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We present a novel image resizing method which attempts to ensure that important local regions undergo a geometric similarity transformation, and at the same time, to preserve image edge structure. To accomplish this, we define handles to describe both local regions and image edges, and assign a weight for each handle based on an importance map for the source image. Inspired by conformal energy, which is widely used in geometry processing, we construct a novel quadratic distortion energy to measure the shape distortion for each handle. The resizing result is obtained by minimizing the weighted sum of the quadratic distortion energies of all handles. Compared to previous methods, our method allows distortion to be diffused better in all directions, and important image edges are well‐preserved. The method is efficient, and offers a closed form solution.