Run-length Statistics Research Articles

Efficient control charting methodology based on Distance Weighted Mean for normal distribution

This research suggests a Distance Weighted Mean (DWM) based control chart under normal distribution implementing Simple Random Sampling (SRS). The control limits are calculated using the quantile point method. The control chart's performance is assessed using the Average Run Length (ARL) statistic. The numerical findings are illustrated using samples of sizes 3 and 5. The ARL1 values are determined using Monte Carlo Simulation for increasing and decreasing shifts in the location parameter ranging from 5% to 30%. Using the ARL1 measurement, the proposed DWM control charts are compared to the existing Shewhart control charts. According to the comparison analysis, the suggested DWM control chart surpasses the competing Shewhart control chart. The real-life application of the proposed DWM control chart is also shown by using the lifetime of the light bulb (in hours). The results suggest that the proposed DWM control chart can be a useful tool for monitoring process mean shifts, especially when the sample size is large, and the magnitude of the shift is significant.

Quantifying corrosion inhibition on mild steel surface using run length statistics-based texture analysis

Automatic detection of corrosion inhibition efficacy by processing the microscopic images of the sample surface by using image texture analysis is a very useful technique in the contemporary research field. The reported technique is less time consuming with the capability of pattern recognition via quantification with preferences of suitable software, coding and various numerical methods ultimately represents data (vide acquisition) more precisely and accurately at agiven condition. An optimal anisotropic diffusion-based pre-processing for image enhancement and run length statistics (RLS) based texture analysis for feature extraction are performed on the microscopic images of mild steel surface treated in 1 M HCl solution with different inhibitors viz., (E)-1-(2,4-dinitrophenyl)-2-(pyridin-4-yl)methylene)hydrazine (abbreviated as DHMP and represented as L1 ), (E)-1-(4-isocyanophenyl)-2-((pyridin-4-yl)methylene)hydrazine) (abbreviated as IMH and represented as L2 ) and (E)-1-(2,4-dinitrophenyl)-2-((pyridin-4-yl)methylene)phenol (abbreviated as DMP and represented as L3 ). Extracted normalized or relative features can be quantified the corrosion inhibition efficiency in an excellent way using multi-regression analysis having R-square values in the range of 0.997 to 0.999. Highlights (E)-1-(2,4-dinitrophenyl)-2-(pyridin-4-yl)methylene)hydrazine (abbreviated as DHMP and represented as L1), (E)-1-(4-isocyanophenyl)-2-((pyridin-4-yl)methylene)hydrazine) (abbreviated as IMH and represented as L2) and (E)-1-(2,4-dinitrophenyl)-2-((pyridin-4-yl)methylene)phenol (abbreviated as DMP and represented as L3) are used as three different corrosion inhibitors over the mild steel surface in presence of 1M HCl solution. Automatic detection of corrosion inhibition efficiency by processing the microscopic images of the targeted sample surface by via image texture analysis. An optimal anisotropic diffusion technique is adopted in this present study for image enhancement before processing the image. Run length statistics (RLS) based texture analysis has been incorporated in this present investigation for extracting run length features to detect the corrosion inhibition efficiency. After selecting the RLS-based features, a multivariable regression model is developed and correlations are set up with the features of conventional parameters of the different inhibitor’s performance.

Data mining framework for breast lesion classification in shear wave ultrasound: A hybrid feature paradigm

Abstract Assessment of elasticity parameters of breast using ultrasound elastography (USE) provides exclusive information about the cancerous tissue. Shear wave elastography (SWE), a new USE imaging procedure is increasingly used for elasticity evaluation of breast lesions. SWE examination is gaining popularity in the characterization of benign and malignant breast lesions as it has high diagnostic performance accuracy. However, some degree of manual errors, such as probe compression or movement may cause inaccurate results. In addition, the systems cannot measure elasticity values in small lesions where the tissues do not vibrate enough. Thus, computer-aided methods suppress these technical or manual limitations of SWE during evaluation of breast lesions. Therefore, this paper proposes, a novel methodology for characterization of benign and malignant breast lesions using SWE. Original SWE image is subjected to three levels of Discrete wavelet transform (DWT) to obtain different coefficients. Second order statistics (Run Length Statistics) and Hu’s moments features are extracted from DWT coefficients. Extracted features are subjected to sequential forward selection (SFS) method to obtain the significant features and ranked using ReliefF feature ranking technique. Ranked features are fed to different classifiers for automated characterization of benign and malignant breast lesions. Our proposed technique achieved a significant accuracy of 93.59%, sensitivity of 90.41% and specificity of 96.39% using only three features. In addition, a unique integrated index named Shear Wave Breast Cancer Risk Index (sBCRI) is formulated for characterization of malignant and benign breast lesion using only two features. The proposed index, sBCRI, provides a single number which characterizes the malignant and benign cancer faster. This system can be employed as an ideal screening tool as it has high sensitivity and low false-positive rate. Hence, the women with benign lesions need not undergo unnecessary biopsies.

Assessment of a Four-View Mammographic Image Feature Based Fusion Model to Predict Near-Term Breast Cancer Risk.

The purpose of this study was to develop and assess a new quantitative four-view mammographic image feature based fusion model to predict the near-term breast cancer risk of the individual women after a negative screening mammography examination of interest. The dataset included fully-anonymized mammograms acquired on 870 women with two sequential full-field digital mammography examinations. For each woman, the first "prior" examination in the series was interpreted as negative (not recalled) during the original image reading. In the second "current" examination, 430 women were diagnosed with pathology verified cancers and 440 remained negative ("cancer-free"). For each of four bilateral craniocaudal and mediolateral oblique view images of left and right breasts, we computed and analyzed eight groups of global mammographic texture and tissue density image features. A risk prediction model based on three artificial neural networks was developed to fuse image features computed from two bilateral views of four images. The risk model performance was tested using a ten-fold cross-validation method and a number of performance evaluation indices including the area under the receiver operating characteristic curve (AUC) and odds ratio (OR). The highest AUC=0.725±0.026 was obtained when the model was trained by gray-level run length statistics texture features computed on dense breast regions, which was significantly higher than the AUC values achieved using the model trained by only two bilateral one-view images (p<0.02). The adjustable OR values monotonically increased from 1.0 to 11.8 as model-generated risk score increased. The regression analysis of OR values also showed a significant increase trend in slope (p<0.01). As a result, this preliminary study demonstrated that a new four-view mammographic image feature based risk model could provide useful and supplementary image information to help predict the near-term breast cancer risk.

Multi-classification of cell deformation based on object alignment and run length statistic.

Cellular morphology is widely applied in digital pathology and is essential for improving our understanding of the basic physiological processes of organisms. One of the main issues of application is to develop efficient methods for cell deformation measurement. We propose an innovative indirect approach to analyze dynamic cell morphology in image sequences. The proposed approach considers both the cellular shape change and cytoplasm variation, and takes each frame in the image sequence into account. The cell deformation is measured by the minimum energy function of object alignment, which is invariant to object pose. Then an indirect analysis strategy is employed to overcome the limitation of gradual deformation by run length statistic. We demonstrate the power of the proposed approach with one application: multi-classification of cell deformation. Experimental results show that the proposed method is sensitive to the morphology variation and performs better than standard shape representation methods.

An empirical study of tests for uniformity in multidimensional data

An important problem in high-dimensional data analysis is determining whether sample points are uniformly distributed (i.e., exhibit complete spatial randomness) over some compact support, or rather possess some underlying structure (e.g., clusters or other nonhomogeneities). We propose two new graph-theoretic tests of uniformity which utilize the minimum spanning tree and a snake (a short non-branching acyclic path connecting each data point). We compare the powers of statistics based on these graphs with other statistics from the literature on an array of non-uniform alternatives in a variety of supports. For data in a hypercube, we find that test statistics based on the minimum spanning tree have superior power when the data displays regularity (e.g., results from an inhibition process). For arbitrarily shaped or unknown supports, we use run length statistics of the sequence of segment lengths along the snake’s path to test uniformity. The snake is particularly useful because no knowledge or estimation of the support is required to compute the test statistic, it can be computed quickly for any dimension, and it shows what kinds of non-uniformities are present. These properties make the snake unique among multivariate tests of uniformity since others only function on specific and known supports, have computational difficulties in high dimension, or have inconsistent type I error rates.

Machined Surfaces Texture Analysis Based on Hough Transform and Run Length Statistics

Conditions of tool wear can be indirectly reflected by the texture features of the machined image due to the direct contact between the work piece and tool in cutting process. In this paper, a new texture analysis method is proposed based on the Hough transform and Run length statistics. In order to remove non uniform illumination and noise, the original machined images are preprocessed by contrast enhancement algorithm and adjacent region average method, and then the edge images are obtained by a canny edge detector. Hough transform is then applied to the edge images to detect all line segments. The length characteristics of line segments are detected by using Run length statistics method. The average length and angle characteristics of edge images are used to determine the tool wear. Through our experiments, we found a high degree of correlation between texture features of machined images and tool wear. The combination of Hough transform and Run length statistics method improve the monitoring performance.

Characterization of masses in digital breast tomosynthesis: Comparison of machine learning in projection views and reconstructed slices

In digital breast tomosynthesis (DBT), quasi-three-dimensional (3D) structural information is reconstructed from a small number of 2D projection view (PV) mammograms acquired over a limited angular range. The authors developed preliminary computer-aided diagnosis (CADx) methods for classification of malignant and benign masses and compared the effectiveness of analyzing lesion characteristics in the reconstructed DBT slices and in the PVs. A data set of MLO view DBT of 99 patients containing 107 masses (56 malignant and 51 benign) was collected at the Massachusetts General Hospital with IRB approval. The DBTs were obtained with a GE prototype system which acquired 11 PVs over a 50 degree arc. The authors reconstructed the DBTs at 1 mm slice interval using a simultaneous algebraic reconstruction technique. The region of interest (ROI) containing the mass was marked by a radiologist in the DBT volume and the corresponding ROIs on the PVs were derived based on the imaging geometry. The subsequent processes were fully automated. For classification of masses using the DBT-slice approach, the mass on each slice was segmented by an active contour model initialized with adaptive k-means clustering. A spiculation likelihood map was generated by analysis of the gradient directions around the mass margin and spiculation features were extracted from the map. The rubber band straightening transform (RBST) was applied to a band of pixels around the segmented mass boundary. The RBST image was enhanced by Sobel filtering in the horizontal and vertical directions, from which run-length statistics texture features were extracted. Morphological features including those from the normalized radial length were designed to describe the mass shape. A feature space composed of the spiculation features, texture features, and morphological features extracted from the central slice alone and seven feature spaces obtained by averaging the corresponding features from three to 19 slices centered at the central slice were compared. For classification of masses using the PV approach, a feature extraction process similar to that described above for the DBT approach was performed on the ROIs from the individual PVs. Six feature spaces obtained from the central PV alone and by averaging the corresponding features from three to 11 PVs were formed. In each feature space for either the DBT-slice or the PV approach, a linear discriminant analysis classifier with stepwise feature selection was trained and tested using a two-loop leave-one-case-out resampling procedure. Simplex optimization was used to guide feature selection automatically within the training set in each leave-one-case-out cycle. The performance of the classifiers was evaluated by the area (Az) under the receiver operating characteristic curve. The test Az values from the DBT-slice approach ranged from 0.87 +/- 0.03 to 0.93 +/- 0.02, while those from the PV approach ranged from 0.78 +/- 0.04 to 0.84 +/- 0.04. The highest test Az of 0.93 +/- 0.02 from the nine-DBT-slice feature space was significantly (p = 0.006) better than the highest test Az of 0.84 +/- 0.04 from the nine-PV feature space. The features of breast lesions extracted from the DBT slices consistently provided higher classification accuracy than those extracted from the PV images.

Performance Comparison of Hmm Discrete Channel Modeling in Cdma Links

The performance comparison of two Markov models namely the Baum Welch Algorithm based HMM and Semi Hidden Markov Model has been evaluated for a DS-CDMA link in this work. The simulation includes the effects of AWGN, Multipath and Multiple Access Interference. Validation includes a comparison of the runlength statistic for the original and regenerated error sequence from estimated models. The SHMM approach is seen to be capable of developing a more accurate model as compared to the BWA. The length of number of symbols processed at a time does not affect the accuracy in both the methods.

Statistics of stained glass images

The notion of applying statistical techniques to stained glass images is an intriguing one. This paper introduces systematic procedures to calculate statistics on digital images, gives a review of first-order statistics, second-order statistics, higher-order statistics and run-length statistics, and applies the measures to a collection of digital images of stained glass windows. Values of the statistics are reported. The scale invariance property of images is examined carefully, and characteristic scaling behaviours of stained glass images are found.

Empirical calibration of time series monitoring methods using receiver operating characteristic curves

Time series monitoring methods, such as the Brown and Trigg methods, have the purpose of detecting pattern breaks (or “signals”) in time series data reliably and in a timely fashion. Traditionally, researchers have used the average run length (ARL) statistic on results from generated signal occurrences in simulated time series data to calibrate and evaluate these methods, with a focus on timeliness of signal detection. This paper investigates the receiver operating characteristic (ROC) framework, well-known in the diagnostic decision making literature, as an alternative to ARL analysis for time series monitoring methods. ROC analysis traditionally uses real data to address the inherent tradeoff in signal detection between the true and false positive rates when varying control limits. We illustrate ROC analysis using time series data on crime at the patrol district level in two cities, and use the concept of Pareto frontier ROC curves and reverse functions for methods such as Brown’s and Trigg’s that have parameters affecting signal-detection performance. We compare the Brown and Trigg methods to three benchmark methods, including one commonly used in practice. The Brown and Trigg methods collapse to the same simple method on the Pareto frontier and dominate the benchmark methods under most conditions. The worst method is the one commonly used in practice.

Combined Statistical and Multiscale View on Ultrasonic Liver Images for Characterization

Combined Statistical and Multiscale View on Ultrasonic Liver Images for Characterization

Texture Analysis of Ultrasonic Images of Symptomatic Carotid Plaques can Identify Those Plaques Associated with Ipsilateral Embolic Brain Infarction

The aim of our study was to determine the association between objective, computerised texture analysis of carotid plaque ultrasonic images and embolic CT-brain infarction in patients presenting with hemispheric neurological symptoms. Cross-sectional study in patients with 50%-99% (ECST) carotid stenosis. Carotid plaque ultrasonic images (n=54, 26 with TIAs and 28 with stroke) obtained during carotid ultrasound were normalised and standardised for resolution and subsequently assessed visually for the presence of discrete echogenic or juxtaluminal echolucent components and overall echogenicity (plaque type). Using computer software, 51 histogram/textural features of the plaque outlines were calculated. Factor analysis was subsequently applied to eliminate redundant variables. Small cortical, large cortical and discrete subcortical infarcts on CT-brain scan were considered as being embolic. Twenty-five cases (46%) had embolic infarcts. On logistic regression, grey-scale median (GSM), a measure of echolucency, spatial grey level dependence matrices (SGLDM) correlation and SGLDM information measure of correlation-1, measures of homogeneity were significant (p<0.05), but not grey level runlength statistics (RUNL) Run Percentage (RP), stenosis severity, type of symptoms or echolucent juxtaluminal components. Using ROC curves methodology, SGLDM information measure of correlation-1 improved the value of GSM in distinguishing embolic from non-embolic CT-brain infarction. Computerised texture analysis of ultrasonic images of symptomatic carotid plaques can identify those that are associated with brain infarction, improving the results achieved by GSM alone. This methodology could be applied to prospective natural history studies of symptomatic patients not operated on or randomised trials of patients undergoing carotid angioplasty and stenting in order to identify high-risk subgroups for cerebral infarction.

Denoising of Chinese calligraphy tablet images based on run-length statistics and structure characteristic of character strokes

In this paper, a novel approach is proposed for denoising of Chinese calligraphy tablet documents. The method includes two phases: First, a partial differential equations (PDE) based the total variation model and Otsu thresholding method are used to preprocess the calligraphy document image. Second, a new method based on run-length statistics and structure characteristics of Chinese characters is proposed to remove some random and ant-like noises. This includes the optimal threshold selection from histogram of run-length probability density, and improved Hough transform algorithm for line shape noise detection and removal. Examples are given in the paper to demonstrate the proposed method.

Computer‐aided diagnosis of pulmonary nodules on CT scans: Segmentation and classification using 3D active contours

We are developing a computer-aided diagnosis (CAD) system to classify malignant and benign lung nodules found on CT scans. A fully automated system was designed to segment the nodule from its surrounding structured background in a local volume of interest (VOI) and to extract image features for classification. Image segmentation was performed with a three-dimensional (3D) active contour (AC) method. A data set of 96 lung nodules (44 malignant, 52 benign) from 58 patients was used in this study. The 3D AC model is based on two-dimensional AC with the addition of three new energy components to take advantage of 3D information: (1) 3D gradient, which guides the active contour to seek the object surface, (2) 3D curvature, which imposes a smoothness constraint in the z direction, and (3) mask energy, which penalizes contours that grow beyond the pleura or thoracic wall. The search for the best energy weights in the 3D AC model was guided by a simplex optimization method. Morphological and gray-level features were extracted from the segmented nodule. The rubber band straightening transform (RBST) was applied to the shell of voxels surrounding the nodule. Texture features based on run-length statistics were extracted from the RBST image. A linear discriminant analysis classifier with stepwise feature selection was designed using a second simplex optimization to select the most effective features. Leave-one-case-out resampling was used to train and test the CAD system. The system achieved a test area under the receiver operating characteristic curve (A(z)) of 0.83 +/- 0.04. Our preliminary results indicate that use of the 3D AC model and the 3D texture features surrounding the nodule is a promising approach to the segmentation and classification of lung nodules with CAD. The segmentation performance of the 3D AC model trained with our data set was evaluated with 23 nodules available in the Lung Image Database Consortium (LIDC). The lung nodule volumes segmented by the 3D AC model for best classification were generally larger than those outlined by the LIDC radiologists using visual judgment of nodule boundaries.

ランレングス統計量による球状黒鉛鋳鉄の定量的破面解析

Fractography is the most popular method for failure analysis. This method, however, has been mainly applied to structural steels, and has not been always effective to cast irons. Since many factors like graphite, matrix, cast defects, and so on affect fracture of cast iron, they made it difficult to estimate failure causes from the fracture surfaces. In this study, therefore, quantitative fracture surface analysis was carried out on spheloidal graphite cast iron to improve accuracy of the estimation.When fracture surface analysis is conducted on images obtained with scanning electron microscopes (SEM) that are commonly used in the failure analysis fields, the characteristic values extracted from the images can possibly depend upon the contrast of the images. To minimize the contrast influence, we proposed the fracture surface analysis method that edges are extracted from the SEM images by differentiating them and fracture surface analysis is conducted on the texture images. The proposed method was applied to the fracture surfaces formed by a fracture toughness test. By computing run length statistics which are parameters widely used in texture analysis, we could divide the fatigue fracture surface produced in introducing a pre-fatigue crack from the rapid fracture surface produced during the fracture toughness test.

Cross‐shore migration of lunate megaripples during Duck94

Remote acoustic observations of lunate megaripple migration are presented from two storm events during the Duck94 nearshore dynamics experiment for time periods during which longshore currents were weak (&lt;20 cm/s). During these periods, significant wave orbital velocities were 50–80 cm/s; megaripple heights were 0.05–0.5 m; megaripple horns were directed shoreward; the crest‐to‐trough slope of the shoreward advancing ripple face was close to the angle of repose; and migration speeds were 10–40 cm/h onshore. The observations also indicate that the megaripples stalled, and may have begun to migrate offshore, when the mean offshore flow exceeded 20 cm/s during the second storm. Stress‐based bed load sediment transport models are moderately successful in predicting the observed dependence of migration velocity on measured fluid velocities separated into zero (mean current), infragravity wave, and sea‐and‐swell wave frequency bands. Wave and mean current friction factors, fw and fc, are obtained by best fit between the predicted and observed migration velocities, for two choices (3/2 and 5/2) for the stress exponent ξ in the bed load transport part of the model. Net transport is computed using wave velocity amplitudes determined from both run length statistics and wave by wave. Improved agreement with observations is obtained for the wave‐by‐wave net transport predictions and for the wave‐like treatment of the infragravity band. The level of agreement is relatively insensitive to the value of ξ. The best fit current and wave friction factor values, for ξ = 5/2 and 3/2 are fc = 4.3 × 10−3 and 8.0 × 10−3 and fw = 1.7 × 10−2 and 4.8 × 10−2, respectively.

Analysis of temporal changes of mammographic features: computer-aided classification of malignant and benign breast masses.

A new classification scheme was developed to classify mammographic masses as malignant and benign by using interval change information. The masses on both the current and the prior mammograms were automatically segmented using an active contour method. From each mass, 20 run length statistics (RLS) texture features, 3 speculation features, and 12 morphological features were extracted. Additionally, 20 difference RLS features were obtained by subtracting the prior RLS features from the corresponding current RLS features. The feature space consisted of the current RLS features, the difference RLS features, the current and prior speculation features, and the current and prior mass sizes. Stepwise feature selection and linear discriminant analysis classification were used to select and merge the most useful features. A leave-one-case-out resampling scheme was used to train and test the classifier using 140 temporal image pairs (85 malignant, 55 benign) obtained from 57 biopsy-proven masses (33 malignant, 24 benign) in 56 patients. An average of 10 features were selected from the 56 training subsets: 4 difference RLS features, 4 RLS features, and 1 speculation feature from the current image, and 1 speculation feature from the prior, were most often chosen. The classifier achieved an average training Az of 0.92 and a test Az of 0.88. For comparison, a classifier was trained and tested using features extracted from the 120 current single images. This classifier achieved an average training Az of 0.90 and a test Az of 0.82. The information on the prior image significantly (p = 0.015) improved the accuracy for classification of the masses.

Fuzzy neural network-based texture analysis of ultrasonic images.

The efficacy of a novel fuzzy neural network classifier for the characterization of ultrasonic liver images based on texture analysis techniques is investigated. Classification features are extracted with the use of image texture analysis techniques such as fractal dimension texture analysis, spatial gray-level dependence matrices, gray-level difference statistics, gray-level run-length statistics, and first-order gray-level parameters. These features are fed to a neural network classifier based on geometrical fuzzy sets. Starting from the construction of the Voronoi diagram of the training patterns, an aggregation of Voronoi regions is performed, leading to the identification of larger regions belonging exclusively to one of the pattern classes. The resulting scheme is a constructive algorithm that defines fuzzy clusters of patterns. Based on observations concerning the grade of membership of the training patterns to the created regions, decision probabilities are computed through which the final classification is performed.

Run length analysis of Shewhart charts applied to drifting processes under an integrative SPC/EPC model

Engineering Process Controllers (EPC) are frequently based on parametrized models. If process conditions change, the parameter estimates used by the controllers may become biased, and the quality characteristics will be affected. To detect such changes it is adequate to use Statistical Process Control (SPC) methods. The run length statistic is commonly used to describe the performance of an SPC chart. This paper develops approximations for the first two moments of the run length distribution of a one-sided Shewhart chart used to detect two types of process changes in a system that is regulated by a given EPC scheme: i) changes in the level parameter; ii) changes in the drift parameter. If the drift parameter shifts, it is further assumed that the form of the drift process changes from a linear trend under white noise (the in-control drift model) into a random walk with drift model. Two different approximations for the run length moments are presented and their accuracy is numerically analyzed.