A Bijective Image Retargeting Algorithm Based on Conformal Energy

Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure bijective warping maps essential for preserving visual information. This paper introduces a novel bijective image retargeting model through conformal energy minimization of the deformation field. The proposed model establishes mathematical rigor by proving the well-posedness for the optimal warping map in both continuous and discrete settings and showing that the discrete solutions converge to their continuous counterpart under mesh refinement. Numerical experiments corroborate the model's efficacy and the convergence of discrete solutions during progressive mesh subdivision processes, validating both theoretical guarantees and practical performance.