Benson S. Y. Lam

General Retinal Vessel Segmentation Using Regularization-Based Multiconcavity Modeling

Detecting blood vessels in retinal images with the presence of bright and dark lesions is a challenging unsolved problem. In this paper, a novel multiconcavity modeling approach is proposed to handle both healthy and unhealthy retinas simultaneously. The differentiable concavity measure is proposed to handle bright lesions in a perceptive space. The line-shape concavity measure is proposed to remove dark lesions which have an intensity structure different from the line-shaped vessels in a retina. The locally normalized concavity measure is designed to deal with unevenly distributed noise due to the spherical intensity variation in a retinal image. These concavity measures are combined together according to their statistical distributions to detect vessels in general retinal images. Very encouraging experimental results demonstrate that the proposed method consistently yields the best performance over existing state-of-the-art methods on the abnormal retinas and its accuracy outperforms the human observer, which has not been achieved by any of the state-of-the-art benchmark methods. Most importantly, unlike existing methods, the proposed method shows very attractive performances not only on healthy retinas but also on a mixture of healthy and pathological retinas.

A Novel Vessel Segmentation Algorithm for Pathological Retina Images Based on the Divergence of Vector Fields

In this paper, a method is proposed for detecting blood vessels in pathological retina images. In the proposed method, blood vessel-like objects are extracted using the Laplacian operator and noisy objects are pruned according to the centerlines, which are detected using the normalized gradient vector field. The method has been tested with all the pathological retina images in the publicly available STARE database. Experiment results show that the method can avoid detecting false vessels in pathological regions and can produce reliable results for healthy regions.

Assessment of Microarray Data Clustering Results Based on a New Geometrical Index for Cluster Validity

A measurement of cluster quality is often needed for DNA microarray data analysis. In this paper, we introduce a new cluster validity index, which measures geometrical features of the data. The essential concept of this index is to evaluate the ratio between the squared total length of the data eigen-axes with respect to the between-cluster separation. We show that this cluster validity index works well for data that contain clusters closely distributed or with different sizes. We verify the method using three simulated data sets, two real world data sets and two microarray data sets. The experiment results show that the proposed index is superior to five other cluster validity indices, including partition coefficients (PC), General silhouette index (GS), Dunn’s index (DI), CH Index and I-Index. Also, we have given a theorem to show for what situations the proposed index works well.

A curve tracing algorithm using level set based affine transform

Extracting centrelines from an unordered data set is an important problem in image processing and pattern recognition. The key strategy of existing methods is to find a curve placed at the middle of the data points. However, if the data set contains noise, these algorithms will converge to a local minimum. In this paper, we propose a new technique, which combines the level set and affine transform methods. In this approach, the user-defined initial curve is driven towards the object data. Experimental results show that the proposed method can enhance the performance of a class of curve extraction algorithms effectively.

A new cluster validity index for data with merged clusters and different densities

Several cluster validity measures have been proposed for evaluating clustering results. However, existing methods may not work well for the following two kinds of data sets. The first one is that the data set contains cluster groups with different densities. The second one is that some of the cluster groups are closely positioned. In this paper, we introduce a new cluster validity index. In this method, we define the index as the ratio between the squared total length of the data eigen-axes and the between-cluster separation. Compared with existing cluster validity indices, the proposed index produces more accurate results and is able to handle the two kinds of data sets mentioned above.

Blood Vessel Extraction Based on Mumford Shah Model and Skeletonization

Locating blood vessels in a retinal image has found wide applications in medical image for diagnosis of diseases. However, due to the presence of noise and uneven distributed image intensity, this is still a challenging task. In this paper, we introduce a new method based on the features that the blood vessel must be a thin concave connected region. Based on Mumford-Shah (MS) model and skeletonization method, the proposed method is able to extract many small branches of vessels. Experimental results show that the proposed method outperforms existing methods and able to yield good results in real world data sets

Improved Clustering Algorithm Based on Calculus of Variation

A major problem in data clustering is the degradation in performance due to outliers. We have developed a robust method to solve this problem using the l2m-FCM algorithm. However, this method has to solve a non-linear equation and can converge to a local optimum. In this paper, we introduce a regularized version of the l2m-FCM algorithm. The essential idea is to constrain the descent direction in the optimization procedure. We employ a novel method to correct the direction using the calculus of variations. Experimental results show that the proposed method has a better performance than seven other clustering algorithms for both synthetic and real world data sets

Jump point detection using empirical mode decomposition

Abstract Real estate is an important form of investment in Hong Kong. Recent researches on the analysis of real estate market have revealed that jump points in the housing price time series play an essential role in the Hong Kong economy. Detecting such jump points thus becomes important as they represent vital findings that enable policy-makers and investors to look forward. In this paper, we propose a jump point detection methodology, which makes use of the empirical mode decomposition algorithm and a derivative-based detector, to detect jump points in the time series of some housing price indices in Hong Kong. Experimental results reveal that our proposed method has a superior performance and outperforms the current state-of-the-art wavelet approach.

Complex curve tracing based on a minimum spanning tree model and regularized fuzzy clustering

The fuzzy curve-tracing (FCT) algorithm can be used to extract a smooth curve from unordered noisy data. However, the model produces good results only if the curve shape is either opened or closed. In this paper, we propose several techniques to generalize the FCT algorithm for tracing complicated curves. We develop a modified clustering algorithm that can produce cluster centers less dependent on the pre-specified number of clusters, which makes the reordering of cluster centers easier. We make use of the Eikonal equation and the Prims algorithm to form the initial curve, which may contain sharp corners and intersections. We also introduce a more powerful curve smoothing method. Our generalized FCT algorithm is able to trace a wide range of complicated curves, such as handwritten Chinese characters.

A Regularized Clustering Algorithm Based on Calculus of Variations

Microarray data clustering has drawn great attention in recent years. However, a major problem in data clustering is convergence to a local optimal solution. In this paper, we introduce a regularized version of the l2m-FCM algorithm to resolve this problem. The strategy is to constrain the descent direction in the optimization procedure. For this we employ a novel method, calculus of variations, to correct the direction. Experimental results show that the proposed method has a better performance than seven other clustering algorithms for three synthetic and six real world data sets. Also, the proposed method produces reliable results for synthetic data sets with a large number of groups, which is a challenging problem for many clustering algorithms. Our method has been applied to microarray data classification with good results.