The number of outline points is the only uncertain parameter when using Fourier descriptors (FDs) to identify or retrieve shapes. By choosing the shape outlines of circle, ellipse and rice planthopper forewings as study object, complex Fourier descriptors and elliptic Fourier descriptors as outline characteristics and intra cluster similarity and inter cluster similarity as evaluation indexes, the essential reason of influence of the outline points number on recognition accuracy was investigated and verified. Experimental result shows that intra cluster similarity/circle boundary energy is changed with the number of boundary points, and thus changing recognition accuracy. And, when the boundary sampling points are more than 64，resampling has no effect on CFD recognition accuracy. However, both of the sampling and resampling point numbers have influence on EFD recognition accuracy. The advantage of CFD is that it can use at least 16 resampling boundary points to express the whole shape of an outline, while EFD needs more than 128 points, especially for identifying quite similar outlines.