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Visual perception of the environment provides a detailed scene representation which contributes to improve motion planning and obstacle avoidance navigation for wheelchairs in non-structured indoor scenes. In this work we develop a mobile representation of the scene based on perspective maps for the automatic navigation in absence of previous information about the scene. Images are captured with a passive low-cost video camera. The main feature for visual navigation in this work is a map of quadrilaterals with apparent motion. From this mobile map, perspective maps are updated following hierarchical grouping in quadrilaterals maps given by pencils of perspective lines through vanishing points. Egomotion is interpreted in terms of maps of mobile quadrilaterals. The main contributions of this paper are the introduction of Lie expansion/contraction operators for quadrilateral/cuboid and the adaptation of Kalman filtering for moving quadrilaterals to estimate and predict the egomotion of a mobile platform. Our approach is enough modular and flexible for adapting to indoor and outdoor scenes provided at least four homologue cuboids be present in the scene between each pair of sampled views of a video sequence.

A DIFFERENTIAL GEOMETRIC APPROACH FOR VISUAL NAVIGATION IN INDOOR SCENES