Introduction

This chapter tackles the motion estimation problem, using affine epipolar geometry as the tool. Given m distinct views of n points located on a rigid object, the task is to compute its 3D motion without any prior 3D knowledge. There are several reasons why many existing point–based motion algorithms are of limited practical use: the inevitable presence of noise is often ignored; unreasonable demands are often made on prior processing (e.g. a suitable perceptual frame must first be selected, the features must appear in every frame, etc.); algorithms often only work in special cases (e.g. rotation about a fixed axis); and some algorithms require batch processing, rather than more natural sequential processing.

Although the epipolar constraint has been widely used in perspective and projective motion applications [43, 57, 87] (e.g. to aid correspondence, recover the translation direction and compute rigid motion parameters), it has seldom been used under affine viewing conditions (though see [66, 79]). This chapter therefore makes the following contributions:

• Affine epipolar geometry is related to the rigid motion parameters, and Koenderink and van Doom's novel motion representation is formalised [79]. The scale, cyclotorsion angle and projected axis of rotation are then computed directly from the epipolar geometry (i.e. using two views). The only camera calibration parameter needed here is aspect ratio. A suitable error model is also derived.

• Images are processed in successive pairs of frames, facilitating extension to the m-view case in a sequential (rather than batch) processing mode.

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