Recognition of perspectively distorted planar grids

In this paper, properties of planar (2D) grids are addressed in a mathematical point of view, and a novel algorithm for recognizing distorted grids with perspective transformations is presented. The proposed approach contains three parts: (a) recognizing parameters of affinely distorted grids by fitting Gaussian mixture models (GMMs) to grid spectrums, (b) rebuilding the grid structures via a generating iteration based on the acquired parameters, and (c) eliminating nonlinear effects caused by perspective transformations with the median of infinite lines from local structures (MILLS) method. All parts are precise and robust to local distortions, the absence of elements, and outliers. The accuracy and robustness are demonstrated by quantitative statistics in experiments on synthesis grids and real grid images.