Tham khảo tài liệu 'active visual inference of surface shape - roberto cipolla part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 174 App. B Orthographic projection and the curvature from is therefore 1 w Wee Depth and curvature are obtained from first and second-order derivatives of the image with respect to viewer orientation. Appendix c Determining ỗtt-n from the spatio-temporal image qfsyt If the surface marking is a discrete point image position q it is possible in principle to measure the image velocity q and acceleration q t directly from the image without any assumption about viewer motion. This is impossible for a point on an image curve. Measuring the real image velocity qs and acceleration qit for a point on an image curve requires knowledge of the viewer motion - equation . Only the normal component of image velocity can be obtained from local measurements at a curve. It is shown below however that for a discrete point curve pair - the normal component of the relative image acceleration - is completely determined from measurements on the spatiotemporal image. This result is important because it demonstrates the possibility of obtaining robust inferences of surface geometry which are independent of any assumption of viewer motion. The proof depends on re-parameterising the spatio-temporal image so that it is independent of knowledge of viewer motion. In the epipolar parameterisation of the spatio-temporal image q s the s-parameter curves were defined to be the image contours while the -parameter curves were defined by equation so that at any instant the magnitude and direction of the tangent to a -parameter curve is equal to the real image velocity qt - more precisely I . A parameterisation which is completely independent of knowledge of viewer motion q s where s s can be chosen. Consider for example a parameterisation where the -parameter curves with tangent are chosen to be orthogonal to the s-parameter curves with tangent - the image contours. Equivalently the -parameter curves are defined to be parallel to the curve normal n aL J C 1 where 3 is the .
