Facade repetition extraction using block matrix based model

Repetition extraction plays an important role in facade image analysis. In this paper, this task is handled within the graph cut based image segmentation framework. To model the repetitions, generalized translation symmetry (GTS) is introduced to enable aperiodic repetition layouts. More importantly, GTS is explicitly formulated in terms of matrix multiplication. That is, GTS is viewed as the product of a repetitive pattern and two block matrices. These two block matrices are employed to represent the vertical and horizontal symmetry respectively. On this basis, repetition extraction is formulated as a GTS constrained energy minimization problem. An alternatively optimization algorithm based on graph cut and dynamic programming is finally developed to solve the problem. Experimental results demonstrate the validity of our method.