Automated cell segmentation and tracking are critical for quantitative analysis of cell cycle behavior using time-lapse fluorescence microscopy. However, the complex, dynamic cell cycle behavior poses new challenges to the existing image segmentation and tracking methods. This paper presents a fully automated tracking method for quantitative cell cycle analysis. In the proposed tracking method, we introduce a neighboring graph to characterize the spatial distribution of neighboring nuclei, and a novel dissimilarity measure is designed based on the spatial distribution, nuclei morphological appearance, migration, and intensity information. Then, we employ the integer programming and division matching strategy, together with the novel dissimilarity measure, to track cell nuclei. We applied this new tracking method for the tracking of HeLa cancer cells over several cell cycles, and the validation results showed that the high accuracy for segmentation and tracking at 99.5% and 90.0%, respectively. The tracking method has been implemented in the cell–cycle analysis software package, DCELLIQ, which is freely available.

It is well known that the convergence rate of the expectation-maximization (EM) algorithm can be faster than those of convention first-order iterative algorithms when the overlap in the given mixture is small. But this argument has not been mathematically proved yet. This article studies this problem asymptotically in the setting of gaussian mixtures under the theoretical framework of Xu and Jordan (1996). It has been proved that the asymptotic convergence rate of the EM algorithm for gaussian mixtures locally around the true solution Theta* is o(e(0. 5-epsilon)(Theta*)), where epsilon > 0 is an arbitrarily small number, o(x) means that it is a higher-order infinitesimal as x --> 0, and e(Theta*) is a measure of the average overlap of gaussians in the mixture. In other words, the large sample local convergence rate for the EM algorithm tends to be asymptotically superlinear when e(Theta*) tends to zero.

Human infertility is considered as a serious disease of the reproductive system that affects more than 10% of couples across the globe and over 30% of the reported cases are related to men. The crucial step in the assessment of male infertility and subfertility is semen analysis that strongly depends on the sperm head morphology, i.e., the shape and size of the head of a spermatozoon. However, in medical diagnosis, the morphology of the sperm head is determined manually, and heavily depends on the expertise of the clinician. Moreover, this assessment as well as the morphological classification of human sperm heads are laborious and non-repeatable, and there is also a high degree of inter and intra-laboratory variability in the results. In order to overcome these problems, we propose a specialized convolutional neural network (CNN) architecture to accurately classify human sperm heads based on sperm images. It is carefully designed with several layers, and multiple filter sizes, but fewer filters and parameters to improve efficiency and effectiveness. It is demonstrated that our proposed architecture outperforms state-of-the-art methods, exhibiting 88% recall on the SCIAN dataset in the total agreement setting and 95% recall on the HuSHeM dataset for the classification of human sperm heads. Our proposed method shows the potential of deep learning to surpass embryologists in terms of reliability, throughput, and accuracy.

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