A number of algorithms have been proposed for intelligent image/video retargeting with image content retained as much as possible. However, they usually suffer from some artifacts in the results, such as ridge or structure twist. In this paper, we present a structure-preserving media retargeting technique that preserves the content and image structure as best as possible. Different from the previous pixel or grid based methods, we estimate the image content saliency from the structure of the content. A block structure energy is introduced with a top-down strategy to constrain the image structure inside to deform uniformly in either x or y direction. However, the flexibilities for retargeting are quite different for different images. To cope with this problem, we propose a compressibility assessment scheme for media retargeting by combining the entropies of image gradient magnitude and orientation distributions. Thus, the resized media is produced to preserve the image content and structure as best as possible. Our experiments demonstrate that the proposed method provides resized images/videos with better preservation of content and structure than those by the previous methods.