Automated reconstruction of neuronal morphology based on local geometrical and global structural models.
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Digital reconstruction of neurons from microscope images is an important and challenging problem in neuroscience.We first formulate a model structure, then develop an algorithm for computing it by carefully taking into account morphological characteristics of neurons, as well as the image properties under typical imaging protocols.The method has been tested on the data sets used in the DIADEM competition and produced promising results for four out of the five data sets.
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PubMed Central - PubMed
Affiliation: Qiushi Academy for Advanced Studies, Zhejiang University, 38 ZheDa Road, Hangzhou 310027, China. tingzhao@gmail.com
ABSTRACT
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Digital reconstruction of neurons from microscope images is an important and challenging problem in neuroscience. In this paper, we propose a model-based method to tackle this problem. We first formulate a model structure, then develop an algorithm for computing it by carefully taking into account morphological characteristics of neurons, as well as the image properties under typical imaging protocols. The method has been tested on the data sets used in the DIADEM competition and produced promising results for four out of the five data sets. Related in: MedlinePlus |
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Mentions: The shape of a neurite fiber can be approximated as a series of circular cross sections along a continuous curve (Fig. 1) that are deformed to an ellipse along the axial direction by the anisotropy of the point spread function (PSF) of the microscope. More formally, its surface N(t,u) for parameters t,u ∈ [0,1] can be defined as:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ N(t,u) = C(t) + O(u,t) \mathbf{R}(t) \mathbf{A} $$\end{document}where C(t) = ( x(t), y(t), z(t) ) is a continuous and differentiable curve, O(u,t) = ( r(t) cos2πu, r(t) sin 2πu, 0 ) is a circle of radius r(t) in the z = 0 plane,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbf{R}(t) = \left( \begin{array}{c} \mathbf{r_y} \times \mathbf{r_z} \\ \mathbf{r_y} = \mathbf{k} \times \mathbf{r_z} \\[4pt] \mathbf{r_z} = \dfrac{\Delta C(t)}{\/ \Delta C(t) \/} \end{array} \right) $$\end{document} is a fixed matrix at each value of t that maps the circle from the z = 0 plane into a plane perpendicular to the tangent of the curve C,1 and\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathbf{A} = \left( \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & a(t) \end{array} \right) $$\end{document}stretches or squeezes the z-dimension by the parameter a(t) > 0 reflecting the asymmetry of the PSF and the sampling rate.Fig. 1 |
View Article: PubMed Central - PubMed
Affiliation: Qiushi Academy for Advanced Studies, Zhejiang University, 38 ZheDa Road, Hangzhou 310027, China. tingzhao@gmail.com