## 1 Introduction
The first aspect deals with the accuracy of layer contour detection for the geometric characterization of manufactured objects [28, 29, 30]. The second aspect focuses on the integration of sensors into MEX/P equipment for process monitoring [30, 31, 32]. Accurately identifying contour points in digitized images is essential for verifying the dimensional and geometric parameters of the fabricated layer. Initial efforts focused on compensating for image distortion [28]. It was found that such distortion exhibits differential characteristics between the scanning direction (\(\overset{-}{\
u}\)) and the direction of the photodetector array (\(\overset{-}{a}\)). Beyond this circumstance, it was also found that global compensation techniques [26] are insufficient to achieve precision levels in point localization comparable to those attainable in coordinate-based metrology. Consequently, a local distortion adjustment (LDA) algorithm was developed. Enhancing the results of global techniques, the LDA allowed for very precise contour reconstruction under high target-to-background contrast scenarios. Focusing on contour identification in images, this complex task has been addressed through various edge-detection algorithms, such as those proposed by [PERSON] [33], [PERSON] [34], and [PERSON] [35]. However, the Canny algorithm [36] stands out as the most-employed algorithm [37]. Nevertheless, these algorithms and those based on second derivatives, like zero-crossing or the Laplacian of Gaussian, were not designed for the dimensionally precise and unambiguous contour detection required in industrial-level dimensional verification and quality control. Instead, they were developed for tasks such as feature extraction [38], image segmentation [39], object recognition [40], and image enhancement [41]. Contour characterization in AM using conventional algorithms has been previously addressed in several works [42; 43; 44; 45; 46]. Thus, [PERSON] et al. compared different algorithms ([PERSON] and Canny) based on qualitative impressions that evaluate the completeness of contour reconstruction in SLS-manufactured parts [42]. [PERSON] et al. reported minimum average errors in the range of tenths of a millimeter when measuring layers with a CCD in powder bed fusion manufacturing [43]. Similar results were reported by [PERSON] and [PERSON], who noted a maximum point-to-point error of 0.480 mm [44]. [PERSON] characterized the layer contour in PBF images where the layer-to-background contrast pattern appeared to be nearly uniform [45]. Nevertheless, quality characterization in AM through image analysis is mostly focused on the detection of coarse defects [46]. From the analysis of these works, it can be deduced that the contour characterization techniques currently applied in AM are focused on the detection of coarse deviations, mainly in the range of tenths of a millimeter. This level of resolution in error characterization is conditioned by the quality of the optical equipment used and the quality of the geometric reconstruction provided by conventional edge-detection algorithms. One of the main problems when using conventional algorithms for tasks that require precise dimensional and geometric characterization of layer contours is their high sensitivity to non-uniformity in contrast patterns or variations in grayscale [42]. This issue has been addressed in two studies [29; 30], which revealed that optimizing the parameters of conventional contour detection algorithms (such as Canny, Prewitt, Sobel, etc.) can enhance the results of contour point identification in terms of both coverage and precision. However, it was also observed that these algorithms can only provide accurate reconstructions of layer contours when the entire contour shows substantial and uniform contrast against the background. They struggle to offer a comprehensive and accurate reconstruction when contrast patterns exhibit significant asymmetries depending on the local orientation of the contour [29].