基于三维分数阶微分增强的边缘曲面重构算法

马瑜; 赵九龙; 余婷; 李爽

doi:doi:10.3788/gzxb20144310.1011004

光子学报, 2014, 43 (10): 1011004, 网络出版: 2014-11-06

基于三维分数阶微分增强的边缘曲面重构算法

The Reconstruction Algorithm of Boundary Surfaces Based on the 3D Fractional Differential Enhancement

论文大纲

马瑜 ^1,*赵九龙 ¹余婷 ¹李爽 ²

作者单位

¹ 宁夏大学研究生院,银川 750021

² 上海交通大学电子与电气工程学院自动化系图像处理与模式识别研究所,上海 200240

摘要

提出一种基于三维分数阶微分增强的三维边缘曲面重构算法,可重构出更多的三维不规则目标的细节结构信息,克服了原边缘曲面重构算法重构细节信息不充分的缺点.根据分数阶微分傅里叶变换的可分离性原理,将二维分数阶微分算子推广至三维并推导出三维分数阶离散滤波模板,利用三维分数阶微分对图像具有非线性增强作用的特性,对三维切片数据场进行三维分数阶微分增强.与传统三维边缘曲面重构算法相比,经过三维分数阶微分增强且采用分数阶梯度追踪细节改进的重构算法,能够重构出更丰富的三维目标细节结构信息.算法运用于神经元细胞的共焦显微图像中三维不规则目标的边缘曲面重构,实验结果验证了该算法的正确性和高效性,可推广应用至生物医学领域的三维可视化研究.

Abstract

An improved reconstruction algorithm of the boundary surfaces within 3D images was proposed based on the fractional differential, which can reconstruct more detailed structures of the 3D irregular biomedical objectives. Thus, the deficiency of reconstruction more detailed information in the was proposed based on the fractional differential, which can reconstruct more detailed structures of the 3D irregular biomedical objectives. Thus, the deficiency of reconstruction more detailed information in the traditional algorithm was overcome. According to the separateness of the Fourier Transformation of the fractional differential, the 2D calculus was extended to 3D, and the 3D discrete templates were deduced. Due to the nonlinear enhancement, the 3D fractional differential can enhancement the 3D slice data significantly. By comparison with the traditional reconstruction method of the 3D boundary surfaces, the improved algorithm could detect and extract more detailed 3D structure information by using the 3D fractional differential. The proposed algorithm was applied in the reconstruction of the 3D irregular structure of the neuron within confocal microscopy images, which demonstrated the high efficiency and property, it can be easily extended to other research fields of 3D visualization.

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马瑜, 赵九龙, 余婷, 李爽. 基于三维分数阶微分增强的边缘曲面重构算法[J]. 光子学报, 2014, 43(10): 1011004. MA Yu, ZHAO Jiu-long, YU Ting, LI Shuang. The Reconstruction Algorithm of Boundary Surfaces Based on the 3D Fractional Differential Enhancement[J]. ACTA PHOTONICA SINICA, 2014, 43(10): 1011004.

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