Multilinear relationships between the coordinates of corresponding image conics

This paper presents a study, based on conic correspondences, on the relationship between multiple images acquired by uncalibrated cameras. Representing image conics as points in the five-dimensional projective space allows one to handle image conics in the same way as image points. We show that the coordinates of corresponding image conics satisfy the multilinear constraints, as shown in the case for points and lines. To be more specific, the coordinates of two corresponding image conics satisfy bilinear constraints. When a third image comes in, the coordinates of three corresponding image conics satisfy trilinear constraints. Moreover, these constraints are naturally extended to the case where more images are available