Vision-based navigation systems with real-time needs often employ hierarchical schemes that break down navigation across multiple temporal and spatial scales. Doing so scales the navigation problem down to real-time realizable problems at the local domains. Such hierarchical architecture often includes environment perception, planning, and control modules, which also lie in three levels from high to low. Leveraging sparse representation for the three modules can reduce the computational cost and have favorable scaling properties across multiple devices. It is important in the context of mobile robot navigation where fast and safe decisions should be made when traversing unknown or partially known environments. In the proposed works, an egocentric perception space is created by the combination of stixel and sparse features estimated from the stereo camera. The perception propagates to maintain temporal information for PiPS collision checking. Local planning formulates potential fields from sparse gaps to generate safe trajectories. The gaps are detected within any laser scan-like egocentric perception. Different from traditional pose-based control, trajectory servoing method is applied to track Cartesian trajectories within image space composed by sparse feature points. Therefore, sparse representation is utilized for three modules in hierarchical stereo navigation.