This paper suggests a new technique for trabecular bone characterization using fractal analysis of X‐Ray and MRI texture images for osteoporosis diagnosis. Osteoporosis is a chronic disease characterized by a decrease in bone density that can lead to fracture and disability. In essence, the proposed fractal model makes use of the differential box‐counting method (DBCM) to estimate the fractal dimension (FD) after an appropriate image preprocessing stage that ensures a robust estimation process. In this study, we showed that within the frequency domain generated through discrete cosine transform (DCT), only a quarter of DCT coefficients are enough to characterize osteoporotic tissues. The algorithmic complexity of the developed approach is of the order of where N stands for the size of the image, which, in turn, likely yields important gain in terms of medication cost. We report a successful separation of healthy and pathological cases in term of both P − value (using statistical Wilcoxon rank sum test) and margin difference. A comparative statistical analysis has been performed using a publicly available database that contains a set of MRI and X‐Ray texture images of both healthy and osteoporotic bone tissues. The statistical results demonstrated the feasibility and accepted performance level of our fractal model‐based diagnosis to discriminate healthy and unhealthy trabecular bone tissues. The developed approach has been implemented on a medical device prototype.

中文翻译：

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基于分形分析的空间频域成像骨微结构表征

本文提出了一种使用X射线分形分析和MRI纹理图像诊断骨质疏松症的小梁骨表征新技术。骨质疏松症是一种慢性疾病，其特征是骨密度降低，可能导致骨折和残疾。本质上，所提出的分形模型利用差分盒计数法（DBCM ）在适当的图像预处理阶段之后估计分形维数（FD），以确保鲁棒的估计过程。在这项研究中，我们表明，在通过离散余弦变换（DCT）生成的频域内，只有四分之一的DCT系数足以表征骨质疏松组织。在发达的方法的算法复杂度是秩序的地方ñ代表图像的大小，这反过来可能会在药物成本方面产生重要的收益。我们报告了根据P- 值（使用统计Wilcoxon秩和检验）和边际差异这两个方面，成功分离出健康和病理病例的成功案例。使用公共数据库进行了比较统计分析，该数据库包含一组健康和骨质疏松性骨组织的MRI和X射线纹理图像。统计结果表明，基于分形模型的诊断方法能够区分健康和不健康的小梁骨组织的可行性和可接受的性能水平。开发的方法已在医疗设备原型上实现。