What Can Be Determined from a Full and a Weak Perspective Image?

This paper presents a first investigation on the structure from motion problem from the combination of full and weak perspective images. This problem arises in multiresolution object modeling, where multiple zoomed-in or closeup views are combined with wider or distant reference views. The narrow field-of-view (FOV) images from the zoomed-in or closeup views can be approximated as weak perspective projection. Using a full perspective projection model for the narrow FOV images, although more accurate, actually leads to instabilities during the estimation process due to the non-linearities in the imaging model. The weak perspective approximation leads to more stable estimation algorithms, although at the cost of a small amount of modeling inaccuracy. Previous work in structure from motion focused either on two (or more) perspective images or on a set of weak perspective (more generally, affine) images. The main contribution of this paper is the study of the SFM problem for the much neglected case of one perspective and one (or more) weak perspective image. We show that in contrast to the case of a pair of weak perspective images, there is adequate information to recover Euclidean structure from a single perspective and a single weak perspective image. The epipolar geometry is simpler than with two perspective images, leading to simpler and more stable estimation algorithms. Computer simulation shows that more stable results can be obtained with the technique presented in this paper than if two images are both considered to be full perspective.