(632f) Automated Characterization and Monitoring of Material Shape Using Riemannian Geometry

The geometric shape of a manufactured material impacts both its chemical and physical properties. This is evident in many areas of manufacturing such as 3-dimensional printing, crystal and co-crystal growth, cell morphology in biomanufacturing, and in the production of granular materials such as sand and ceramic microspheres [1,2,3]. For example, granular materials like sand and ceramic microspheres can be added into liquids such as paints, coatings, and cements to improve hardness, decrease viscosity, increase insulating capability, and reduce the overall amount of volatile organic compounds (VOC's) [4]. However, these improvements are directly dependent on the morphology of the individual grains, with spherical grains providing the largest improvement and irregularly shaped particles resulting in decreased performance due to how the particles coalesce at a larger scale [5]. This also holds true for granular materials used in metal casting and hydraulic fracturing where the flow of organic materials through the granular medium needs to be closely controlled to prevent metal casting defects and optimal extraction of natural gas and oil from deep rock formations [6]. Thus, there is a need for methods to automatically quantify and monitor the morphological characteristics of manufactured materials.

Unfortunately, many of the geometric methods employed in manufacturing are application specific. An example is the use of rigid geometric structures for the analysis of crystal morphology in the production of pharmaceuticals. Crystal structure (i.e., crystal form) of an active pharmaceutical ingredient (API) impacts its density, solubility, reactivity, and stability, among other properties [7]. The structure of crystals allows their shape to be quantified with measures such as aspect ratio, form factor, and roundedness, or complex transforms such as wavelet and Fourier transforms [8,9,10]. However, these methods are difficult to apply to amorphous structures such as those found in cells used in the production of biopharmaceuticals, in crystal polymorphisms, or in the mining and refinement of natural materials such as sand [11,12]. Machine learning (ML) methods, such as convolutional neural networks, have recently been proposed as generalizable measures of morphology for materials [3,13]. However, these methods require large amounts of well-sampled training data which may not be readily available and are difficult to physically interpret.

To address these challenges, we propose the use of a mathematical framework to automatically characterize the morphology of manufactured materials using Riemannian geometry. The framework is based on the realization that geometric shapes can be represented as points on a Riemannian manifold [14]. The structure of this Riemannian manifold can be used to directly quantify differences between shapes based on geodesic distances on the manifold. These geodesic distances can be used to develop statistical measures (e.g., means, variances) of a material's intrinsic morphology which can be used in process monitoring and quality control. Furthermore, the Riemannian manifold structure allows us to project data from the manifold onto a tangent (vector) space which can be directly integrated in data analysis tasks such as dimensionality reduction and classification [15].

In this presentation, we discuss the mathematical foundations of shape analysis through a Riemannian geometric framework and illustrate its application on a manufactured/mined granular material dataset provided by Covia Corp. We focus on samples of sand and manufactured ceramic microspheres. We analyze microscope images of these samples and develop an automated method for extracting particle shapes from the images. We leverage the presented Riemannian framework to perform dimensionality reduction to visualize the structure of the data and hypothesis testing to understand the morphological differences in the samples. The automated, computationally efficient nature of this framework, coupled with its statistical power, suggests a powerful statistical process control technique for the continuous improvement and quality control of processes in which shape is a key factor.

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