Nowadays manufacturing industry faces increasing demands to customize products according to personal needs. This trend leads to a proliferation of complex product designs. To cope with this complexity, manufacturing systems are equipped with advanced sensing capabilities. However, traditional statistical process control methods are not concerned with the stream of in-process imaging data. Also, very little has been done to investigate nonlinearity, irregularity, and inhomogeneity in image stream collected from manufacturing processes. This paper presents the multifractal spectrum and lacunarity measures to characterize irregular and inhomogeneous patterns of image profiles, as well as detect the hidden dynamics of the underlying manufacturing process. Experimental studies show that the proposed method not only effectively characterizes the surface finishes for quality control of ultra-precision machining but also provides an effective model to link process parameters with fractal characteristics of in-process images acquired from additive manufacturing. This, in turn, will allow a swift response to processes changes and consequently reduce the number of defective products. The proposed fractal method has strong potentials to be applied for process monitoring and control in a variety of domains such as ultra-precision machining, additive manufacturing, and biomanufacturing.

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