# Novel Boundary Edge Detection for Accurate 3D Surface Profilometry Using Digital Image Correlation
## 1 Introduction  
Nowadays, optical surface profilometry has a broad range of applications, especially for the measurement of critical dimensions and the process automation of industrial workpieces. Three-dimensional surface profilometry is a crucial technology for the quality inspection of various manufacturing processes. However, one of the significant challenges in digital image correlation (DIC)-based profilometry is surface edge detection. Figure 1 shows the depth image of a square box with four surface line edges detected using traditional DIC. As can be seen, the measurement and reconstruction of the edges are far from accurate [1], indicating that the current DIC-based approach cannot accurately detect and reconstruct 3D surface edges. Such inaccuracy also suggests that pattern cross-correlation in DIC is not effective in determining the geometric information of surface edges. Conventional DIC-based surface profilometry often suffers poor accuracy due to noisy data along surface edges. The commonly used structured light projection techniques include phase-shifting, structured-code, random-speckle, and digital image correlation (DIC) detection approaches. This article focuses on the 3D DIC-based random-speckle processing method, which is an efficient full-field on-shot measurement technique, and can provide absolute depth information. To achieve single-exposure full-field surface profilometry, the 3D DIC-based random-speckle methodology projects random laser speckles on the tested surface and evaluates absolute depth through correlating the captured image with pre-calibrated reference images [2; 3]. In such a process, a set of image blocks with uniquedeformed random-speckle patterns is acquired to correlate mathematically with the images in the pre-calibrated database. In random-speckle profilometry, small lens apertures are often employed to obtain high depth-of-field (DOF) measurements. However, both depth resolution and accuracy are often undermined due to increased depth range. For precise 3D absolute measurement, a fundamental problem is the random variation of light intensity in each small sub-area of the projected random-speckle image without a repeating pattern. Current studies on DIC detection accuracy aim at the optimization of measuring parameters, enhanced quality of random-speckle patterns, improvement in speckle-generating methods, and speckle image-processing algorithms. Measuring parameters including the size, shape, and contrast of laser speckles, as well as the correlation subset size, are closely related to speckle quality [4; 5]. In general, a larger speckle size and correlation subset can obtain a higher contrast in speckle quality which can diminish the measured noise but increase the calculation time in DIC. Some speckle quality indexes were developed to determine the quality of a speckle pattern and the optimal subset size for accurate and efficient DIC operation [6; 7]. In 2013, [PERSON] pointed out potential limitations on contrast-type criteria that fail to provide a reliable indication for the randomness of the speckle pattern [8]. Speckle size distribution and speckle shapes are regarded as important local unique features for achieving a steady DIC. For better accuracy of 3D DIC-based measurements, different strategies such as ground-glass laser emission, white-paint spray, or computer simulation have been developed to generate random image features to enhance the uniqueness of speckle patterns [9; 10; 11]. Moreover, some speckle image-processing algorithms have been proposed to optimize the signal-to-noise ratio in cross-correlation. Some approaches, utilizing manifold reference image sets or through implementing correlation peak detection, overcome discontinuous displacement with a split subset [12; 13]. Other methods use either adaptive binarization or reliable-point matching to enhance the image contrast to improving measurement accuracy [14].