In this paper, we apply the conformal Clifford algebra framework for the construction of image viewpoint representations. We start by generalizing the standard conformal model of the Euclidean plane by a family of two-parameters horospheres of \(\mathbb {R}^4\) . This is obtained by applying a metric change of the 4-dimensional space and a variation of the vector at infinity through the action of a rotation. Next, we show that we can linearize the viewpoint changes by constructing a groupoid. A viewpoint is described by an object of the groupoid, that is a generalized horosphere where the point at infinity models the latitude. We get a robust and natural modeling of the viewpoint changes by the morphisms of the groupoid, such that a variation of the latitude is encoded by a rotation of the point at infinity. Also, the zoom parameter of the camera acts by dilating the point at infinity.
