Minimum Error Thresholding Research Articles

A new multi-object image thresholding method based on correlation between object class uncertainty and intensity gradient

Image thresholding and gradient analysis have remained popular image preprocessing tools for several decades due to the simplicity and straight-forwardness of their definitions. Also, optimum selection of threshold and gradient strength values are hidden steps in many advanced medical imaging algorithms. A reliable method for threshold optimization may be a crucial step toward automation of several medical image based applications. Most automatic thresholding and gradient selection methods reported in literature primarily focus on image histograms ignoring a significant amount of information embedded in the spatial distribution of intensity values forming visible features in an image. Here, we present a new method that simultaneously optimizes both threshold and gradient values for different object interfaces in an image that is based on unification of information from both the histogram and spatial image features; also, the method works for unknown number of object regions. A new energy function is formulated by combining the object class uncertainty measure, a histogram-based feature, of each pixel with its image gradient measure, a spatial contextual feature in an image. The energy function is designed to measure the overall compliance of the theoretical premise that, in a probabilistic sense, image intensities with high class uncertainty are associated with high image gradients. Finally, it is expressed as a function of threshold and gradient parameters and optimum combinations of these parameters are sought by locating pits and valleys on the energy surface. A major strength of the algorithm lies in the fact that it does not require the number of object regions in an image to be predefined. The method has been applied on several medical image datasets and it has successfully determined both threshold and gradient parameters for different object interfaces even when some of the thresholds are almost impossible to locate in the histogram. Both accuracy and reproducibility of the method have been examined on several medical image datasets including repeat scan 3D multidetector computed tomography (CT) images of cadaveric ankles specimens. Also, the new method has been qualitatively and quantitatively compared with Otsu's method along with three other algorithms based on minimum error thresholding, maximum segmented image information and minimization of homogeneity- and uncertainty-based energy and the results have demonstrated superiority of the new method. We have developed a new automatic threshold and gradient strength selection algorithm by combining class uncertainty and spatial image gradient features. The performance of the method has been examined in terms of accuracy and reproducibility and the results found are better as compared to several popular automatic threshold selection methods.

Adaptive Minimum Error Thresholding Algorithm

A robust minimum error thresholding method is proposed to combine the three-dimensional (3D) minimum error thresholding scheme based on 2D method with the principle of rebuilding and dimension reduction of the 3D histogram. Considering the global behavior of this approach and its ability to process even illumination images only, a water flow model is used to estimate the background of uneven illumination images for improving adaptability of the proposed method. Then, the difference image between the original image and background can be readily obtained to reduce the interference of uneven illumination during the binarization process. To improve execution performance of the segmentation procedure, gamma correction is employed to enhance image in addition to a global segmentation using robust minimum error thresholding algorithm. Subsequently, image segmentation tests are carried out with even and uneven illumination, and then comparison on misclassification error and time expenditure are performed between the proposed method and other approaches, i.e., 1D/2D minimum error thresholding, Otsu thresholding algorithm based on 3D histogram rebuilding and dimensionality reduction, adaptive gray wave transformation thresholding scheme, as well as a modified FCM method. The results show that the proposed approach yields better thresholding performance than those methods.

Multitemporal Spaceborne SAR Data for Urban Change Detection in China

The objective of this research is to examine effective methods for urban change detection using multitemporal spaceborne SAR data in two rapid expanding cities in China. One scene of ERS-2 SAR C-VV image was acquired in Beijing in 1998 and in shanghai in 1999 respectively and one scene of ENVISAT ASAR C-VV image was acquired in near-anniversary dates in 2008 in Beijing and Shanghai. To compare the SAR images from different dates, a modified ratio operator that takes into account both positive and negative changes was developed to derive a change image. A generalized version of Kittler-Illingworth minimum-error thresholding algorithm was then tested to automatically classify the change image into two classes, change and no change. Various probability density functions such as Log normal, Generalized Gaussian, Nakagami ratio, and Weibull ratio were investigated to model the distribution of the change and no change classes. The results showed that Kittler-Illingworth algorithm applied to the modified ratio image is very effective in detecting temporal changes in urban areas using SAR images. Log normal and Nakagami density models achieved the best results. The Kappa coefficients of these methods were of 0.82 and 0.71 for Beijing and Shanghai respectively while the false alarm rates were 2.7% and 4.75%. The findings indicated that the change accuracies obtained using Kittler-Illingworth algorithm vary depending on how the assumed conditional class density function fits the histograms of change and no change classes.

Thresholding-based detection of fine and sparse details

Fine and sparse details appear in many quality inspection applications requiring machine vision. Especially on flat surfaces, such as paper or board, the details can be made detectable by oblique illumination. In this study, a general definition of such details is given by defining sufficient statistical properties from histograms. The statistical model allows simulation of data and comparison of methods designed for detail detection. Based on the definition, utilization of the existing thresholding methods is shown to be well motivated. The comparison shows that minimum error thresholding outperforms the other standard methods. Finally, the results are successfully applied to a paper printability inspection application, and the IGT picking assessment, in which small surface defects must be detected. The provided method and measurement system prototype provide automated assessment with results comparable to manual expert evaluations in this laborious task.

Particle swarm optimization for image minimum error thresholding

A scheme for image minimum error thresholding based on Particle Swarm Optimization(PSO) was proposed in this paper.Minimum error thresholding is a popular technique for image segmentation,and our scheme applies PSO algorithm to image minimum error thresholding.This scheme solves the problem of large calculation burden of the regular minimum error thresholding method.The results we obtained demonstrate that our scheme can efficiently reduce calculation burden of the regular method and achieve better performance on convergence and robustness,compared with Genetic Arithmetic(GA).

ITK Implementation Of The Minimum Error Image Thresholding Algorithm

An implementation of the minimum error thresholding algorithm is presented. In this implementation, two versions of the minimum error thresholding algorithm are made available, one utilizing a Gaussian- and the other utilizing a Poisson- mixture model. Two ITK classes are created: The first one (MinErrorThresholdImageCalculator) is used to compute the threshold; the second (MinErrorThresholdImageFilter) is used as an image-thresholding filter. The results indicate code correctness and are comparable to those of Otsu’s thresholding algorithm.

Verification of helical tomotherapy delivery using autoassociative kernel regressiona)

Quality assurance (QA) is a topic of major concern in the field of intensity modulated radiation therapy (IMRT). The standard of practice for IMRT is to perform QA testing for individual patients to verify that the dose distribution will be delivered to the patient. The purpose of this study was to develop a new technique that could eventually be used to automatically evaluate helical tomotherapy treatments during delivery using exit detector data. This technique uses an autoassociative kernel regression (AAKR) model to detect errors in tomotherapy delivery. AAKR is a novel nonparametric model that is known to predict a group of correct sensor values when supplied a group of sensor values that is usually corrupted or contains faults such as machine failure. This modeling scheme is especially suited for the problem of monitoring the fluence values found in the exit detector data because it is able to learn the complex detector data relationships. This scheme still applies when detector data are summed over many frames with a low temporal resolution and a variable beam attenuation resulting from patient movement. Delivery sequences from three archived patients (prostate, lung, and head and neck) were used in this study. Each delivery sequence was modified by reducing the opening time for random individual multileaf collimator (MLC) leaves by random amounts. The errof and error-free treatments were delivered with different phantoms in the path of the beam. Multiple autoassociative kernel regression (AAKR) models were developed and tested by the investigators using combinations of the stored exit detector data sets from each delivery. The models proved robust and were able to predict the correct or error-free values for a projection, which had a single MLC leaf decrease its opening time by less than 10 msec. The model also was able to determine machine output errors. The average uncertainty value for the unfaulted projections ranged from 0.4% to 1.8% of the detector signal. The low model uncertainty indicates that the AAKR model is extremely accurate in its predictions and also suggests that the model may be able to detect errors that cause the fluence to change by less than 2%. However, additional evaluation of the AAKR technique is needed to determine the minimum detectable error threshold from the compressed helical tomotherapy detector data. Further research also needs to explore applying this technique to electronic portal imaging detector data.

Generalized minimum-error thresholding for unsupervised change detection from SAR amplitude imagery

The availability of synthetic aperture radar (SAR) data offers great potential for environmental monitoring due to the insensitiveness of SAR imagery to atmospheric and sunlight-illumination conditions. In addition, the short revisit time provided by future SAR-based missions will allow a huge amount of multitemporal SAR data to become systematically available for monitoring applications. In this paper, the problem of detecting the changes that occurred on the ground by analyzing SAR imagery is addressed by a completely unsupervised approach, i.e., by developing an automatic thresholding technique. The image-ratioing approach to SAR change detection is adopted, and the Kittler and Illingworth minimum-error thresholding algorithm is generalized to take into account the non-Gaussian distribution of the amplitude values of SAR images. In particular, a SAR-specific parametric modeling approach for the ratio image is proposed and integrated into the thresholding process. Experimental results, which confirm the accuracy of the method for real X-band SAR and spaceborne imaging radar C-band images, are presented

On minimum variance thresholding

Variance-based thresholding methods could be biased from the threshold found by expert and the underlying mechanism responsible for this bias is explored in this paper. An analysis on the minimum class variance thresholding (MCVT) and the Otsu method, which minimizes the within-class variance, is carried out. It turns out that the bias for the Otsu method is due to differences in class variances or class probabilities and the resulting threshold is biased towards the component with larger class variance or larger class probability. The MCVT method is found to be similar to the minimum error thresholding.

ABNORMALITY DETECTION IN BRAIN MR IMAGES USING MINIMUM ERROR THRESHOLDING METHOD

Medical image segmentation plays an instrumental role in clinical diagnosis. An ideal medical image segmentation scheme should possess some preferred properties such as minimum user interaction, fast computation, and accurate and robust segmentation results. In this paper, an automated algorithm is proposed to enable the doctors to detect the presence of abnormal tissues in brain magnetic resonance images (MRIs). The merged image of different weighted images of each slice is obtained by averaging the intensities of pixels and is enhanced based on their local information by variance mapping. The abnormal regions are segmented by using minimum error thresholding method by formulating a criterion function. The segmentation is performed on the real data of MRI images for different abnormalities and the results are compared with radiologist labeled ground truth. Quantitative analysis between ground truth and segmented abnormal region is presented in terms of Percent Match and Correspondence Ratio. A maximum average percent match of 98.56% and correspondence ratio of 0.8892 of an MRI data is obtained.

Survey and comparative analysis of entropy and relative entropy thresholding techniques

Entropy-based image thresholding has received considerable interest in recent years. Two types of entropy are generally used as thresholding criteria: Shannon's entropy and relative entropy, also known as Kullback–Leibler information distance, where the former measures uncertainty in an information source with an optimal threshold obtained by maximising Shannon's entropy, whereas the latter measures the information discrepancy between two different sources with an optimal threshold obtained by minimising relative entropy. Many thresholding methods have been developed for both criteria and reported in the literature. These two entropy-based thresholding criteria have been investigated and the relationship among entropy and relative entropy thresholding methods has been explored. In particular, a survey and comparative analysis is conducted among several widely used methods that include Pun and Kapur's maximum entropy, Kittler and Illingworth's minimum error thresholding, Pal and Pal's entropy thresholding and Chang et al.'s relative entropy thresholding methods. In order to objectively assess these methods, two measures, uniformity and shape, are used for performance evaluation.

Segmentation algorithms for road marking digital image analysis

The road user costs accruing on road networks due to the poor quality of road markings are significant. There is therefore a need for an automated process to provide an objective assessment of the performance characteristics of road marking, such as wear and both day- and night-time visibility. Digital analysis of road surface images seems to be a versatile approach that may enable road agencies to evaluate the state of markings in an objective manner with increased accuracy. The analysis is effected by a series of processes that include image acquisition and digitisation, storage, segmentation, enhancement and feature description. This paper focuses on image segmentation, the process by which the road markings are identified from their background. The paper presents a number of techniques used for image segmentation that have been considered for inclusion in a prototype road marking analysis system. The techniques presented are the variance method, moment preserving thresholding, minimum error thresholding, relaxation thresholding, and a technique known as sub-image thresholding, which combines minimum error thresholding with a method suggested for the analysis of images of the heart. Each of the techniques is presented, discussed and evaluated for its ability to segment images containing road markings. By considering a set of appropriate test data, an investigation was carried out that indicated that the sub-image thresholding method performed satisfactorily on all images analysed in terms of accuracy and speed of computation.

Segmentation algorithms for road marking digital image analysis

The road user costs accruing on road networks due to the poor quality of road markings are significant. There is therefore a need for an automated process to provide an objective assessment of the performance characteristics of road marking, such as wear and both day- and night-time visibility. Digital analysis of road surface images seems to be a versatile approach that may enable road agencies to evaluate the state of markings in an objective manner with increased accuracy. The analysis is effected by a series of processes that include image acquisition and digitisation, storage, segmentation, enhancement and feature description. This paper focuses on image segmentation, the process by which the road markings are identified from their background. The paper presents a number of techniques used for image segmentation that have been considered for inclusion in a prototype road marking analysis system. The techniques presented are the variance method, moment preserving thresholding, minimum error thresholding, relaxation thresholding, and a technique known as sub-image thresholding, which combines minimum error thresholding with a method suggested for the analysis of images of the heart. Each of the techniques is presented, discussed and evaluated for its ability to segment images containing road markings. By considering a set of appropriate test data, an investigation was carried out that indicated that the sub-image thresholding method performed satisfactorily on all images analysed in terms of accuracy and speed of computation.

Rayleigh-distribution based minimum error thresholding for SAR images

This paper presents a minimum error thresholding (MET) algorithm under the hypothesis that the gray level histogram of SAR image fits to a mixture model of shifted Rayleigh distribution. This algorithm is applied to real SAR images and compared with traditional Otsu algorithm and other MET algorithms based on various models of histogram. The hypothesis of using Rayleigh distribution model is confirmed by Kolmogorov-Smirnov testing and the comparison results obtained show that the proposed new algorithm has good performance in thresholding SAR images.

Evaluating Fibrous Architecture of Nonwovens with Computer-Assisted Microscopy 1

A new computerized imaging, circular polarized light microscopy technique is de veloped to measure the orientation of fibers in images of nonwovens. The system consists of a modified Olympus BX50 polarized microscope, a Sony AVC-D7 video camera, and a Silicon Graphics Indy computer. There are two methods of image seg mentation : Gaussian distribution' based minimum error thresholding and Poisson dis tribution based minimum error thresholding. Segments of fiber midlines are traced with vertical and horizontal scanlines or, alternatively, whole midlines are identified recur sively with the Hilditch technique. The fiber midlines produced with this technique are traversed by a midline traversal algorithm, and the orientation distribution is obtained by least squares line fitting. The accuracy of the technique is evaluated against synthetic images composed of straight lines and sinuous curves. Kupier's statistic is used to evaluate the consistency of the fiber orientation calculations. A statistical analysis of the results shows that the proposed Hilditch connectivity, which preserves skeletoni zation, produces the most accurate results.

Notes on Poisson distribution-based minimum error thresholding

Pal and Bhandari [On object background classification. Int. J. Syst. Sci. 23 (1992) 1903–1920] modified the minimum error threshold originated by Kittler and Illingworth wMinimum error thresholding. Pattern Recognition 19 (1986) 41–47], proposing the Poisson distribution-based minimum error threshold. In this paper, Poisson distribution-based minimum error thresholding is explained using relative entropy and the maximum likelihood principle.

Minimum error thresholding: A note

We explain the minimum error thresholding originated by Kittler and Illingworth using relative entropy.

Unified formulation of a class of image thresholding techniques

In this paper, we show that Otsu's image thresholding, Kittler and Illingworth's minimum error thresholding, and Huang and Wang's fuzzy thresholding methods can be derived under a similar mathematical formulation. The difference among the three methods is the choice of different weighting functions for computing a criterion function that can be considered as a weighted summation of the image gray level histogram. We can have a better understanding of the three thresholding techniques and derive other thresholding methods based on this unified formulation.

Image thresholding: Some new techniques

Some of the existing threshold selection techniques have been critically reviewed. Two algorithms based on a new conditional entropy measure of a partitioned image have been formulated. The approximate minimum error thresholding algorithm of Kittler and Illingworth has been implemented considering the Poisson distribution for the gray level instead of the commonly used normal distribution. Justification in support of the Poisson distribution has also been given. This method is found to be much better both from the point of view of convergence and segmented output. The proposed methods have been applied on a number of images and are found to produce good results. Objective evaluation of the thresholds has been done using divergence, region uniformity, correlation between original image and the segmented image, and second order entropy.

On object background classification

Limitations of some of the existing threshold selection techniques have been discussed. The approximate minimum error thresholding algorithm of Kittler and Illingworth has been modified considering a Poisson distribution for the grey level instead of the commonly used normal distribution. Justification in support of a Poisson distribution has also been given. The modified method is found to be much better from the point of view of both convergence and segmented output. Two algorithms based on a new conditional entropy measure of a partitioned image have been formulated. The proposed methods have been applied on a number of images and are found to produce good results.