# _Skin Imaging_: A Digital Twin for Geometric Deviations on Manufactured Surfaces
## 5 Experimental Results and Discussion
### Skin Image Analyzing  
Studying the behavior of the intensity of the _skin image_, the geometric deviation behavior of the manufactured surface is inspectable. In [45], it is demonstrated that by considering the intensity distribution of a _skin image_, e.g., the histogram graph, one can detect that the surface has general deformation or only has imperfection on some parts of it, and also by extracting the objects of the _skin image_ can determine the location and the required characteristics of the local imperfections on the surface. For instance, in Figure 21 the histogram of the _skin images_ generated in the previous section are shown. According to the figure, the histogram of the wavy sphere (Figure 21a) appears in a wide shape, while the histograms of the gudgeon pin (Figure 21b) and the suspension ball joint (Figure 21c,d) are in compressed form. This is because the wavy sphere is a deformed surface and its deviation gradually changes between ups and downs in a wide area, and consequently the intensity of its corresponding _skin image_ gradually varies from a maximum value to a minimum in the whole image, in which almost all intensity bins have considerable counts. In contrast, for the two latter case studies just the defected parts have considerable deviations with respect to the surface which leads to a limited number of intensity bins with considerable counts in their histograms. The wide histogram represents a deformation on whole the surface (general defect), while the compressed histogram shows local defects existence on the surface. The defective area of the surface appears as an object on the generated _skin image_ due to its different deviation in comparison with its surrounding areas, which allows the use of image processing methods such as global thresholding in defect detection [45]. The defective regions of the surface are extracted from its corresponding _skin image_, and hence their locations are detected on the 3D surface, which can be reported to any manufacturing process upstream or downstream, as the most likely locations of the manufactured surface that are prone to the occurrence of crucial geometric errors such as out of cylindricity or out of sphericity. The accurate magnitude of the errors can also be reported. For instance, a wide histogram conveys the message that there may be crater tool wear in the machining process, which changes the cutting force and temperature. This affects the material properties and ultimately causes the deformation of the surface. Detected local geometric errors on the  
Figure 21: Histogram of _skin images_ of: (**a**) wavy sphere, (**b**) defective gudgeon pin, (**c,d**) upper and down hemispheres of defective ball joint. surface can be a sign of inappropriate clamping force, or excessive and uncontrolled cutting temperature that causes thermal expansion in the detected areas. It must be mentioned that the interpretation of the information that the _skin image_ provides, depends on the specific desired application and not on the ones mentioned. Figure 22a,d shows the detected imperfections of the gudgeon pin on its _skin image_ and on the measured surface in the original coordinate system (scanner frame), respectively; the defects are also labeled according to the labels in Figure 13. Additionally, the defective regions are displayed in Deviation-Coordinate system of the points in Figure 22b,c. Furthermore, Table 1 includes the out of cylindricity value for each region. According to this table the maximum out of cylindricity on the surface is 0.65 mm and occurs in the location of label 1. The maximum deviation for the defective regions with label 3 and 6 is 0.18 mm and 0.19 mm, which is the lowest among other regions, hence they have appeared as objects with minimum intensity value in the generated _skin image_ (namely Magnitude in Table 1) as is also illustrated in the Figure 22a.