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Gabor function and log Gabor function are compared in this paper. The log Gabor wavelet is developed and its performance is analyzed. Compared with Gabor wavelet, the excellent performance of log Gabor wavelet is shown. Finally, log Gabor wavelet is applied to image edge detection, and it is shown that using log Gabor wavelet can not only improve the detection property, but also save about half the computational load compared with Gabor wavelet, in the case of similar detection effect.