Topological Auto-Calibration of Central Imaging Sensors

This paper departs from traditional calibration in the sense that the pixels forming the camera have a completely unknown topology. Previous works have shown that the statistical properties of natural scenes, and a uniform motion of a camera both in translation and rotation, allow determining the topology of a central camera [10, 6]. Here we show that there is a quasi-linear relationship between time-correlation and angular inter-pixel distance, considering small angles and a simple scenario encompassing one bright light on a dark background. The topology reconstruction algorithm is therefore based on correlating time series (pixel streams) acquired by the pixels of the moving camera. Correlations are converted to inter-pixel distances using a fixed linear transformation. Distances are finally embedded on a plane using a manifold learning methodology, namely Isomap. Experiments on real datasets have been conducted and have shown that the theoretical derivations are accurate for the considered scenario.