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Independent Motion Estimation. Luv Kohli COMP290-089 Multiple View Geometry May 7, 2003. Outline. The motion segmentation problem Motivation Background Recursive RANSAC More sophisticated algorithms Results. Motion segmentation.
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Independent Motion Estimation Luv Kohli COMP290-089 Multiple View Geometry May 7, 2003
Outline • The motion segmentation problem • Motivation • Background • Recursive RANSAC • More sophisticated algorithms • Results
Motion segmentation • The problem according to Phil Torr: how to detect a set of independently moving objects in the 2D projection of an otherwise rigid scene, given that the camera is moving in an arbitrary and unpredetermined manner
Motivation • Many practical applications for motion segmentation • Navigation • Image compression and representation • Video indexing • Recovery of 3D structure • Difficult to generalize for all types of scenes
Background • The methods thus far proposed for motion segmentation can be split into several categories • Methods for a stationary camera: do not distinguish several independently moving objects in the scene – can determine that there is motion but now how many objects
Background (2) • Methods based on image motion constraints • For example, compute velocities in the image using a local correspondence scheme and group similar velocities
Background (3) • Methods that require knowledge of the camera motion • Methods based on world constraints and epipolar geometry • An object undergoing a rigid transformation is equivalent to a camera moving in the opposite direction – effective motion can be described by epipolar geometry
Recursive RANSAC • RANSAC can be used to robustly estimate the fundamental matrix • Determines a highly probable solution to the problem and separates matches into a set of inliers and a set of outliers • Outliers may correspond to a second rigid motion in the scene
Recursive RANSAC (2) • Run RANSAC on set of putative matches to get inliers and outliers • Remove inliers from putative match set, and run RANSAC on outliers • This can be repeated multiple times, but generally it is difficult to fit data for more than 2 or 3 objects • Each matrix can then be improved through nonlinear minimization
Degeneracy • Data is degenerate if insufficient to determine a unique solution • This can cause many problems especially when there is a significant level of noise in the data • Phil Torr created the PLUNDER (Pick Least UNDEgenerate Randomly) algorithm for detecting degeneracy
Degeneracy (2) • The PLUNDER algorithm essentially determines which model (affinity, projectivity, etc.) a data set is consistent with • Fundamental matrices for different subsets of data can be estimated using different models • Phil Torr’s thesis goes into much more detail
References • P.H.S. Torr and D.W. Murray. Outlier detection and motion segmentation. In P.S. Schenker, editor, Sensor Fusion VI, pages 432-443. SPIE volume 2059, 1993. Boston. • P.H.S. Torr. Motion Segmentation and Outlier Detection. Ph.D Thesis, Department of Engineering Science, University of Oxford, 1995.