Correspondence and Affine Shape from Two Orthographic Views: Motion and Recognition

The paper presents a simple model for recovering affine shape and correspondence from two orthographic views of a 3D object. It is shown that four corresponding points along two orthographic views, taken under similar illumination conditions, determine affine shape and correspondence for all other points. The scheme is useful for purposes of visual recognition by generating novel views of an object given two model views. It is also shown that the scheme can handle objects with smooth boundaries, to a good approximation, without introducing any modifications or additional model views

Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views

We investigate the differences --- conceptually and algorithmically --- between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. We then use the affine invariant to derive new algebraic connections between perspective views. It is shown that three perspective views of an object are connected by certain algebraic functions of image coordinates alone (no structure or camera geometry needs to be involved)

Projective Structure from Two Uncalibrated Images: Structure from Motion and RecRecognition

This paper addresses the problem of recovering relative structure, in the form of an invariant, referred to as projective structure, from two views of a 3D scene. The invariant structure is computed without any prior knowledge of camera geometry, or internal calibration, and with the property that perspective and orthographic projections are treated alike, namely, the system makes no assumption regarding the existence of perspective distortions in the input images