A number of lane detection methods depend on a proposal-free instance segmentation because of its adaptability to flexible object shape, occlusion, and real-time application. This paper addresses the problem that pixel embedding in proposal-free instance segmentation based lane detection is difficult to optimize. A translation invariance of convolution, which is one of the supposed strengths, causes challenges in optimizing pixel embedding. In this work, we propose a lane detection method based on proposal-free instance segmentation, directly optimizing spatial embedding of pixels using image coordinate. Our proposed method allows the post-processing step for center localization and optimizes clustering in an end-to-end manner. The proposed method enables real-time lane detection through the simplicity of post-processing and the adoption of a lightweight backbone. Our proposed method demonstrates competitive performance on public lane detection datasets.