A comparative study between Elliptic Fourier and B-spline descriptors for object contour representation

Abstract

In this work, a comparative study between Elliptic\ud Fourier and B-spline descriptors is carried out for comparing\ud their efficiency in characterizing the contour shape of image\ud objects. In both cases, the goal is to obtain the least\ud representation error using the fewest possible number of\ud coefficients. With Fourier descriptors, different number of\ud harmonics are used while the remaining ones are set to zero. In\ud the B-spline case, coefficients are obtained iteratively using a\ud least-square filter, followed by a decimation procedure. Linear\ud and cubic B-splines are considered. In general, data will be more\ud compressed when the lower number of coefficients is used, but\ud the representation error also increases considerably. We use a\ud signal/error ratio, expressed in dBs, to measure the similarity of\ud each approximation. The signal value is obtained from the\ud ‘modulo’ addition of all coordinate points, whereas the error\ud value is computed accumulating the ‘modulo’ distance between\ud original and reconstructed shape. It can be shown that for a\ud lower compression rate, the results do not vary significantly in all\ud three methods. For higher compression rates, Elliptic Fourier\ud Descriptors are more efficient than linear and cubic B-splines,\ud especially in soft contours, but B-splines have lower\ud computational cost.Peer ReviewedPostprint (published version

A Parallel Resonant Converter Polynomial Model Implemented in a Digital Signal Controller

“…However, data fitting results in big outliers once applied to coefficients a i and b i , as in Figure 8a, which were immediately ignored. Therefore, an alternative was to apply Bspline [23][24][25][26]. The last is part of numerical analysis, which is mostly applied in curve-fitting and numerical differentiations of data.…”