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A new multiscale corner detection method is proposed based on dyadic wavelet transform (WT) of the orientation function of a contour image. As the decomposition of the dyadic WT is complete and its scales are sparse, all the scales are defined as natural scales for corner detection. The points that are wavelet transform modulus maxima (WTMM) at different scales are taken as corner candidates. For each corner candidate, the sum of the corresponding normalized WTMM at all the natural scales is used as significance measure of the "cornerness". The utilization of the complete information makes the performance of the proposed detector independent to the type of input images. The decomposition scales of the WT are restricted by the contour length, which makes the algorithm adaptable for both long contours and short contours. Both subjective and objective evaluation illustrate better performance of the proposed corner detector compared to the conventional methods.