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Abstract: The gray-scale digital image is two-dimensional, and most of the previous polynomial fitting methods for edge detection are one-dimensional. The new method of two-dimensional orthogonal polynomial fitting for edge detection is presented. The two-dimensional fitting is actually more suitable for the two-dimensional image, and the fitting results are significantly better than that of the one-dimensional one. Because of the orthogonality of the polynomial function, the fitting coefficients can be determined by simple arithmetic method instead of the solution of algebra equation. So the high-order polynomial function can be used in the data fitting, and the fitting results are significantly better than that of ordinary polynomial. It is shown through the analysis of the synthesis image and the test of simply supported beam that the results of surface fitting and edge identification used of the proposed method are quite good. Within a certain image coverage, the precision of the beam measurement by proposed method is relatively same with dial gage results at the measurement point. Intense deflection data along the beam can be obtained by the proposed method, while only point deflection can be obtained by dial gage measurement.#br# Key words: two dimension polynomial fitting; orthogonal polynomial fitting; surface fitting; edge detection; deformation measurement
