• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.3
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• pp.1434-1449
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• 2019

Video object segmentation is a significant task in computer vision, but its performance is not very satisfactory. A method of video object segmentation using weakly temporal information is presented in this paper. Motivated by the phenomenon in reality that the motion of the object is a continuous and smooth process and the appearance of the object does not change much between adjacent frames in the video sequences, we use a feed-forward architecture with motion estimation to predict the mask of the current frame. We extend an additional mask channel for the previous frame segmentation result. The mask of the previous frame is treated as the input of the expanded channel after processing, and then we extract the temporal feature of the object and fuse it with other feature maps to generate the final mask. In addition, we introduce multi-mask guidance to improve the stability of the model. Moreover, we enhance segmentation performance by further training with the masks already obtained. Experiments show that our method achieves competitive results on DAVIS-2016 on single object segmentation compared to some state-of-the-art algorithms.