Simulating Classic Mosaics with Graph Cuts

Classic mosaic is one of the oldest and most durable art forms. There has been a growing interest in simulating classic mosaics from digital images recently. To be visually pleasing, a mosaic should satisfy the following constraints: tiles should be non-overlapping, tiles should align to the perceptually important edges in the underlying digital image, and orientation of the neighbouring tiles should vary smoothly across the mosaic. Most of the existing approaches operate in two steps: first they generate tile orientation field and then pack the tiles according to this field. However, previous methods perform these two steps based on heuristics or local optimisation which, in some cases, is not guaranteed to converge. Some other major disadvantages of previous approaches are: (i) either substantial user interaction or hard decision making such as edge detection is required before mosaicing starts (ii) the number of tiles per mosaic must be fixed beforehand, which may cause either undesired overlap or gap space between the tiles. In this work, we propose a novel approach by formulating the mosaic simulating problem in a global energy optimisation framework. Our algorithm also follows the two-step approach, but each step is performed with global optimisation. For the first step, we observe that the tile orientation constraints can be naturally formulated in an energy function that can be optimised with the α-expansion algorithm. For the second step of tightly packing the tiles, we develop a novel graph cuts based algorithm. Our approach does not require user interaction, explicit edge detection, or fixing the number of tiles, while producing results that are visually pleasing.