Fractured metal fragments with rough and irregular surfaces are often found at crime scenes. Current forensic practice visually inspects the complex jagged trajectory of fractured surfaces to recognize a ``match'' using comparative microscopy and physical pattern analysis. We developed a novel computational framework, utilizing the basic concepts of fracture mechanics and statistical analysis to provide quantitative match analysis for match probability and error rates. The framework employs the statistics of fracture surfaces to become non-self-affine with unique roughness characteristics at relevant microscopic length scale, dictated by the intrinsic material resistance to fracture and its microstructure. At such a scale, which was found to be greater than two grain-size or micro-feature-size, we establish that the material intrinsic properties, microstructure, and exposure history to external forces on an evidence fragment have the premise of uniqueness, which quantitatively describes the microscopic features on the fracture surface for forensic comparisons. The methodology utilizes 3D spectral analysis of overlapping topological images of the fracture surface and classifies specimens with very high accuracy using statistical learning. Cross correlations of image-pairs in two frequency ranges are used to develop matrix variate statistical models for the distributions among matching and non-matching pairs of images, and provides a decision rule for identifying matches and determining error rates. A set of thirty eight different fracture surfaces of steel articles were correctly classified. The framework lays the foundations for forensic applications with quantitative statistical comparison across a broad range of fractured materials with diverse textures and mechanical properties.

翻译：在犯罪现场经常发现有粗糙和不规则表面的断裂金属碎片。目前的法医实践通过比较显微镜和物理图案分析,对断裂表面的复杂支离破碎的轨迹进行视觉检查,以识别“Match'”的比较显微镜和物理图案分析。我们开发了一个新的计算框架,利用断裂机理学和统计分析的基本概念,为匹配概率和误差率提供定量匹配分析。框架利用骨折表面的统计,在相关的微镜长度范围内,成为具有独特粗糙特征的非自因的骨折体。根据对骨折及其微结构的内在物质抵抗力,对骨折表面及其微结构的复杂轨迹进行了视觉检查。在这种规模中,发现“Matchet ” 使用比重大于两个颗粒大小或微法体积大小的“Match ”,我们确定材料的内在特性、微缩结构以及外部力量在证据碎片碎片碎片块上暴露历史史史的历史特征,并用3D光谱分析分析,利用统计学的样本和非常精确的样本进行统计学学习。在两个频率基地基上的图像和精确度上进行对比,用于确定一个用于测定的顺序图层图层图层的统计结构图层的对比。