Parsing façade with rank-one approximation

The binary split grammar is powerful to parse façade in a broad range of types, whose structure is characterized by repetitive patterns with different layouts. We notice that, as far as two labels are concerned, BSG parsing is equivalent to approximating a façade by a matrix with multiple rank-one patterns. Then, we propose an efficient algorithm to decompose an arbitrary matrix into a rank-one matrix and a residual matrix, whose magnitude is small in the sense of l0-norm. Next, we develop a block-wise partition method to parse a more general façade. Our method leverages on the recent breakthroughs in convex optimization that can effectively decompose a matrix into a low-rank and sparse matrix pair. The rank-one block-wise parsing not only leads to the detection of repetitive patterns, but also gives an accurate façade segmentation. Experiments on intensive façade data sets have demonstrated that our method outperforms the state-of-the-art techniques and benchmarks both in robustness and efficiency.