In this paper, we consider the norms related to spectral geometric means and geometric means. When A and B are positive and invertible, we have ||A<sup>-1</sup>#B|| ≤ ||A<sup>-1</sup>σ<sub...In this paper, we consider the norms related to spectral geometric means and geometric means. When A and B are positive and invertible, we have ||A<sup>-1</sup>#B|| ≤ ||A<sup>-1</sup>σ<sub>s</sub>B||. Let H be a Hilbert space and B(H) be the set of all bounded linear operators on H. Let A ∈ B(H). If ||A#X|| = ||Aσ<sub>s</sub>X||, ?X ∈ B(H)<sup>++</sup>, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσ<sub>s</sub>B||, then is commutative.展开更多
Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we in...Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we investigated the movement regulation. Two movement patterns are extracted from various trajectories through analysis on turning angle. Then we applied this classification on trajectory regulation on the compound gradient field, and theoretical results corresponded with experiments well, which can initially verify the conclusion. Our breakthrough is performed computational geometric analysis on trajectories. Several independent features were combined to describe movement properties by principal composition analysis (PCA) and support vector machine (SVM). After normalizing all data sets, no-supervising machine learning was processed along with some training under certain supervision. The final classification results performed perfectly, which indicates the further application of such computational analysis in biology researches combining with machine learning.展开更多
边缘信息对图像分割是十分重要的。把图像的边缘信息融入C-V模型(active contours without edges),提出一个新的几何模型,它同时利用同质区域信息和边缘信息使演化曲线在目标边缘处停止。实验显示:新模型能够克服C-V模型的一些缺点;在...边缘信息对图像分割是十分重要的。把图像的边缘信息融入C-V模型(active contours without edges),提出一个新的几何模型,它同时利用同质区域信息和边缘信息使演化曲线在目标边缘处停止。实验显示:新模型能够克服C-V模型的一些缺点;在减少分割时间的同时,对目标灰度不均匀或背景灰度不均匀、含弱边缘或强噪声的图像,分割效果不仅优于C-V模型,也优于C-V模型的两个最新改进模型(LBF和GACV)。展开更多
文摘In this paper, we consider the norms related to spectral geometric means and geometric means. When A and B are positive and invertible, we have ||A<sup>-1</sup>#B|| ≤ ||A<sup>-1</sup>σ<sub>s</sub>B||. Let H be a Hilbert space and B(H) be the set of all bounded linear operators on H. Let A ∈ B(H). If ||A#X|| = ||Aσ<sub>s</sub>X||, ?X ∈ B(H)<sup>++</sup>, then A is a scalar. When is a C*-algebra and for any , we have that ||logA#B|| = ||logAσ<sub>s</sub>B||, then is commutative.
文摘Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we investigated the movement regulation. Two movement patterns are extracted from various trajectories through analysis on turning angle. Then we applied this classification on trajectory regulation on the compound gradient field, and theoretical results corresponded with experiments well, which can initially verify the conclusion. Our breakthrough is performed computational geometric analysis on trajectories. Several independent features were combined to describe movement properties by principal composition analysis (PCA) and support vector machine (SVM). After normalizing all data sets, no-supervising machine learning was processed along with some training under certain supervision. The final classification results performed perfectly, which indicates the further application of such computational analysis in biology researches combining with machine learning.
文摘边缘信息对图像分割是十分重要的。把图像的边缘信息融入C-V模型(active contours without edges),提出一个新的几何模型,它同时利用同质区域信息和边缘信息使演化曲线在目标边缘处停止。实验显示:新模型能够克服C-V模型的一些缺点;在减少分割时间的同时,对目标灰度不均匀或背景灰度不均匀、含弱边缘或强噪声的图像,分割效果不仅优于C-V模型,也优于C-V模型的两个最新改进模型(LBF和GACV)。
