspace separation of the half rays of the images under multiplicative equivalence. Using this geometry, a new self-normalized classification strategy is proposed. This strategy eliminates the normalizing region altogether. The theory is used to classify DaTscan images of 365 Parkinson's disease (PD) subjects and 208 healthy control (HC) subjects from the Parkinson's Progression Marker Initiative (PPMI). The theory is also used to understand PD progression from baseline to year 4.

The Hamilton Depression Rating Scale provides ordinal ratings for evaluating different aspects of depression. These ratings are usually quite noisy, and longitudinal patterns in the ratings can be difficult to discern. This paper proposes a hierarchical maximum-a-posteriori (MAP) method for denoising the ordinal time series of such ratings. Real-world data from a clinical trial are analyzed using the model. Denoising reveals subject-specific longitudinal patterns, predicts future ratings, and reveals progression patterns via principal component analysis.

This paper proposes a mixture of linear dynamical systems model for quantifying the heterogeneous progress of Parkinson's disease from DaTscan Images. The model is fitted to longitudinal DaTscans from the Parkinson's Progression Marker Initiative. Fitting is accomplished using robust Bayesian inference with collapsed Gibbs sampling. Bayesian inference reveals three image-based progression subtypes which differ in progression speeds as well as progression trajectories. The model reveals characteristic spatial progression patterns in the brain, each pattern associated with a time constant. These patterns can serve as disease progression markers. The subtypes also have different progression rates of clinical symptoms measured by MDS-UPDRS Part III scores.

A critical step in cryogenic electron microscopy (cryo-EM) image analysis is to calculate the average of all images aligned to a projection direction. This average, called the class mean, improves the signal-to-noise ratio in single-particle reconstruction. The averaging step is often compromised because of the outlier images of ice, contaminants, and particle fragments. Outlier detection and rejection in the majority of current cryo-EM methods are done using cross-correlation with a manually determined threshold. Empirical assessment shows that the performance of these methods is very sensitive to the threshold. This paper proposes an alternative: a w-estimator of the average image, which is robust to outliers and which does not use a threshold. Various properties of the estimator, such as consistency and influence function are investigated. An extension of the estimator to images with different contrast transfer functions is also provided. Experiments with simulated and real cryo-EM images show that the proposed estimator performs quite well in the presence of outliers.

This paper proposes a deterministic explanation for mutual-information-based image registration (MI registration). The explanation is that MI registration works because it aligns certain image partitions. This notion of aligning partitions is new, and is shown to be related to Schur- and quasi-convexity. The partition-alignment theory of this paper goes beyond explaining mutual- information. It suggests other objective functions for registering images. Some of these newer objective functions are not entropy-based. Simulations with noisy images show that the newer objective functions work well for registration, lending support to the theory. The theory proposed in this paper opens a number of directions for further research in image registration. These directions are also discussed.

Intensity nonuniformity in magnetic resonance (MR) images, represented by a smooth and slowly varying function, is a typical artifact that is a nuisance for many image processing methods. To eliminate the artifact, we have to estimate the nonuniformity as a smooth and slowly varying function and factor it out from the given data. We reformulate the problem as a problem of finding a unique smooth function in a particular set of piecewise smooth functions and propose a variational method for finding it. We deliver the main idea using a simple one-dimensional example first and provide a thorough analysis of the problem in a three-phase scenario in three dimensions whose application can be found in the brain MR images. Experiments with synthetic and real MR images and a comparison with a state-of-the-art method, N3, show our algorithm's satisfactory performance in estimating the nonuniformity with and without noise. An automated procedure is also proposed for practical use.

Segmenting cardiac ultrasound images requires a model for the statistics of speckle in the images. Although the statistics of speckle are well understood for the raw transducer signal, the statistics of speckle in the image are not. This paper evaluates simple empirical models for first-order statistics for the distribution of gray levels in speckle. The models are created by analyzing over 100 images obtained from commercial ultrasound machines in clinical settings. The data in the images suggests a unimodal scalable family of distributions as a plausible model. Four families of distributions (Gamma, Weibull, Normal, and Log-normal) are compared with the data using goodness-of-fit and misclassification tests. Attention is devoted to the analysis of artifacts in images and to the choice of goodness-of-fit and misclassification tests. The distribution of parameters of one of the models is investigated and priors for the distribution are suggested.

NHANES II is a nationally significant medical image database of spine x-ray images located at the National Library of Medicine. A key feature of spine disease in these images is the presence of osteoytes which are bony processes that alter the shape of vertebrae. Shapes of vertebrae are conveniently described in shape spaces which are non-linear manifolds. Indexing in such non-linear manifolds is an open problem. In this paper, we describe a technique of embedding shape manifolds in Euclidean spaces in a way that allows the use of classical indexing techniques for indexing shape. Application of this to the NHANES II database is also described.

In this note we present a coupled optimization model for boundary determination. One part of the model incorporates a prior shape into a geometric active contour model with a fixed parameter. The second part determines the 'best' parameter used in the first part by maximizing the mutual information of the image geometry between the prior and an aligned novel image over all the alignments that are the solutions of the first part corresponding to different parameters. We also present an alternative method, which generates an intensity model formed as the average of a set of aligned training images. Experimental results on cardiac ultrasound images are presented. These results indicate that the proposed model provides close agreement with expert traced borders, and the parameter determined in this model for one image can be used for images with similar properties. The existence of a solution to the proposed minimization problem is also discussed.

A precise analysis of an entire image is computationally wasteful if one is interested in finding a target object located in a subregion of the image. A useful "attention strategy" can reduce the overall computation by carrying out fast but approximate image measurements and using their results to suggest a promising subregion. The paper proposes a maximum-likelihood attention mechanism that does this. The attention mechanism recognizes that objects are made of parts and that parts have different features. It works by proposing object part and image feature pairings which have the highest likelihood of coming from the target. The exact calculation of the likelihood as well as approximations are provided. The attention mechanism is adaptive, that is, its behavior adapts to the statistics of the image features. Experimental results suggest that, on average, the attention mechanism evaluates less than 2 percent of all part-feature pairs before selecting the actual object, showing a significant reduction in the complexity of visual search.

We present a new theoretical result for the problem of surface reconstruction from stereo images. For a given initial seed point, i.e. for a pair of corresponding points in the left and right image, the proposed algorithm grows the surface without directly computing the point correspondences. The method assumes the Lambertian surface reflectance model. Our approach is based on a surface normal calculation from the left and right image gradients. Knowing the surface normal, the algorithm grows the surface in the directions defined by the tangent plane. The algorithm is independent of the camera model, and requires placement of an initial seed point for each surface to be reconstructed. Technical problems associated with errors in the image gradient estimates and camera calibration are discussed and a solution is suggested. In addition to this algorithm, we present a theoretical result that permits one to track surfaces deforming in time, which is often encountered in medical applications (e.g. brain surface deforms during the surgery). These methods of surface reconstruction and deformable surface tracking are applied to the particular problem of brain shift, commonly recognized as one of the main source of errors in surgical navigation systems used in neurosurgery. We also suggest a way to overcome problems associated with brain surface specularities caused by fluids on the brain surface and lights in the operating room. We conclude with experimental results on real brain images and show that the surface reconstruction algorithm is robust to the position of the initial seed point.

OBJECTIVE: Currently, when cytopathology images are archived, they are typically stored with a limited text-based description of their content. Such a description inherently fails to quantify the properties of an image and refers to an extremely small fraction of its information content. This paper describes a method for automatically indexing images of individual cells and their associated diagnoses by computationally derived cell descriptors. This methodology may serve to better index data contained in digital image databases, thereby enabling cytologists and pathologists to cross-reference cells of unknown etiology or nature. DESIGN: The indexing method, implemented in a program called PathMaster, uses a series of computer-based feature extraction routines. Descriptors of individual cell characteristics generated by these routines are employed as indexes of cell morphology, texture, color, and spatial orientation. MEASUREMENTS: The indexing fidelity of the program was tested after populating its database with images of 152 lymphocytes/lymphoma cells captured from lymph node touch preparations stained with hematoxylin and eosin. Images of "unknown" lymphoid cells, previously unprocessed, were then submitted for feature extraction and diagnostic cross-referencing analysis. RESULTS: PathMaster listed the correct diagnosis as its first differential in 94 percent of recognition trials. In the remaining 6 percent of trials, PathMaster listed the correct diagnosis within the first three "differentials." CONCLUSION: PathMaster is a pilot cell image indexing program/search engine that creates an indexed reference of images. Use of such a reference may provide assistance in the diagnostic/prognostic process by furnishing a prioritized list of possible identifications for a cell of uncertain etiology.

External energies of active contours are often formulated as Euclidean arc length integrals. In this paper, we show that such formulations are biased. By this we mean that the minimum of the external energy does not occur at an image edge. In addition, we also show that for certain forms of external energy the active contour is unstable--when initialized at the true edge, the contour drifts away and becomes jagged. Both of these phenomena are due to the use of Euclidean arc length integrals. We propose a non-Euclidean arc length which eliminates these problems. This requires a reformulation of active contours where a single external energy function is replaced by a sequence of energy functions and the contour evolves as an integral curve of the gradient of these energies. The resulting active contour not only has unbiased external energy, but is also more controllable. Experimental evidence is provided in support of the theoretical claims.

A common problem in many biomedical imaging studies is that of finding a correspondence between two plane curves which aligns their shapes. A mathematical formulation and solutions to this problem is proposed in this paper. The formulation exhibits desirable properties. It allows for one-to-one as well as non-one-to-one correspondences, it consistently compares shape, even in nonrigid situations, and it is completely symmetric with respect to the two curves. A numerical implementation of the algorithm for finding the optimal correspondence is also reported. The algorithm is used to estimate nonrigid motion of the endocardium in MRI image sequences of normal and post-infarct dog hearts. The return error (the difference between the starting and ending positions of a point) is used as a performance measure to evaluate the technique. Since heart motion is periodic, the return error is a measure of consistency of the algorithm. Preliminary applications to other data sets are reported as well.

The problem of place recognition is central to robot map learning. A robot needs to be able to recognize when it has returned to a previously visited place, or at least to be able to estimate the likelihood that it has been at a place before. Our approach is to compare images taken at two places, using a stochastic model of changes due to shift, zoom, and occlusion to predict the probability that one of them could be a perturbation of the other. We have performed experiments to gather the valve of a /spl chi//sup 2/ statistic applied to image matching from a variety of indoor locations. Image pairs gathered from nearby locations generate low /spl chi//sup 2/ values, and images gathered from different locations generate high values. The rate of false positive and false negative matches is low.

Information contained in medical images differs considerably from that residing in alphanumeric format. The difference can be attributed to four characteristics: (1) the semantics of medical knowledge extractable from images is imprecise; (2) image information contains form and spatial data, which are not expressible in conventional language; (3) a large part of image information is geometric; (4) diagnostic inferences derived from images rest on an incomplete, continuously evolving model of normality. This paper explores the differentiating characteristics of text versus images and their impact on design of a medical image database intended to allow content-based indexing and retrieval. One strategy for implementing medical image databases is presented, which employs object-oriented iconic queries, semantics by association with prototypes, and a generic schema.

In this paper a new formulation of the two-dimensional (2-D) deformable template matching problem is proposed. It uses a lower-dimensional search space than conventional methods by precomputing extensions of the deformable template along orthogonal curves. The reduction in search space allows the use of dynamic programming to obtain globally optimal solutions and reduces the sensitivity of the algorithm to initial placement of the template. Further, the technique guarantees that the result is a curve which does not collapse to a point in the absence of strong image gradients and is always nonself intersecting. Examples of the use of the technique on real-world images and in simulations at low signal-to-noise ratios (SNR's) are also provided.

A geometric criterion is developed for establishing shape based non rigid correspondence between plane curves. Unlike previous efforts, the criterion does not use rigid invariants of shape. Instead, shapes are compared non rigidly from the vantage point of the correspondence. Geometric invariants are proposed for curves whose shapes can be exactly matched by a non rigid correspondence. The invariants are based on angular deviations of convex and concave segments of the curves. Examples of correspondences between curves obtained from medical images are provided.>

Medical tomographic images are formed by the intersection of the image plane and an object. As the image plane changes, different parts of the object come in view or drop out of view. However, for small changes of the image plane, most parts continue to remain visible and their qualitative embedding in the image remains similar. Therefore, similarity of part embeddings can be used to infer similarity of image planes. Part embeddings are useful features for other vision applications as well. In view of this, a spatial relation called "arrangement" is proposed to describe part embeddings. The relation describes how each part is surrounded by its neighbors. Further, a metric for arrangements is formulated by expressing arrangements in terms of the Voronoi diagram of the parts. Arrangements and their metric are used to retrieve images by image plane similarity in a cardiac magnetic resonance image database. Experiments with the database are reported which (1) validate the observation that similarity of image planes can be inferred from similarity of part embeddings, and (2) compare the performance of arrangement based image retrieval with that of expert radiologists.>

CT images were obtained of the wrist region of 15 cadavers and several living patients. Boundaries of bones were located using a technique based on dynamic programming. The resulting set of surface points on each bone was used to compute principal and antipodal axes and distances between surfaces of the bones, and an interpolation technique was developed to increase the apparent resolution of the 3-D reconstruction. A spatial coordinate system was established based on internal landmarks in the carpal anatomy. The angular orientations of all carpal bones were determined with respect to this system. The principal axes for the same bone among the multiple wrist specimens proved to be more widely dispersed than the antipodal axes for the same bones. The antipodal axes also correspond more closely to an intuitive notion of the "longest axis" of the bones. A method was developed to interpolate surface points between the coarsely-distributed points located by our boundary tracker, and to interpolate data between CT slices, producing a uniformly spaced 3-D data set. The surface of this representation of the bone was used to determine the spacing between the bones in the wrist. The enhanced resolution of the interpolated data improves the resolution of the spacing determination, compared to determinations based only on the points actually located by the boundary tracker.>

A discussion of the step edge model and the zero crossings of edge detectors is provided to justify the authors' previous analysis (see ibid., vol. 12, p. 1186-1189) of the localization performance error. It is shown that the previous analysis is consistent with its assumptions. The exact solution to the zero crossing density of the edge detection filter is also provided.

A qualitative spatial relation called 'arrangement' is proposed. Given an image, the relation describes the sequence in which neighbors of each part are situated around it. The relation captures a perceptual gestalt of the image. An application of the relation to similarity retrieval in medical image databases is discussed. 'Arrangement' is closely related to directional relations and extends the notion of directional relations to parts that have complex shapes. A metric for comparing 'arrangements' is also proposed. The metric is obtained by interpreting 'arrangements' in terms of Voronoi diagrams. The metric enables robust use of the relation in real-world situations.>

A theory of photometric stereo is proposed for a large class of non-Lambertian reflectance maps. The authors review the different reflectance maps proposed in the literature for modeling reflection from real-world surfaces. From this, they obtain a mathematical class of reflectance maps to which the maps belong. They show that three lights can be sufficient for a unique inversion of the photometric stereo equation for the entire class of reflectance maps. They also obtain a constraint on the positions of light sources for obtaining this solution. They investigate the sufficiency of three light sources to estimate the surface normal and the illuminant strength. The issue of completeness of reconstruction is addressed. They show that if k lights are sufficient for a unique inversion, 2k lights are necessary for a complete inversion.>

The authors address the issue of whether the shape of an object and certain parameters of its reflectance map can be jointly estimated using photometric stereo. This problem has been addressed in the literature for the case where the Lambertian and non-Lambertian components in the image can be easily separated. The authors do not assume each separability. They highlight some aspects of the detailed solution to the above problem.>

The localization performance measure of edge detectors is addressed. A one-dimensional formulation of the problem is considered. A linear space-invariant filter is used for the detection. The locations of local maxima in the thresholded output of the filter are declared to be the edges. The limitations of conventional performance measures are shown, and a localization performance measure for edge detection is suggested. This performance measure is based on the theory of zero-crossings of stochastic processes. It is shown that the derivative of a Gaussian is the optimal edge detector for the measure.>

The authors present the main results of a theory of photometric stereo for non-Lambertian surfaces. First, they propose a class of reflectance maps that can be used for a realistic representation of real-world reflection. Second, they ask how many light sources are needed for inverting this class of reflectance maps. It is shown that three light sources are sufficient for a globally unique inversion for the entire class of reflectance maps. Finally, the authors address the issue of completeness of reconstruction. They show that if k lights are sufficient for a globally unique inversion, 2k lights are necessary for a complete inversion.>

As a generalization of the median and rank filters [1]-[3], the concept of an order filter as a useful signal and image processing tool is introduced. This filter obtains a best estimate of the signal based on its order statistics. The optimal design of such a filter is illustrated in the context of the problem of envelope estimation. Other applications are also briefly mentioned.