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Active Visual Inference of Surface Shape - Roberto Cipolla Part 10

Tham khảo tài liệu 'active visual inference of surface shape - roberto cipolla part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 5.3. Differential invariants of the image velocity field 127 The magnitude of the depth gradient determines the tangent of the slant of the surface angle between the surface normal and the visual direction . It vanishes for a frontal view and is infinite when the viewer is in the tangent plane of the surface. Its direction specifies the direction in the image of increasing distance. This is equal to the tilt of the surface tangent plane T. The exact relationship between the magnitude and direction of F and the slant and tilt of the surface T r is given by F tana 5.23 ZF T 5.24 With this new notation equations 5.16 5.17 5.18 and 5.19 can be re-written to show the relation between the differential invariants the motion parameters and the surface position and orientation curlv -2fi.q F A A 5.25 divv 2U.q -q i F. A A 5.26 defv F A 5.27 where which specifies the axis of maximum extension bisects A and F ZA ZF 2 ------1----. 5.28 The geometric significance of these equations is easily seen with a few examples see below . Note that this formulation clearly exposes both the speed-scale ambiguity - translational velocities appear scaled by depth making it impossible to determine whether the effects are due to a nearby object moving slowly or a far-away object moving quickly - and the bas-relief ambiguity. The latter manifests itself in the appearance of surface orientation F with A. Increasing the slant of the surface F while scaling the movement by the same amount will leave the local image velocity field unchanged. Thus from two weak perspective views and with no knowledge of the viewer translation it is impossible to determine whether the deformation in the image is due to a large IA large turn of the object or vergence angle and a small slant or a large slant and a small rotation around the object. Equivalently a nearby shallow object will produce the same effect as a far away deep structure. We can only recover the depth gradient F up to an unknown scale. These .