Run-length Statistics Research Articles

Design of a high-sensitivity classifier based on a genetic algorithm: application to computer-aided diagnosis

A genetic algorithm (GA) based feature selection method was developed for the design of high-sensitivity classifiers, which were tailored to yield high sensitivity with high specificity. The fitness function of the GA was based on the receiver operating characteristic (ROC) partial area index, which is defined as the average specificity above a given sensitivity threshold. The designed GA evolved towards the selection of feature combinations which yielded high specificity in the high-sensitivity region of the ROC curve, regardless of the performance at low sensitivity. This is a desirable quality of a classifier used for breast lesion characterization, since the focus in breast lesion characterization is to diagnose correctly as many benign lesions as possible without missing malignancies. The high-sensitivity classifier, formulated as the Fisher's linear discriminant using GA-selected feature variables, was employed to classify 255 biopsy-proven mammographic masses as malignant or benign. The mammograms were digitized at a pixel size of mm, and regions of interest (ROIs) containing the biopsied masses were extracted by an experienced radiologist. A recently developed image transformation technique, referred to as the rubber-band straightening transform, was applied to the ROIs. Texture features extracted from the spatial grey-level dependence and run-length statistics matrices of the transformed ROIs were used to distinguish malignant and benign masses. The classification accuracy of the high-sensitivity classifier was compared with that of linear discriminant analysis with stepwise feature selection . With proper GA training, the ROC partial area of the high-sensitivity classifier above a true-positive fraction of 0.95 was significantly larger than that of , although the latter provided a higher total area under the ROC curve. By setting an appropriate decision threshold, the high-sensitivity classifier and correctly identified 61% and 34% of the benign masses respectively without missing any malignant masses. Our results show that the choice of the feature selection technique is important in computer-aided diagnosis, and that the GA may be a useful tool for designing classifiers for lesion characterization.

Computerized characterization of masses on mammograms: the rubber band straightening transform and texture analysis.

A new rubber band straightening transform (RBST) is introduced for characterization of mammographic masses as malignant or benign. The RBST transforms a band of pixels surrounding a segmented mass onto the Cartesian plane (the RBST image). The border of a mammographic mass appears approximately as a horizontal line, and possible speculations resemble vertical lines in the RBST image. In this study, the effectiveness of a set of directional textures extracted from the images before the RBST. A database of 168 mammograms containing biopsy-proven malignant and benign breast masses was digitized at a pixel size of 100 microns x 100 microns. Regions of interest (ROIs) containing the biopsied mass were extracted from each mammogram by an experienced radiologist. A clustering algorithm was employed for automated segmentation of each ROI into a mass object and background tissue. Texture features extracted from spatial gray-level dependence matrices and run-length statistics matrices were evaluated for three different regions and representations: (i) the entire ROI; (ii) a band of pixels surrounding the segmented mass object in the ROI; and (iii) the RBST image. Linear discriminant analysis was used for classification, and receiver operating characteristic (ROC) analysis was used to evaluate the classification accuracy. Using the ROC curves as the performance measure, features extracted from the RBST images were found to be significantly more effective than those extracted from the original images. Features extracted from the RBST images yielded an area (Az) of 0.94 under the ROC curve for classification of mammographic masses as malignant and benign.

Run length statistics and the Hurst exponent in random and birth-death random walks

This paper considers a modified and parametric Hurst exponent using fixed amplitudes and sampling intervals given by run length statistics. Such an approach allows us to calculate a modified and theoretical Hurst exponent based on run length statistics. We then calculate the Hurst exponent for the Wiener process, its discrete time equivalent as well as a birth-death random walk.

Correlation between individual waves in a real sea state

The correlation between individual waves in a real sea state has a central role in existing theories of wave grouping. The attractive Kimura (1980) theory has two critical assumptions, that the sequence of individual wave heights follows a Markov process and that the joint distribution of consecutive wave heights follows a bivariate Rayleigh form. Analysis of measured water surface records suggests that sequences of individual waves can reasonably be described as a first order mixed autoregressive, moving-average or ARMA process, though a distinction among ARMA (1,0), ARMA (0,1) and ARMA (1,1) models was beyond the resolution of the data. These include the Markov or ARMA (1,0) model. The decisive detail, the joint distribution of consecutive wave heights in the sea state, was evaluated by a simulation methodology that is consistent with the Gaussian random wave model. The estimates are dependent on spectral shape and are consistently narrower and more sharply focussed at the peak than the corresponding bivariate Rayleigh estimate. The resulting predictions of run and group length statistics differ from the Kimura theory, though not by a sufficient margin to displace the Kimura theory as a pragmatic choice for wave grouping.

Application of artificial neural networks for the classification of liver lesions by image texture parameters

Ultrasound imaging is a powerful tool for characterizing the state of soft tissues; however, in some cases, where only subtle differences in images are seen as in certain liver lesions such as hemangioma and malignancy, existing B-scan methods are inadequate. More detailed analyses of image texture parameters along with artificial neural networks can be utilized to enhance differentiation. From B-scan ultrasound images, 11 texture parameters comprising of first, second and run length statistics have been obtained for normal, hemangioma and malignant livers. Tissue characterization was then performed using a multilayered backpropagation neural network. The results for 113 cases have been compared with a classification based on discriminant analysis. For linear discriminant analysis, classification accuracy is 79.6% and with neural networks the accuracy is 100%. The present results show that neural networks classify better than discriminant analysis, demonstrating a much potential for clinical application.

US tissue characterization workstation: applications and design.

This article discusses the purpose, design, and uses of an ultrasonographic tissue characterization workstation. The distinguishing characteristic of a tissue characterization workstation is its ability to analyze and classify image textures. Texture is defined as regularly or randomly repeating patterns. Small texture differences in an image are difficult to observe in the presence of noise. Therefore, it is necessary to analyze the image quantitatively. Quantitative measurements include run-length statistics, fractal dimension, and correlation statistics. The workstation is designed so that a radiologist can analyze the patient's images through an easy-to-use graphical user interface. The workstation software is based on standards, so that it can be run on a variety of different hardware platforms. The workstation can be used in a research environment to distinguish between images of malignant and benign breast lesions, which are difficult to diagnose visually. Further work is being done to make the workstation software into a useful clinical tool.

Noninvasive diagnosis of cardiac rejection through echocardiographic tissue characterization

Ultrasonic tissue characterization is based on the assumption that microscopic tissue structures are identifiable by their acoustic properties. Our study group consisted of 23 cardiac recipients. Two-dimensional images were obtained within 2 hours of endomyocardial biopsy. The end-diastolic echo frames were digitized into the matrix of an image-processing system. A region of interest was placed into the anteroseptal segment of the left ventricle. The texture within the region of interest was analyzed using four major groups of texture analysis (first-order histogram, co-occurrence matrix, run-length statistic, and power spectrum). A total of 408 echocardiographic examinations were compared with histologic findings. The 117 initially calculated texture parameters were reduced incrementally using a series of discriminant analyses. A set of three texture parameters (inverse difference moment undirected, run-length nonuniformity vertical, and sector sum) was able to describe changed echocardiographic texture when rejection occurred. Using these three parameters, echocardiographic sensitivity was 89.0% and specificity was 83.6% for moderate rejection. We conclude that cardiac rejection is associated with echocardiographic texture alterations and that serial echocardiographic texture analysis can reliably identify rejection.

The clinical value of ultrasonic tissue characterization in the management of heart transplant patients.

The purpose of this study was to evaluate the rejection process by ultrasonic tissue characterization. Serial 2D echocardiographic images were obtained within 24 h prior to an endomyocardial biopsy. The end-diastolic echoframes were digitized into a computer matrix. A region of interest was placed into the anteroseptal segment of each scan. Image texture was analysed by four major groups of texture analysis (first-order histogram, co-occurrence matrix, run-length statistic, power spectrum). In 23 patients, 408 biopsies were taken after each examination, so that correlation between the ultrasonic tissue measurements and the histological state of the tissue could be determined. When rejection occurred, heterogeneity, brightness and contrast of texture increased. Of 117 texture parameters originally claculated, three parameters (inverse difference moment, run-length non-uniformity, ring sums of power spectrum) that characterized rejection were determined by means of discriminance analysis. Compared with biopsy findings, echocardiographic sensitivity for moderate rejection was 93.3% and specifity 83.6%. Our study indicates that acute rejection is associated with changes in echocardiographic texture. Serial echocardiographic texture analysis can reliably identify heart transplant rejection.

The clinical value of ultrasonic tissue characterization in the management of heart transplant patients

The purpose of this study was to evaluate the rejection process by ultrasonic tissue characterization. Serial 2D echocardiographic images were obtained within 24 h prior to an endomyocardial biopsy. The end-diastolic echoframes were digitized into a computer matrix. A region of interest was placed into the anteroseptal segment of each scan. Image texture was analysed by four major groups of texture analysis (first-order histogram, co-occurrence matrix, run-length statistic, power spectrum). In 23 patients, 408 biopsies were taken after each examination, so that correlation between the ultrasonic tissue measurements and the histological state of the tissue could be determined. When rejection occurred, heterogeneity, brightness and contrast of texture increased. Of 117 texture parameters originally claculated, three parameters (inverse difference moment, run-length non-uniformity, ring sums of power spectrum) that characterized rejection were determined by means of discriminance analysis. Compared with biopsy findings, echocardiographic sensitivity for moderate rejection was 93.3% and specifity 83.6%. Our study indicates that acute rejection is associated with changes in echocardiographic texture. Serial echocardiographic texture analysis can reliably identify heart transplant rejection.

Run-length coding method for black-and-white facsimile with a ternary code as an intermediate step

A code is presented that consists of codewords of variable length. This allows a good adaptation to the different run-length statistics of various kinds of documents: printed matter, drawings, weather maps etc. Compared with other run-length codes, the new code yields, in most cases, a better compression ratio.

Optimum Run Length Codes

To realize the full redundancy reducing potential of run length coding over a collection of picture segments with varying run length statistics, adaptive coding techniques have been proposed. This paper compares results for a previously proposed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> -code, for which the block length was varied adaptively, with those obtained using a fixed block length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</tex> -code first proposed here. Both codes use variable length codewords integrally related to the code block length. For all pictures analyzed, the fixed block length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</tex> -code performed nearly as well as the adaptive <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> -code. For both, the bit rates were close to the entropy bound. The reasons for these results are discussed. It is Shown that, due to the prevalence of exceptionally long runs, the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> -code, which is nearly optimal for exponentially distributed run lengths, performs poorly for actual pictures unless the block length is varied adaptively. The strategy used to implement the A-code adaptively is described. The optimal block length of the B-code,on the other hand, is shown to be largely independent of the picture statistics and need therefore not be varied adaptively. The hardware implementation of both coding techniques, the influence of channel disturbances on image quality, and the problems of error correction and line synchronization are discussed.

Some Possibilities of Picture Signal Bandwidth Compression

An experimental appraisal of the Cherry-Gouriet proposals, for the bandwidth compression of television signals by variable-velocity coding, has been made. A flying-spot variablevelocity scanner was built for this purpose. The encoding of the signal in this system is done by a nonlinear feedback loop. Qualitative studies on the stability of the loop have been made. It has been found that the effect of the source noise on the encoder performance is extremely important. It is concluded that owing to the limitations of the devices, the variable-velocity scanner is not practically feasible for television transmissions. However, this system seems ideally suited for LF transmission of pictures. The potential bandwidth compression of the B.B.C. test card C has been determined from its run-length statistics. An open-loop system of bandwidth compression has been described which uses variable-rate sampling. Using the statistics obtained from the test card C, the storage requirement of the open-loop system has been assessed.