Lifted Fundamental Matrices for Mixtures of Central Projection Systems

We study the epipolar geometry between views acquired by mix tures of central projection systems including catadioptric sensors and cameras with lens d istortion. Since the projection models are in general non-linear, a new representation for the geom etry 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, t here is a bilinear form relating the lifted coordinates of corresponding image points. We analy ze the properties of the embedding and explicitly construct the lifted fundamental matrices i n order to understand their structure. The usefulness of the framework is illustrated by estimating th e epipolar geometry between images acquired by a paracatadioptric system and a camera with radi al distortion.

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