Despite the proliferation of ultra wide-angle lenses on smartphone cameras, such lenses often come with severe image distortion (e.g. curved linear structure, unnaturally skewed faces). Most existing rectification methods adopt a global warping transformation to undistort the input wide-angle image, yet their performances are not entirely satisfactory, leaving many unwanted residue distortions uncorrected or at the sacrifice of the intended wide FoV (field-of-view). This paper proposes a new method to tackle these challenges. Specifically, we derive a locally-adaptive polar-domain conformal mapping to rectify a wide-angle image. Parameters of the mapping are found automatically by analyzing image contents via deep neural networks. Experiments on large number of photos have confirmed the superior performance of the proposed method compared with all available previous methods.