Smart algorithms are used in Machine vision to organize or extract high-level information from the available data. The resulted high-level understanding the content of images received from certain visual sensing system and belonged to an appearance space can be only a key first step in solving various specific tasks such as mobile robot navigation in uncertain environments, road detection in autonomous driving systems, etc. Appearance-based learning has become very popular in the field of machine vision. In general, the appearance of a scene is a function of the scene content, the lighting conditions, and the camera position. Mobile robots localization problem in machine learning framework via appearance space analysis is considered. This problem is reduced to certain regression on an appearance manifold problem, and newly regression on manifolds methods are used for its solution.