# Overview of Algorithms for Using Particle Morphology in Pre-Detonation Nuclear Forensics
###### Abstract  
A major goal in pre-detonation nuclear forensics is to infer the processing conditions and/or facility type that produced radiological material. This review paper focuses on analyses of particle size, shape, texture (\"morphology\") signatures that could provide information on the provenance of interdicted materials. For example, uranium one concentrates (UOC or yellowake) include ammonium diuranate (ADU), ammonium uranyl carbonate (AUC), sodium diuranate (SDU), magnesium diuranate (MDU), and others, each prepared using different salts to precipitate U from solution. Once precipitated, UOCs are often dried and calcined to remove adsorbed water. The products can be allowed to react further, forming uranium oxides UO3, U3O8, or UO2 powders, whose surface morphology can be indicative of precipitation and/or calcination conditions used in their production. This review paper describes statistical issues and approaches in using quantitative analyses of measurements such as particle size and shape to infer production conditions. Statistical topics include multivariate \(t\) tests (Hotelling's \(T^{2}\)), design of experiments, and several machine learning (ML) options including decision trees, learning vector quantization neural networks, mixture discriminant analysis, and approximate Bayesian computation (ABC). ABC is emphasized as an attractive option to include the effects of model uncertainty in the selected and fitted forward model used for inferring processing conditions. nuclear forensics; experimental design; particle morphology; machine learning +
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some example SEM images acquired from nuclear materials. The left image is the raw unprocessed SEM image and the right image is the image following manual particle segmentation using the Morphological Analysis of Materials (MAMA) software [2; 8; 9; 10]. Morphological features are proving to be useful signatures to infer the chemical processing histories (which relate to forensics goals [1; 2; 3]) of uranium oxides. Particle morphology analysis has recently been developed and applied with image analysis software to segment fully visible particles in SEM images and then compute attributes, such as circularity, area, perimeter, and ellipse aspect ratio of the segmented particles. One example of such software is MAMA, which performs segmentation and quantification. SEM images of nuclear materials can be difficult to segment due to overlapping particles, charging effects, and image clarity. Manual segmentation (locating, recognizing, and assigning boundaries to particles) requires significant time-consuming user inputs to only segment fully visible particles. An alternative automated segmentation method using a deep learning model (a U-net based on convolutional neural networks) was shown in [8] to effectively segment fully visible particles (see also Reference [11] for another segmentation option); however, this paper's focus is on inferring processing conditions using currently-available segmentation software, such as MAMA, that can also provide the 22 quantitative particle morphological metrics. Figure 2 highlights representative SEM images of ADU, SDU, MDU, and AUC and the materials generated throughout the calcination and reduction pathway of each respective starting material. In [1; 2], each of the ADU, AUC, MDU, and SDU conditions have three processing pathways involving UO3, U3O8, or UO2, at 400 \({}^{\circ}\)C, 800 \({}^{\circ}\)C, and 510 \({}^{\circ}\)C (in H2), respectively. The main inference goal is to use particle morphology to distinguish among ADU, AUC, MDU, and SDU processing routes.