Binary descriptors have been widely used in many real-time applications due to their efficiency. These descriptors are commonly designed for perspective images but perform poorly on omnidirectional images, which are severely distorted. To address this issue, this paper proposes tangent plane BRIEF (TPBRIEF) and adapted log polar grid-based motion statistics (ALPGMS). TPBRIEF projects keypoints to a unit sphere and applies the fixed test set in BRIEF descriptor on the tangent plane of the unit sphere. The fixed test set is then backprojected onto the original distorted images to construct the distortion invariant descriptor. TPBRIEF directly enables keypoint detecting and feature describing on original distorted images, whereas other approaches correct the distortion through image resampling, which introduces artifacts and adds time cost. With ALPGMS, omnidirectional images are divided into circular arches named adapted log polar grids. Whether a match is true or false is then determined by simply thresholding the match numbers in a grid pair where the two matched points located. Experiments show that TPBRIEF greatly improves the feature matching accuracy and ALPGMS robustly removes wrong matches. Our proposed method outperforms the state-of-the-art methods.