BACKGROUND AND OBJECTIVE:Periodontitis involves progressive loss of alveolar bone around the teeth. Hence, automatic alveolar bone loss measurement in periapical radiographs can assist dentists in diagnosing such disease. In this paper, we propose an automatic length-based alveolar bone loss measurement system with emphasis on a cementoenamel junction (CEJ) localization method: CEJ_LG.METHOD:The bone loss measurement system first adopts the methods TSLS and ABLifBm, which we presented previously, to extract teeth contours and bone loss areas from periodontitis radiograph images. It then applies the proposed methods to locate the positions of CEJ, alveolar crest (ALC), and apex of tooth root (APEX), respectively. Finally the system computes the ratio of the distance between the positions of CEJ and ALC to the distance between the positions of CEJ and APEX as the degree of bone loss for that tooth. The method CEJ_LG first obtains the gradient of the tooth image then detects the border between the lower enamel and dentin (EDB) from the gradient image. Finally, the method identifies a point on the tooth contour that is horizontally closest to the EDB.RESULTS:Experimental results on 18 tooth images segmented from 12 periodontitis periapical radiographs, including 8 views of upper-jaw teeth and 10 views of lower-jaw teeth, show that 53% of the localized CEJs are within 3 pixels deviation (∼ 0.15 mm) from the positions marked by dentists and 90% have deviation less than 9 pixels (∼ 0.44 mm). For degree of alveolar bone loss, more than half of the measurements using our system have deviation less than 10% from the ground truth, and all measurements using our system are within 25% deviation from the ground truth.CONCLUSION:Our results suggest that the proposed automatic system can effectively estimate degree of horizontal alveolar bone loss in periodontitis radiograph images. We believe that our proposed system, if implemented in routine clinical practice, can serve as a valuable tool for early and accurate diagnosis of alveolar bone loss in periodontal diseases and also for assessing the status of alveolar bone following various types of non surgical and surgical and regenerative therapy. For overall system improvement, a more objective comparison by using transgingival bone measurement with a periodontal probe as the ground truth and enhancing the localization algorithms of these three critical points are the two major tasks.

A cluster validity index is to evaluate the correct number of clusters when partitioning a dataset. In this paper, we propose a new cluster validity index based on two measures called dispersion and overlap for Gaussian-distributed clusters. The dispersion measure is used to estimate the situation of data spreading in a cluster. A small dispersion measure for a cluster means that data points are distributed closely in that cluster. The overlap measure represents the degree of overlap between any pair of clusters in the dataset. By combining these two metrics, we obtain a very effective new cluster validity index. Several experiments were conducted to demonstrate the effectiveness of our validity index by exercising eight synthetic datasets and four real datasets. The results show that our validity index can correctly find the optimal number of clusters that may widely differ in size, dispersion and overlapping. As compared to other ten cluster validity indices, our new index has the best performance in term of accuracy.

Cluster validity index Is used for estimating the quality of partitions to a dataset by clustering algorithms, and finding the optimal number of clusters to be partitioned. In this paper, we propose a new validity index, which is based on a dispersion measure and an overlap measure. The dispersion measure estimates the overall data density of the clusters in the dataset; whereas the overlap measure estimates the degree of isolation among all clusters. Low degree of dispersion means that the overall clusters are densely distributed and hence are compact; and low degree of overlap means that clusters are overall well separated. Thus, a good clustering result is expected to have a lower dispersion measure and a lower overlap measure. We conducted several experiments to validate the effectiveness of our validity indexing method, including artificial datasets and public real datasets. Experimental results show that our validity indexing method has superior effectiveness and reliability for estimating the optimal number of clusters that widely differ in degrees of dispersion and overlap, when compared to nine other indices proposed in the literature.

In this paper, a validity index method VDOGK, a variation of the index method VDO, for estimating the optimal number of clusters in datasets with concave-/elongated-shaped clusters is presented. The new index uses Gustafson-Kessel FCM to partition the dataset so that geometric-shape-sensitivity problem of FCM can be reduced. It is based on both dispersion and overlap measures, where the dispersion measure estimates the overall cluster compactness and the overlap measure estimates the total ambiguity degree of data belonging to any pair of clusters in the dataset. A good clustering result is expected to have both measures small. Examples of synthetic datasets comprising concave, elongated, spherical, and/or elliptical clusters are presented. Experimental results on various datasets including synthetic and real datasets from UCI Machine Learning Laboratory demonstrate that the proposed VDOGK made correct estimation on number of clusters for all nine tested datasets, whereas VDO only scored three real datasets.

Traditional fuzzy c-means (FCM) algorithm, a popular method in data clustering and image segmentation, is known to be sensitive to noise and cluster size, as it does not consider any spatial information and tends to balance cluster populations. FLICM (fuzzy local information c-means) and siibFCM (size-insensitive integrity-based FCM) are two of FCM variation algorithms, each demonstrated effective on overcoming noise or size sensitivity problem. This paper presents a variation of siibFCM, called noise- and size-insensitive integrity-based FCM and denoted as nsiibFCM. Similar to FLICM, nsiibFCM incorporates a local similarity measure based on intensity and purity of each neighboring pixel to remove noise while preserving details, where purity is defined as the normalized difference between the distance from the data point to the center of its assigned cluster and the distance from the data point to its nearest cluster center. Meanwhile, nsiibFCM uses a condition value calculated by using both size and integrity of a cluster, which are presented in siibFCM, to prevent centers of small clusters from drifting toward the adjacent larger and dispersive distributed clusters. Experimental results on both synthetic and real-world images show that our proposed nsiibFCM can effectively partition noisy images with balance- or unbalance-populated and dispersive-distributed clusters.

BACKGROUND AND OBJECTIVE:Periodontitis involves progressive loss of alveolar bone around the teeth. Hence, automatic alveolar bone-loss (ABL) measurement in periapical radiographs can assist dentists in diagnosing such disease. In this paper, we propose an effective method for ABL area localization and denote it as ABLIfBm.METHOD:ABLIfBm is a threshold segmentation method that uses a hybrid feature fused of both intensity and texture measured by the H-value of fractional Brownian motion (fBm) model, where the H-value is the Hurst coefficient in the expectation function of a fBm curve (intensity change) and is directly related to the value of fractal dimension. Adopting leave-one-out cross validation training and testing mechanism, ABLIfBm trains weights for both features using Bayesian classifier and transforms the radiograph image into a feature image obtained from a weighted average of both features. Finally, by Otsu's thresholding, it segments the feature image into normal and bone-loss regions.RESULTS:Experimental results on 31 periodontitis radiograph images in terms of mean true positive fraction and false positive fraction are about 92.5% and 14.0%, respectively, where the ground truth is provided by a dentist. The results also demonstrate that ABLIfBm outperforms (a) the threshold segmentation method using either feature alone or a weighted average of the same two features but with weights trained differently; (b) a level set segmentation method presented earlier in literature; and (c) segmentation methods based on Bayesian, K-NN, or SVM classifier using the same two features.CONCLUSION:Our results suggest that the proposed method can effectively localize alveolar bone-loss areas in periodontitis radiograph images and hence would be useful for dentists in evaluating degree of bone-loss for periodontitis patients.

Data clustering technique can be used in many fields, such as data mining, statistical data analysis, image analysis, pattern recognition, etc. Good clustering can result in computational reduction in related application programs; however, it is hard to achieve without knowing how many clusters that a data set should be partitioned, which is common in many applications. The way to find the optimal number of clusters is called cluster validity. In this paper, we proposed a new cluster validity indexing method that aims to solve cluster overlapping problem. Our method adapts the concept of cluster validity index defined as the ratio of compactness and separation and enhances it by integrating an entropy-based weight to the definition of separation so that the new weighted-separation of two overlapped clusters will be larger than that of two non-overlapped clusters, where the distance between the two cluster-centroids are the same. Experiments on six synthetic datasets comprising 3 to 10 clusters with some clusters overlapped each other demonstrate that our proposed method achieves 100% accuracy of validity index for all these datasets and is superior to all other compared methods.

One approach to image segmentation is to apply a data clustering method such as fuzzy c-means (FCM) to the pixels of the image. FCM and its variations all require an appropriately predefined number of clusters for a given set of data in order to obtain a correct clustering result However, an optimal number of clusters is usually unknown. Mok et al. proposed a robust adaptive clustering analysis method to identify the desired number of clusters and produce a reliable clustering solution at the same time based on a judgment matrix which represents the clustering relationship between any two data points. When applying the Mok's method to image segmentation, the method becomes very impractical because the judgment matrix is too huge to be handled efficiently. In this paper, a more efficient clustering analysis method is proposed for segmenting images with noise. The efficiency comes from the size of the judgment matrix which is only 256 by 256. Experimental results show that our method is better than Mok's method for segmenting both synthetic and real images with noise.

We propose an effective method to detect alveolar bone-loss areas in dental periapical radiographs in this paper. By analyzing the texture of alveolar bone tissues measured by Gray Level Co-occurrence Matrix (GLCM) or the H-value of fractal Brownian motions (fBm) model, we transfer radiograph images into bone-texture images. Then by auto-thresholding, we segment the bone-texture images into normal and bone-loss regions. Experimental results on six periapical images demonstrate that our method using fBm-H value as the texture feature can detect bone-loss areas best conforming to the areas marked by a dentist both visually and quantitatively among all the features used.

Teeth segmentation for periapical raidographs is one of the most critical tasks for effective periapical lesion or periodontitis detection, as both types of anomalies usually occur around tooth boundaries and dental radiographs are often subject to noise, low contrast, and uneven illumination. In this paper, we propose an effective scheme to segment each tooth in periapical radiographs. The method consists of four stages: image enhancement using adaptive power law transformation, local singularity analysis using Hölder exponent, tooth recognition using Otsu's thresholding and connected component analysis, and tooth delineation using snake boundary tracking and morphological operations. Experimental results of 28 periapical radiographs containing 106 teeth in total and 75 useful for dental examination demonstrate that 105 teeth are successfully isolated and segmented, and the overall mean segmentation accuracy of all 75 useful teeth in terms of (TP, FP) is (0.8959, 0.0093) with standard deviation (0.0737, 0.0096), respectively.

Automatic detection of alveolar bone-loss areas in dental periapical radiographs is a very challenging task because of the common uneven illumination problem of dental radiographs and complex topology of bone-loss areas. In this paper, we propose an effective automatic detection method ABL-IfBm, which uses weighted average of both the intensity and the texture measured by the H-value of fractal Brownian motions (fBm) model. The weights are trained with receiver operating characteristics (ROC) curve based on leave-one-out cross validation mechanism and the principle of the minimum area under the ROC curve (AUC). Through the weighted average of both features, radiograph images are transformed into feature images with the histogram near bimodal distribution. Finally, feature images are segmented into normal and bone-loss regions by Otsu's auto-thresholding. We test on eight periodontitis radiograph images using the proposed ABL-IfBm, the methods with only the feature of fBm-H or the intensity, and a method based on level set segmentation, respectively. Experimental results showed that among all the test methods, our proposed ABL-IfBm has the highest average TPVF and the lowest average FPVF, when compared with the ground truth (GT) provided by dentists.

In this paper, we present a PET and MR brain image fusion method based on wavelet transform for low- and high-activity brain image regions, respectively. Our method can generate very good fusion result by adjusting the anatomical structural information in the gray matter (GM) area, and then patching the spectral information in the white matter (WM) area after the wavelet decomposition and gray-level fusion. We used normal axial, normal coronal, and Alzheimer's disease brain images as the three datasets for testing and comparison. Experimental results showed that the performance of our fusion method is better than that of IHS+RIM fusion method in terms of spectral discrepancy (SD) and average gradient (AG). In fact, our method is superior to IHS+RIM method both visually and quantitatively.

In this paper, we present a classification system for differentiating malignant pulmonary nodules from benign nodules in computed tomography (CT) images based on a set of fractal features derived from the fractional Brownian motion (fBm) model. In a set of 107 CT images obtained from 107 different patients with each image containing a solitary pulmonary nodule, our experimental result show that the accuracy rate of classification and the area under the Receiver Operating Characteristic (ROC) curve are 83.11% and 0.8437, respectively, by using the proposed fractal-based feature set and a support vector machine classifier. Such a result demonstrates that our classification system has highly satisfactory diagnostic performance by analyzing the fractal features of lung nodules in CT images taken from a single post-contrast CT scan.

Fuzzy c-means (FCM) is one of the most popular techniques for data clustering. Since FCM tends to balance the number of data points in each cluster, centers of smaller clusters are forced to drift to larger adjacent clusters. For datasets with unbalanced clusters, the partition results of FCM are usually unsatisfactory. Cluster size insensitive FCM (csiFCM) dealt with ''cluster-size sensitivity'' problem by dynamically adjusting the condition value for the membership of each data point based on cluster size after the defuzzification step in each iterative cycle. However, the performance of csiFCM is sensitive to both the initial positions of cluster centers and the ''distance'' between adjacent clusters. In this paper, we present a cluster size insensitive integrity-based FCM method called siibFCM to improve the deficiency of csiFCM. The siibFCM method can determine the membership contribution of every data point to each individual cluster by considering cluster's integrity, which is a combination of compactness and purity. ''Compactness'' represents the distribution of data points within a cluster while ''purity'' represents how far a cluster is away from its adjacent cluster. We tested our siibFCM method and compared with the traditional FCM and csiFCM methods extensively by using artificially generated datasets with different shapes and data distributions, synthetic images, real images, and Escherichia coli dataset. Experimental results showed that the performance of siibFCM is superior to both traditional FCM and csiFCM in terms of the tolerance for ''distance'' between adjacent clusters and the flexibility of selecting initial cluster centers when dealing with datasets with unbalanced clusters.

Dental radiographs play an important role for dental diagnosis, as most anomalies are hidden under the surface and cannot be seen during a visual examination. For effective computer-aided dental diagnosis, accurate teeth segmentation is one of the most critical tasks, because cysts and inflammatory lesions usually occur around tooth periapical (tooth-roots) areas and these areas in radiographs are often subject to noise, low contrast, and uneven illumination. In this paper, we propose an effective scheme to segment each tooth in dental periapical radiographs based on local singularity analysis. At first, a proposed adaptive power law transformation is applied to reduce variations of contrasts between teeth and alveolar bones (gums). Then local singularities measured by Hölder exponent are computed to obtain a structure image in which the structures of teeth are much smoother than the structures of gums. Otsu's thresholding is applied to segment teeth from gums and finally, connected component analysis and morphological operations are applied to isolate each tooth. Experimental results demonstrate that out of 18 teeth in six tested periapical images, all teeth are successfully segmented with 17 extracted tooth-contours almost completely conforming to human visual perception.

This paper presents an enhanced dental identification method based on both the contours of teeth and dental works. To reduce the alignment error caused from unreliable contours, we propose a point-reliability measuring method and weigh each point based on its reliability when calculating the Hausdorff distance (HD) between the contours. For reducing the alignment error caused from incomplete tooth contours, we propose an outlier detection method to prune the outliers from each contour and realign the pruned contours. And for compensating the error when matching with the spatial feature of dental works due to imperfect alignment of the teeth in which they reside, we propose using an additional alignment-invariant frequency feature of dental works. Experimental results show that our method can achieve (1) 94.3% and 100% image retrieval accuracy of the top-1 and -5 retrievals, respectively, when matching with the weighted HD for the pruned contour of a single tooth; (2) 100% accuracy of top-2 (top 6%) image retrievals when matching with both contours of teeth and dental works.

Tooth isolation is a very important pre-processing step for both computer-aided dental diagnosis and automatic dental identification systems. The accuracy of tooth isolation will directly affect the accuracy of feature extraction and thereby the final results of both types of systems. This paper presents a very effective and fully automatic tooth isolation method for bitewing dental X-ray images. Our upper-lower jaw separation mechanism is based on gray-scale integral projection to avoid possible information loss and incorporates with angle adjustment to handle skewed images. In single tooth isolation, we propose an adaptive windowing scheme for locating gap valleys to improve the accuracy. Furthermore, excessive isolation-curves can be removed and separating lines can be added to indicate the locations of missing teeth. Experimental results show that our method achieves higher tooth isolation accuracy rates for both upper- and lower-jaw images, when compared to Nomir and Abdel-Mottaleb's method.

Dental radiographs have been widely used by dentists in finding periodontal lesions or monitoring the progress of the periodontal defect treatment that is either impossible or difficult for human naked eyes. In this paper we propose a fully automatic gums lesion detection method for periapical dental X-ray images. The method includes two stages: (i) teeth- parts removing and (ii) lesion-region localization and severance labeling. In stage (i), morphological operations and histogram equalizations are first applied to enlarge the contrast between teeth and gums parts, then thresholding is used to separate the two types of regions. In stage (ii), gums-parts are first segmented into regions of normal, possible lesion or lesion, and serious lesion using a level set method with three coupled level set functions, and then the possible lesion or lesion region are further segmented into lesion and possible lesion regions using the same level set method. The experimental results demonstrate that our proposed method can detect and label all lesion regions in six periapical dental X-ray images which conform very well to human visual perception, and is robust to illumination variation to ± 30 intensity levels, as well.