Epipolar Geometry of Central Projection Systems Using Veronese Maps

We study the epipolar geometry between views acquired by mixtures of central projection systems including catadioptric sensors and cameras with lens distortion. Since the projection models are in general non-linear, a new representation for the geometry of central images is proposed. This representation is the lifting through Veronese maps of the image plane to the 5D projective space. It is shown that, for most sensor combinations, there is a bilinear form relating the lifted coordinates of corresponding image points. We analyze the properties of the embedding and explicitly construct the lifted fundamental matrices in order to understand their structure. The usefulness of the framework is illustrated by estimating the epipolar geometry between images acquired by a paracatadioptric system and a camera with radial distortion.

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