*Article* **Appearance-Based Sequential Robot Localization Using a Patchwise Approximation of a Descriptor Manifold**

**Alberto Jaenal, Francisco-Angel Moreno \* and Javier Gonzalez-Jimenez**

Machine Perception and Intelligent Robotics Group (MAPIR), Department of System Engineering and Automation Biomedical Research Institute of Malaga (IBIMA), University of Malaga, 29071 Málaga, Spain; ajaenal@uma.es (A.J.); javiergonzalez@uma.es (J.G.-J.)

**\*** Correspondence: famoreno@uma.es

**Abstract:** This paper addresses appearance-based robot localization in 2D with a sparse, lightweight map of the environment composed of descriptor–pose image pairs. Based on previous research in the field, we assume that image descriptors are samples of a low-dimensional Descriptor Manifold that is locally articulated by the camera pose. We propose a piecewise approximation of the geometry of such Descriptor Manifold through a tessellation of so-called *Patches of Smooth Appearance Change* (PSACs), which defines our *appearance map*. Upon this map, the presented robot localization method applies both a Gaussian Process Particle Filter (GPPF) to perform camera tracking and a Place Recognition (PR) technique for relocalization within the most likely PSACs according to the observed descriptor. A specific Gaussian Process (GP) is trained for each PSAC to regress a Gaussian distribution over the descriptor for any particle pose lying within that PSAC. The evaluation of the observed descriptor in this distribution gives us a likelihood, which is used as the weight for the particle. Besides, we model the impact of appearance variations on image descriptors as a white noise distribution within the GP formulation, ensuring adequate operation under lighting and scene appearance changes with respect to the conditions in which the map was constructed. A series of experiments with both real and synthetic images show that our method outperforms state-of-the-art appearance-based localization methods in terms of robustness and accuracy, with median errors below 0.3 m and 6◦ .

**Keywords:** appearance-based localization; computer vision; Gaussian processes; manifold learning; robot vision systems; indoor positioning; image manifold; descriptor manifold
