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Independent Motion Estimation
Luv KohliCOMP290-089
Multiple View GeometryMay 7, 2003
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Outline
• The motion segmentation problem• Motivation• Background• Recursive RANSAC• More sophisticated algorithms• Results
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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
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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
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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
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Background (2)
• Methods based on image motion constraints– For example, compute velocities in
the image using a local correspondence scheme and group similar velocities
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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
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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
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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
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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
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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
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Results (Rec. RANSAC)
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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Results
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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Results
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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Results
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Results (putative)
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Results (segmentation)
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Results (segmentation)
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Results (outliers)
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Results (epipolar)
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Results (epipolar)
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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.