A Robust Multi-Camera 3D Ellipse Fitting for Contactless Measurements

Ellipses are a widely used cue in many 2D and 3D object recognition pipelines. In fact, they exhibit a number of useful properties. First, they are naturally occurring in many man-made objects. Second, the projective invariance of the class of ellipses makes them detectable even without any knowledge of the acquisition parameters. Finally, they can be represented by a compact set of parameters that can be easily adopted within optimization tasks. While a large body of work exists in the literature about the localization of ellipses as 2D entities in images, less effort has been put in the direct localization of ellipses in 3D, exploiting images coming from a known camera network. In this paper we propose a novel technique for fitting elliptical shapes in 3D space, by performing an initial 2D guess on each image followed by a multi-camera optimization refining a 3D ellipse simultaneously on all the calibrated views. The proposed method is validated both with synthetic data and by measuring real objects captured by a specially crafted imaging head. Finally, to evaluate the feasibility of the approach within real-time industrial scenarios, we tested the performance of a GPU-based implementation of the algorithm.