The book Multiple View Geometry in Computer Vision by Richard Hartley and Andrew Zisserman talks about lines, points and conics. A conic is a curve described by a second-degree equation in the plane, so a parabola would be an example of a conic. The purpose and usage of points and lines in computer vision are quite clear. For example, a set of points defines an object, or we can project a 3-dimensional point to a 2-dimensional point in the image plane, or a line represents the space to look for the corresponding point in the second plane of another point in the first plane (epipolar geometry). However, probably because I haven't yet read the part of the book related to the applications of conics in computer vision, it's not clear why do we even care about conics in computer vision.
So, why are conics important in computer vision? Note that I know that conics are defined by points and, given the point-line duality, they can also be defined by lines, but this doesn't still enlightens me on the purpose of conics in computer vision. So, I am looking for applications where conics are used to define the underlying CV model, in a similar way that points and lines are used to describe the pinhole camera model.