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

作　　者：马瑜[1] 赵九龙[1] 余婷[1] 李爽[2] 

机构地区：[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

出　　处：《光子学报》2014年第10期21-28,共8页Acta Photonica Sinica

基　　金：国家自然科学基金(No.31060233);宁夏回族自治区2012年科技攻关计划项目(No.2012ZYG011)资助

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.An improved reconstruction algorithm of the boundary surfaces within 3Dimages was proposed based on the fractional differential,which can reconstruct more detailed structures of the 3Dirregular 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 2Dcalculus was extended to 3D,and the 3Ddiscrete templates were deduced.Due to the nonlinear enhancement,the 3Dfractional differential can enhancement the 3Dslice data significantly.By comparison with the traditional reconstruction method of the 3Dboundary surfaces,the improved algorithm could detect and extract more detailed 3Dstructure information by using the 3D fractional differential.The proposed algorithm was applied in the reconstruction of the 3Dirregular 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 3Dvisualization.

关 键 词：科学可视化 三维图像 共焦显微图像 三维分数阶微分 增强 边缘曲面重构 追踪 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]