Abstract Fractal dimension (FD) has become a very useful tool in neuroscience with a wide range of applications in characterizing several neurodegenerative diseases. The most commonly used method for computing the FD of brain tissues is box-counting. This technique performs very well on 2D images and 3D volumes; however, it presents several drawbacks when processing cortical surfaces in 3D. In this study, we present a MATLAB program for computing the FD of 3D surfaces based on spherical harmonics. We developed a novel MATLAB program, called UJA-SHFD, based on a spherical harmonics FD algorithm which overcomes the limitations of the classical box-counting algorithm when processing 3D surfaces. Moreover, spherical-harmonic-based FD (SHFD) enables the processing of both global (providing a single FD value for the entire surface) and local level assessments in each cortical surface vertex. UJA-SHFD has been specifically designed and tested for processing cortical surfaces obtained from the FreeSurfer software suite. Nevertheless, the program can also process any kind of surface in the Wavefront OBJ format. UJA-SHFD can be used both through a graphical user interface and at the command line. The present study demonstrates the usefulness of UJA-SHFD through its application to a neuroimaging study looking at the progression of brain atrophy in Alzheimer’s disease. UJA-SHFD is a novel MATLAB program with the goal of developing neuroimaging analyses of FD computation for the investigation of brain morphological changes in neurodegenerative and neuropsychiatric disorders. The MATLAB source code of UJA-SHFD is freely available. Program summary Program title: UJA-SHFD CPC Library link to program files: http://dx.doi.org/10.17632/wzzv2wc7fd.1 Licensing provisions: GNU General Public License version 3 Programming language: MATLAB, C++ Nature of problem: To compute the fractal dimension of 3D surfaces avoiding the common problems of software based on the box-counting algorithm. Solution method: Spherical harmonics are used to obtain a set of reconstructed surfaces approximating the shape of the original surface. The areas of the reconstructed surfaces are used to obtain the global fractal dimension of the original surface. The areas of the triangles associated to each vertex of the reconstructed surfaces are used to obtain local fractal dimension maps.

中文翻译：

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一种计算大脑皮层球谐分形维数的MATLAB工具

摘要分形维数 (FD) 已成为神经科学中非常有用的工具，在表征几种神经退行性疾病方面具有广泛的应用。计算脑组织 FD 最常用的方法是盒数计数。这种技术在 2D 图像和 3D 体积上表现非常好；然而，它在处理 3D 皮质表面时存在几个缺点。在这项研究中，我们提出了一个 MATLAB 程序，用于计算基于球谐函数的 3D 表面的 FD。我们开发了一种名为 UJA-SHFD 的新型 MATLAB 程序，该程序基于球谐函数 FD 算法，该算法在处理 3D 表面时克服了经典盒计数算法的局限性。而且，基于球形谐波的 FD (SHFD) 可以处理每个皮质表面顶点的全局（为整个表面提供单个 FD 值）和局部水平评估。UJA-SHFD 专为处理从 FreeSurfer 软件套件获得的皮质表面而设计和测试。尽管如此，该程序还可以处理 Wavefront OBJ 格式的任何类型的表面。UJA-SHFD 可以通过图形用户界面和命令行使用。本研究通过将 UJA-SHFD 应用于研究阿尔茨海默病脑萎缩进展的神经影像学研究，证明了 UJA-SHFD 的有用性。UJA-SHFD 是一个新的 MATLAB 程序，其目标是开发 FD 计算的神经影像分析，以研究神经退行性疾病和神经精神疾病的大脑形态变化。UJA-SHFD 的 MATLAB 源代码是免费提供的。程序摘要 程序名称：UJA-SHFD CPC 库程序文件链接：http://dx.doi.org/10.17632/wzzv2wc7fd.1 许可条款：GNU 通用公共许可证第 3 版 编程语言：MATLAB、C++ 问题性质：至计算 3D 曲面的分形维数，避免了基于框计数算法的软件常见问题。求解方法：使用球谐函数来获得一组近似于原始表面形状的重建表面。重建表面的面积用于获得原始表面的全局分形维数。与重建表面的每个顶点相关联的三角形面积用于获得局部分形维数图。