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Recent advances in the joint processing of images have certainly shown its advantages over individual processing. Different from the existing works geared towards co-segmentation or co-localization, in this paper, we explore a new joint processing topic: image co-skeletonization, which is defined as joint skeleton extraction of objects in an image collection. Object skeletonization in a single natural image is a challenging problem because there is hardly any prior knowledge about the object. Therefore, we resort to the idea of object co-skeletonization, hoping that the commonness prior that exists across the images may help, just as it does for other joint processing problems such as co-segmentation. We observe that the skeleton can provide good scribbles for segmentation, and skeletonization, in turn, needs good segmentation. Therefore, we propose a coupled framework for co-skeletonization and co-segmentation tasks so that they are well informed by each other, and benefit each other synergistically. Since it is a new problem, we also construct a benchmark dataset by annotating nearly 1.8k images spread across 38 categories. Extensive experiments demonstrate that the proposed method achieves promising results in all the three possible scenarios of joint-processing: weakly-supervised, supervised, and unsupervised.