Jayaram K. Udupa

Fuzzy connectedness and object definition: theory, algorithms, and applications in image segmentation

Images are by nature fuzzy. Approaches to object information extraction from images should attempt to use this fact and retain fuzziness as realistically as possible. In past image segmentation research, the notion of “hanging togetherness” of image elements specified by their fuzzy connectedness has been lacking. We present a theory of fuzzy objects forn-dimensional digital spaces based on a notion of fuzzy connectedness of image elements. Although our definitions lead to problems of enormous combinatorial complexity, the theoretical results allow us to reduce this dramatically, leading us to practical algorithms for fuzzy object extraction. We present algorithms for extracting a specified fuzzy object and for identifying all fuzzy objects present in the image data. We demonstrate the utility of the theory and algorithms in image segmentation based on several practical examples all drawn from medical imaging.

Shape-based interpolation of multidimensional objects

A shape-based interpolation scheme for multidimensional images is presented. This scheme consists of first segmenting the given image data into a binary image, converting the binary image back into a gray image wherein the gray value of a point represents its shortest distance (positive value for points of the object and negative for those outside) from the cross-sectional boundary, and then interpolating the gray image. The set of all points with nonnegative values associated with them in the interpolated image constitutes the interpolated object. The method not only minimizes user involvement in interactive segmentation, but also leads to more accurate representation and depiction of dynamic as well as static objects. The general methodology and the implementation details of the method are presented and compared on a qualitative and quantitative basis to the existing methods. The generality of the proposed scheme is illustrated with a number of medical imaging examples.

New variants of a method of MRI scale standardization

One of the major drawbacks of magnetic resonance imaging (MRI) has been the lack of a standard and quantifiable interpretation of image intensities. Unlike in other modalities, such as X-ray computerized tomography, MR images taken for the same patient on the same scanner at different times may appear different from each other due to a variety of scanner-dependent variations and, therefore, the absolute intensity values do not have a fixed meaning. The authors have devised a two-step method wherein all images (independent of patients and the specific brand of the MR scanner used) can be transformed in such a may that for the same protocol and body region, in the transformed images similar intensities will have similar tissue meaning. Standardized images can be displayed with fixed windows without the need of per-case adjustment. More importantly, extraction of quantitative information about healthy organs or about abnormalities can be considerably simplified. This paper introduces and compares new variants of this standardizing method that can help to overcome some of the problems with the original method.

On standardizing the MR image intensity scale

The lack of a standard image intensity scale in MRI causes many difficulties in image display and analysis. A two‐step postprocessing method is proposed for standardizing the intensity scale in such a way that for the same MR protocol and body region, similar intensities will have similar tissue meaning. In the first step, the parameters of the standardizing transformation are “learned” from a set of images. In the second step, for each MR study these parameters are used to map their histogram into the standardized histogram. The method was tested quantitatively on 90 whole‐brain studies of multiple sclerosis patients for several protocols and qualitatively for several other protocols and body regions. Measurements using mean squared difference showed that the standardized image intensities have statistically significantly (P < 0.01) more consistent range and meaning than the originals. Fixed gray level windows can be established for the standardized images and used for display without the need of per case adjustment. Preliminary results also indicate that the method facilitates improving the degree of automation of image segmentation. Magn Reson Med 42:1072–1081, 1999.

Scale-based fuzzy connected image segmentation: theory, algorithms, and validation

This paper extends a previously reported theory and algorithms for object definition based on fuzzy connectedness. In this approach, a strength of connectedness is determined between every pair of image elements. This is done by considering all possible connecting paths between the two elements in each pair. The strength assigned to a particular path is defined as the weakest affinity between successive pairs of elements along the path. Affinity specifies the degree to which elements hang together locally in the image. Although the theory allowed any neighborhood size for affinity definition, it did not indicate how this was to be selected. By bringing object scale into the framework in this paper, not only the size of the neighborhood is specified but also it is allowed to change in different parts of the image. This paper argues that scale-based affinity, and hence connectedness, is natural in object definition and demonstrates that this leads to more effective object segmentation.The approach presented here considers affinity to consist of two components. The homogeneity-based component indicates the degree of affinity between image elements based on the homogeneity of their intensity properties. The object-feature-based component captures the degree of closeness of their intensity properties to some expected values of those properties for the object. A family of non-scale-based and scale-based affinity relations are constructed dictated by how we envisage the two components to characterize objects. A simple and effective method for giving a rough estimate of scale at different locations in the image is presented. The original theoretical and algorithmic framework remains more-or-less the same but considerably improved segmentations result. The method has been tested in several applications qualitatively. A quantitative statistical comparison between the non-scale-based and the scale-based methods was made based on 250 phantom images. These were generated from 10 patient MR brain studies by first segmenting the objects, then setting up appropriate intensity levels for the object and the background, and then by adding five different levels for each of noise and blurring and a fixed slow varying background component. Both the statistical and the subjective tests clearly indicate that the scale-based method is superior to the non-scale-based method in capturing details and in robustness to noise. It is also shown, based on these phantom images, that any (global) optimum threshold selection method will perform inferior to the fuzzy connectedness methods described in this paper.

Multiple sclerosis lesion quantification using fuzzy-connectedness principles

Multiple sclerosis (MS) is a disease of the white matter. Magnetic resonance imaging (MRI) is proven to be a sensitive method of monitoring the progression of this disease and of its changes due to treatment protocols. Quantification of the severity of the disease through estimation of MS lesion volume via MR imaging is vital for understanding and monitoring the disease and its treatment. This paper presents a novel methodology and a system that can be routinely used for segmenting and estimating the volume of MS lesions via dual-echo fast spin-echo MR imagery. A recently developed concept of fuzzy objects forms the basis of this methodology. An operator indicates a few points in the images by pointing to the white matter, the grey matter, and the cerebrospinal fluid (CSF). Each of these objects is then detected as a fuzzy connected set. The holes in the union of these objects correspond to potential lesion sites which are utilized to detect each potential lesion as a three-dimensional (3-D) fuzzy connected object. These objects are presented to the operator who indicates acceptance/rejection through the click of a mouse button. The number and volume of accepted lesions is then computed and output. Based on several evaluation studies, the authors conclude that the methodology is highly reliable and consistent, with a coefficient of variation (due to subjective operator actions) of 0.9% (based on 20 patient studies, three operators, and two trials) for volume and a mean false-negative volume fraction of 1.3%, with a 95% confidence interval of 0%-2.8% (based on ten patient studies).

An ultra-fast user-steered image segmentation paradigm: live wire on the fly

The authors have been developing general user steered image segmentation strategies for routine use in applications involving a large number of data sets. In the past, they have presented three segmentation paradigms: live wire, live lane, and a three-dimensional (3-D) extension of the live-wire method. Here, they introduce an ultra-fast live-wire method, referred to as live wire on the fly for further reducing users time compared to the basic live-wire method. In live wire, 3-D/four-dimensional (4-D) object boundaries are segmented in a slice-by-slice fashion. To segment a two-dimensional (2-D) boundary, the user initially picks a point on the boundary and all possible minimum-cost paths from this point to all other points in the image are computed via Dijkstras algorithm. Subsequently, a live wire is displayed in real time from the initial point to any subsequent position taken by the cursor. If the cursor is close to the desired boundary, the live wire snaps on to the boundary. The cursor is then deposited and a new live-wire segment is found next. The entire 2-D boundary is specified via a set of live-wire segments in this fashion. A drawback of this method is that the speed of optimal path computation depends on image size. On modestly powered computers, for images of even modest size, some sluggishness appears in user interaction, which reduces the overall segmentation efficiency. In this work, the authors solve this problem by exploiting some known properties of graphs to avoid unnecessary minimum-cost path computation during segmentation. In live wire on the fly, when the user selects a point on the boundary the live-wire segment is computed and displayed in real time from the selected point to any subsequent position of the cursor in the image, even for large images and even on low-powered computers. Based on 492 tracing experiments from an actual medical application, the authors demonstrate that live wire on the fly is 1.331 times faster than live wire for actual segmentation for varying image sizes, although the pure computational part alone is found to be about 120 times faster.

Shape-based interpolation of multidimensional grey-level images

Shape-based interpolation as applied to binary images causes the interpolation process to be influenced by the shape of the object. It accomplishes this by first applying a distance transform to the data. This results in the creation of a grey-level data set in which the value at each point represents the minimum distance from that point to the surface of the object. (By convention, points inside the object are assigned positive values; points outside are assigned negative values.) This distance transformed data set is then interpolated using linear or higher-order interpolation and is then thresholded at a distance value of zero to produce the interpolated binary data set. Here, the authors describe a new method that extends shape-based interpolation to grey-level input data sets. This generalization consists of first lifting the n-dimensional (n-D) image data to represent it as a surface, or equivalently as a binary image, in an (n+1)-dimensional [(n+1)-D] space. The binary shape-based method is then applied to this image to create an (n+1)-D binary interpolated image. Finally, this image is collapsed (inverse of lifting) to create the n-D interpolated grey-level data set. The authors have conducted several evaluation studies involving patient computed tomography (CT) and magnetic resonance (MR) data as well as mathematical phantoms. They all indicate that the new method produces more accurate results than commonly used grey-level linear interpolation methods, although at the cost of increased computation.

Surface Shading in the Cuberille Environment

Computed tomography and the cuberiile model¿an effort to better serve the medical profession and its patients.

Atrophy and high intensity lesions: complementary neurobiological mechanisms in late-life major depression.

The primary objective of our study was to examine the role of atrophy, high intensity lesions and medical comorbidity in the pathophysiology of major depressive disorder in the elderly (late-life MDD). Our sample was comprised of 51 patients with late-life MDD and 30 non-depressed controls. All subjects were scanned on 1.5 tesla magnetic resonance imaging scanner (MRI) and absolute and normalized measures of brain and lesion volumes were obtained and used for comparison between groups. Patients with MDD had significantly smaller frontal lobe volumes, together with larger whole brain lesion volumes when compared with controls (p < .05). Whole brain lesion volumes correlated significantly (r = 0.41, p = .006) with overall medical comorbidity. The odds ratio (OR) for existing MDD increases significantly with a decrease in frontal lobe volume and an increase in whole brain lesion volumes (p < .05). Our findings suggest that atrophy and high intensity lesions represent relatively independent pathways to late-life MDD. While medical disorders lead to neuropathological changes that are captured on MR imaging as high intensity signals, atrophy may represent a relatively autonomous phenomenon. These findings have broad implications for the pathophysiology of mood disorders and suggest that complementary neurobiological processes may lead to cumulative neuronal injury thereby predisposing to clinical depression.The primary objective of our study was to examine the role of atrophy, high intensity lesions and medical comorbidity in the pathophysiology of major depressive disorder in the elderly (late-life MDD). Our sample was comprised of 51 patients with late-life MDD and 30 non-depressed controls. All subjects were scanned on 1.5 tesla magnetic resonance imaging scanner (MRI) and absolute and normalized measures of brain and lesion volumes were obtained and used for comparison between groups. Patients with MDD had significantly smaller frontal lobe volumes, together with larger whole brain lesion volumes when compared with controls (p < .05). Whole brain lesion volumes correlated significantly (r = 0.41, p = .006) with overall medical comorbidity. The odds ratio (OR) for existing MDD increases significantly with a decrease in frontal lobe volume and an increase in whole brain lesion volumes (p < .05). Our findings suggest that atrophy and high intensity lesions represent relatively independent pathways to late-life MDD. While medical disorders lead to neuropathological changes that are captured on MR imaging as high intensity signals, atrophy may represent a relatively autonomous phenomenon. These findings have broad implications for the pathophysiology of mood disorders and suggest that complementary neurobiological processes may lead to cumulative neuronal injury thereby predisposing to clinical depression.