Modeling Practical Multi-Center-of-Projection Using Ellipsoid

Traditional 3D projection models, such as perspective and orthographic projection, are limited to two types of projective ray fields: rays passing through a single point and parallel rays. In this paper, we introduce an ellipsoidal-based 3D projection model to overcome the sparsity of 3D projections. Our ellipsoidal 3D projection model comprises an ellipsoid and an axis-aligned geometry such as a line or a plane. By linearly mapping these two geometries along their principal axes, our model enables us to explore the continuous domain of projective ray fields while taking advantage of the anisotropy in ellipsoids. We introduce the intrinsic characteristic of our projection field, called the ellipse property, that enables testing isomorphism with other projection models. We prove the difference between ours and the catadioptric projection model employing an elliptic mirror. Besides, we propose a perspectivity metric for the intuitive control over the parameter space. We present both forward and backward projections of our model, demonstrating its applicability across several visual applications, ranging from image synthesis to scene reconstruction.