JOURNAL OF COSMETIC SCIENCE 12 surface profi le and can be easily converted into a surface normal format. An object de- scription expressed in the gradient domain can offer advantage in terms of surface orienta- tion independence and thus can facilitate object recognition tasks (10). However, this format is not intuitive when compared with a description method based on 3D profi le data. To obtain a 3D description of the skin surface, the gradient must be further inte- grated to produce a height-map format. This is found to be diffi cult and sensitive to noise as the surface gradient recovered by photometric stereo can only characterize the surface locally (11). Errors in the reconstruction process are unavoidably accumulated when an integration process is carried out. If the outliers in the recovered surface gradients caused by specularities and shadows are signifi cant, the results from reconstruction may deviate far from the original shape of the object. To deal with these problems, there has emerged a large body of work aimed at integrating the surface shape from noisy gradient data accurately (12). To make the data extracted using the photometric stereo technique comparable with that of the pure 3D data output from the PRIMOS device, we transform the 3D data from the PRIMOS into a gradient representation format using a procedure of partial differentia- tion, which will not introduce any error because of the local calculation. In addition, the surface profi le is reconstructed on a relatively small specifi ed area in order that the accu- mulated errors can be minimized. The evaluation procedure on the acquired topography data is carried out using three test objects, i.e., a painted ball bearing, replica of skin, and live skin. THE EXPERIMENTAL SUBJECTS Ball bearing. A ball bearing with diameter of 10 mm in Figure 2 is chosen as a reference because it is manufactured with high precision, i.e., tolerance of diameter and sphericity is ±0.002 inches. In addition, the spherical shape of the ball bearing contains a full range of gradient values, which makes the ball an ideal object to test most surface recovery Figure 2. One image of ball bearing able to be approximated as a Lambertian surface.

EVALUATION ON AN OPTICAL SCANNING DEVICE 13 Figure 3. Repli ca made from the dorsal side of a volunteer’s hand and one region selected for the conve- nience of comparison. methods. A matt paint uniformly sprayed onto the ball surface eliminates the effect of mirror refl ection from the metal component and makes the surface nearly Lambertian. Replica of skin. The replica shown in Figure 3 is taken from normal skin on the back of a hand. The reconstruction is only carried out on an area defi ned by the window with a size of 140 × 100 pixels (or a physical size of 3.28 × 2.34 mm) to avoid the effect of accumulated errors associated with the integration process. Skin in vivo. Normal skin on the dorsal side of a volunteer’s hand is acquired by both the Skin Analyzer and the PRIMOS device. Markers shown in Figure 4 are drawn for rough alignment during acquisition of data by using the two different devices. RESULTS AND DISCUSSION Figures 5A and B are plots of recovered and calculated surface vectors composed of the gradient components in x and y directions. The length of the arrow represents the relative Figure 4. Skin su rface on the dorsal side of a volunteer’s hand.