Tissue segregation plays a crucial role in the measurement of breast density in breast magnetic resonance (MR) images. This paper proposes a mathematical analysis of the new distribution mixture model for the intensity spectrum of breast MR images using Gamma and Gaussian distribution for fibro-glandular and adipose tissues, respectively. The thorough regression analysis and mapping presented in this paper clearly indicate that the distribution of Gamma is best suited to the spectrum of fibro-glandular tissue intensities relative to the standard Gaussian distribution. Moreover, Gamma distribution can represent both symmetric and non-symmetric (skewed) intensity distributions in a more efficient way, leading to a more accurate segmentation of fibro-glandular and adipose tissues. The efficiency of the segmentation is quantified by measuring the standard performance appraisal steps : Dice similarity coefficient, Jaccard index and dissimilarity index. The whole mathematical analysis is performed on a data set of 200 patients with 160 axial slices per subject with various breast sizes and densities. The Gamma Gaussian mixture model (GaGMM’s) assessment metrics indicate an improvement of 39.4 %, 46.8 % and 54.9 %, respectively, in relation to the Gaussian mixture model.

组织分离在乳房磁共振 (MR) 图像中的乳房密度测量中起着至关重要的作用。本文分别针对纤维腺体和脂肪组织，分别使用 Gamma 和 Gaussian 分布，对乳房 MR 图像强度谱的新分布混合模型进行了数学分析。本文中提出的彻底回归分析和映射清楚地表明，伽玛分布最适合相对于标准高斯分布的纤维腺体组织强度谱。此外，伽玛分布可以更有效地表示对称和非对称（偏斜）强度分布，从而更准确地分割纤维腺体和脂肪组织。通过衡量标准绩效评估步骤来量化分割的效率：骰子相似系数、Jaccard 指数和相异指数。整个数学分析是对 200 名患者的数据集进行的，每个受试者有 160 个轴向切片，具有不同的乳房大小和密度。Gamma 高斯混合模型 (GaGMM) 的评估指标表明，相对于高斯混合模型，分别提高了 39.4%、46.8% 和 54.9%。