ECE 549CS 543: COMPUTER VISION LECTURE 23

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ECE 549/CS 543 COMPUTER VISION LECTURE
23 SEGMENTATION I
From Projective to Euclidean SFM The Segmentation
Problem Human Vision Clustering Merging and
Splitting

• Reading Chapters 13 and 14
• A list of potential projects is at
• http//www-cvr.ai.uiuc.edu/ponce/fall04/project
  s.pdf
• I will be gone next Thursday. Substitute a
  lecture this
• Friday, or a class on Monday???

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Motion estimation from fundamental matrices
Q
Once M and M are known, P can be computed with
LLS.
Facts
b can be found using LLS.
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Projective Structure from Motion and Factorization
Factorization??

• Algorithm (Sturm and Triggs, 1996)
• Guess the depths
• Factorize D
• Iterate.

Does it converge? (Mahamud, Hebert, Omori Ponce
2001)
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Relative reconstruction error 0.2
Mean reprojection error 0.9pixel
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Bundle adjustment (Photogrammetry)
Minimize
with respect to the matrices Mi and the point
positions Pj .
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Relative reconstruction error 0.2
Mean reprojection error 0.8pixel
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From Projective to Euclidean Images
If z , P , R and t are solutions, so are l z
, l P , R and l t .
Absolute scale cannot be recovered! The Euclidean
shape (defined up to an arbitrary similitude) is
the best that can be recovered.
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From uncalibrated to calibrated cameras
Perspective camera
Calibrated camera
Problem what is Q ?
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Relative reconstruction error 1.2
Mean reprojection error 0.9pixel
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From uncalibrated to calibrated cameras II
Perspective camera
Calibrated camera
Problem what is Q ?
Example known image center
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Relative reconstruction error 1.5
Mean reprojection error 0.9pixel
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(Pollefeys, Koch and Van Gool, 1999)
Reprinted from Self-Calibration and Metric 3D
Reconstruction from Uncalibrated
Image Sequences, by M. Pollefeys, PhD Thesis,
Katholieke Universiteit, Leuven (1999).
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Why do these tokens belong together?
What is foreground and what is background?
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Grouping and Gestalt (Muller-Lyer Illusion)
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Gestalt Cues for Grouping
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Gestalt Cues for Grouping
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Segmentation as clustering

• Cluster together (pixels, tokens, etc.) that
  belong together
• Agglomerative clustering
• attach closest to cluster it is closest to
• repeat
• Divisive clustering
• split cluster along best boundary
• repeat

• Point-Cluster distance
• single-link clustering
• complete-link clustering
• group-average clustering
• Dendrograms
• yield a picture of output as clustering process
  continues

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