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Accurate and reliable assessment of chlorophyll-a (Chl-a) concentration in turbid waters by remote sensing is challenging due to optical complexity of case II waters. Recently, an optimization procedure based on minimizing root mean square error (RMSE) with three-band model was suggested to retrieve the Chl-a concentration in the Pearl River Estuary (PRE) in China. However, it is sensitive to initial values of model parameters and it doesn’t consider other two bands information to determine each optimal band. To estimate the Chl-a concentration according to information of all bands without initial values, we proposed an optimization procedure based on maximizing correlation of the Chl-a concentration in situ and the Chl-a concentration estimated. Firstly, correlations are computed with the three-band model, in which each band varies from the minimal value to the maximal value. Secondly, the sum of correlations for all values of other two bands is computed to find the optimal value for the first band. Lastly, the sum of correlations for all values of other one band with the first optimal band is computed to find the second and third optimal bands. The calibrated three-band model is applied to retrieve the Chl-a concentration from the reflectance data in the PRE on May 16, 2008. RMSE and correlation indices of our method and two state-of-the-art methods in this dataset are shown the effectiveness of our method. These findings imply that the extensive database of remote sensing could be used to quantitatively monitor the Chl-a concentration in the PRE.

Kernel density estimators (KDE) used for many medical image applications only consider the intensity information of each pixel or its neighbors without the ability of expressing the structure and shape of tissues and organs, and they suffer from boundary bias problem. In this paper, we propose a new first-order kernel density estimation (FOKDE) method for 1D intensity information and 2D spatial information of medical image in two steps. First, the FOKDE of intensity information is estimated and applied to medical image segmentation with the multi-thresholding algorithm. Second, we estimate the FOKDE of spatial information on the initial segmentation, which can express the structure and shape of organs and tissues. In order to evaluate the FOKDE and KDE of the 2D spatial information, we apply them to medical image segmentation with the hill-climbing strategy. Density estimation experiments and segmentation application results on the simulated dataset and real abdomen CT images show us that the FOKDE has smaller boundary bias than the KDE, and that it can estimate the structure and shape of tissues and organs with spatial information effectively.

Clustering gene expression data is an important research topic in bioinformatics because knowing which genes act similarly can lead to the discovery of important biological information. Many clustering algorithms have been used in the field of gene clustering. The multivariate Gaussian mixture distribution function was frequently used as the component of the finite mixture model for clustering, however the clustering cannot be restricted to the normal distribution in the real dataset. In order to make the cluster algorithm strong adaptability, this paper proposes a new scheme for clustering gene expression data based on the multivariate elliptical contoured mixture models (MECMMs). To solve the problem of over-reliance on the initialization, we propose an improved expectation maximization (EM) algorithm by adding and deleting initial value for the classical EM algorithm, and the number of clusters can be treated as a known parameter and inferred with the QAIC criterion. The improved EM algorithm based on the MECMMs is tested and compared with some other clustering algorithms, the performance of our clustering algorithm has been extensively compared over several simulated and real gene expression datasets. Our results indicated that improved EM clustering algorithm is superior to the classical EM algorithm and the support vector machines (SVMs) algorithm, and can be widely used for gene clustering.

An important but difficult problem of Gaussian mixture models (GMM) for medical image analysis is estimating and testing the number of components by model selection criterion. There are many available methods to estimate the k based on likelihood function. However, some of them need the maximum number of components is known as priori and data is usually over-fitted by them when log-likelihood function is far larger than penalty function. We investigate the log-characteristic function of the GMM to estimate the number of models adaptively for medical image. Our method defines the sum of weighted real parts of all log-characteristic functions of the GMM as a new convergent function and model selection criterion. Our new model criterion makes use of the stability of the sum of weighted real parts of all log-characteristic functions of the GMM when the number of components is larger than the true number of components. The univariate acidity, simulated 2D datasets and real 2D medical images are used to test and experiment results suggest that our method without any priori is more suited for large sample applications than other typical methods.