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Visual localization for planar moving robot is important to various indoor service robotic applications. To handle the textureless areas and frequent human activities in indoor environments, a novel robust visual localization algorithm which leverages dense correspondence and sparse depth for planar moving robot is proposed. The key component is a minimal solution which computes the absolute camera pose with one 3D-2D correspondence and one 2D-2D correspondence. The advantages are obvious in two aspects. First, the robustness is enhanced as the sample set for pose estimation is maximal by utilizing all correspondences with or without depth. Second, no extra effort for dense map construction is required to exploit dense correspondences for handling textureless and repetitive texture scenes. That is meaningful as building a dense map is computational expensive especially in large scale. Moreover, a probabilistic analysis among different solutions is presented and an automatic solution selection mechanism is designed to maximize the success rate by selecting appropriate solutions in different environmental characteristics. Finally, a complete visual localization pipeline considering situations from the perspective of correspondence and depth density is summarized and validated on both simulation and public real-world indoor localization dataset. The code is released on github.