A novel scheme for an object's surface area measurement is proposed that is suitable for area computation of a planar object with smooth and irregular edges. This scheme consists of four steps. First, a photoelectric image collimation system is devised to obtain a target image of a detected object. Second, a multiscale active contour is applied in the defocusing and focusing image sequence so that it gradually converges to the target's contour edge from coarse to fine scales. Third, for the convergent active contour, two formulas for the area and centroid computation of a closed B-spline curve are applied to compute the image target's area and centroid exactly. Finally, a novel centroid-self-calibration technology is applied, which measures the pixel's size equivalence with the computed centroid and uses a dual-frequency laser to measure the object's true surface area exactly. An experiment on a circular aperture area measurement indicates that this scheme's repetition error decreases to 0.11%, when the control point number of the B-spline active contour is 25.
"Surface area measurement based on a photoelectric image collimation system and an active contour," Optical Engineering 46(10), 103601 (1 October 2007). https://doi.org/10.1117/1.2799996