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In this paper, we propose a new method to detect local interest points as junctions in line-drawing images. Our approach takes advantages of different aspects. Firstly, we extract skeleton of image and then construct a Skeleton Connective Graph with the expectation that it provides a first level of junction detection from shapes. Secondly, instead of employing low-level operators to detect junctions as described in many traditional techniques, our method works at path level taking different skeleton branches into account to gain robustness. Thirdly, we exploit the benefits of wavelet transform (e.g. multi-resolution analysis, discontinuity detection, fast computation, less sensitive to noises) to efficiently detect the dominant points from 1D representations of the paths. Finally, a post-process of pruning and connecting the skeleton segments is performed to discard false detected points and to refine the skeleton. We present in experiments interesting results compared to different methods.