Emergence in the high-resolution sensing and imaging technologies have allowed us to track the variability in manufacturing processes occurring at every conceivable resolution of interest. However, representation of the underlying manufacturing processes using streaming sensor data remains a challenge. Efficient representations are critical for enabling real-time monitoring and quality assurance in smart manufacturing. Towards this, we present graph-based methods for efficient representation of the image data gathered from advanced manufacturing processes. In this dissertation, we first focus on experimental studies involving the finishing of complex additively manufactured components and discuss the important phenomenological details of the polishing process. Our experimental studies point to a material redistribution theory of polishing where material flows in the form of thin fluid like layers, eventually bridging up the neighboring asperities. Subsequently, we use the physics of the process gathered from this study to develop a random planar graph approach to represent the evolution of the surface morphology as gathered from electron microscopic images during mechanical polishing. In the next half of the dissertation, we focus on unsupervised image segmentation using graph cuts by iteratively estimating the image labels by solving the max-flow problem while optimally estimating the tuning parameters using maximum a posteriori estimation. We also establish the consistency of the posterior estimates. Applications of the method in benchmark and manufacturing case studies show more than 90% improvement in the segmentation performance as compared to state-of-the-art unsupervised methods. While the characterization of the advanced manufacturing processes using image and sensor data is increasingly sought after, it is equally important to perform characterization rapidly. The last chapter of this dissertation is set to focus on the rapid characterization of the salient microstructural phases present on a metallic workpiece surface via a nanoindentation-based lithography process. A summary of the contributions and directions of future work are also presented.
