Facade labeling via explicit matrix factorization

Abstract

Facade labeling, namely semantically segmenting the facade images, requires exploiting the facade regularity. To model the regularity, this paper proposes a novel matrix multiplication based formulation. In the model, the regularity is described as generalized translation symmetry (GTS) which enables varying distances between the repeated elements. Moreover, an explicit and intuitive formulation via matrix multiplication is also derived for the GTS. That is, the symmetry is interpreted as the product of a repetitive pattern and two block matrices. These two block matrices respectively represent the vertical and horizontal repetitions. Based on the formulation, facade labeling is reformulated into factorizing the facade to calculate the block matrices. An alternating optimization algorithm is thus developed to solve the matrix factorization problem, where dynamic programming is used to optimize the block matrices. Extensive experiments demonstrate the fidelity of our model and the efficiency of the algorithm. © 2014 Springer International Publishing.