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Machine Learning and Robot Perception - Bruno Apolloni et al (Eds) Part 8

Tham khảo tài liệu 'machine learning and robot perception - bruno apolloni et al (eds) part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 170 G. Unal et al. The direction of motion of an object boundary B monitored through a small aperture A small with respect to the moving unit see Figure 5.1 can not be determined uniquely known as the aperture problem . Experimentally it can be observed that when viewing the moving edge B through aperture A it is not possible to determine whether the edge has moved towards the direction c or direction d. The observation of the moving edge only allows for the detection and hence computation of the velocity component normal to the edge vector towards n in Figure 5.1 with the tangential component remaining undetectable. Uniquely determining the velocity field hence requires more than a single measurement and it necessitates a combination stage using the local measurements 25 . This in turn means that computing the velocity field involves regularizing constraints such as its smoothness and other variants. Fig. 5.1. The aperture problem when viewing the moving edge B through aperture A it is not possible to determine whether the edge has moved towards the direction c or direction d Horn and Schunck in their pioneering work 26 combined the optical flow constraint with a global smoothness constraint on the velocity field to define an energy functional whose minimization arg min í VI V It 2 T2 Vu 2 Vu 2 Jx u v Q can be carried out by solving its gradient descent equations. A variation on this theme would adopt an L1 norm smoothness constraint in contrast to 5 Efficient Incorporation of Optical Flow 171 Horn-Schunck s L2 norm on the velocity components and was given in 27 . Lucas and Kanade in contrast to Horn and Schunck s regularization based on post-smoothing minimized a pre-smoothed optical constraint JW 2 x VI x t V It x t 2dx R where W x denotes a window function that gives more weight to constraints near the center of the neighborhood R 28 . Imposing the regularizing smoothness constraint on the velocity over the whole image leads to over-smoothed motion estimates at