2. Contents
• Why compute vanishing points ?
• Application on architectural scenes
• What is a vanishing point ?
• Chasles-Steiner theorem
• Algorithm
• Results
• Summary & conclusion
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3. Vanishing points :
Why ?
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2D image : 3D information LOST• Real life : Parallel lines
• Environments created by humans contains many parallel lines
4. Vanishing points :
Why ?
• Providing strong information about 3D
structure of a scene (Best way)
• Applications :
– Camera calibration
– Augmented Reality
– Create 3D map
– Help land surveyor to
align buildings
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5. • Compute the photo orientation
Vertical of the scene
• Minimize the error
High numbers of segments
Purpose :
Application on architectural scene
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Allows to :
6. Vanishing points :
What is it ?
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2D image : Converging linesReal life : Parallel lines
Vanishing point
Vanishing line
7. Related works
• Different methods were proposed :
– Gaussian sphere : more accurate but complex
– Projective Geometry approach
• Chasles-Steiner theorem :
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« An homography between two
bundles of converging lines define
a conic section, and reciprocally »
8. Algorithm steps
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1. Extract segments
• Based on Canny-Deriche detection
2. Transform segments in points
• Apply the Chasles-Steiner theorem
3. Extract circles among previous points found
• RanSac method adapted
4. Compute coordinates of the vanishing points
9. 2 steps :
-Smoothing
- Calculation of magnitude and gradient direction
- Non-maximum suppression
- Hysteresis thresholding
Extract segments
Canny-Deriche
detection
Local maxima
detection
Polygonization
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10. 4th step : Thanks to the circle parameters (especially, center coordinates),
We can determine the vanishing points as the opposite point of the image origin
Chasles-Steiner Theorem
• Applied to vanishing points computing :
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O
P
C
Image
H1
H2
H3
S1
S2
S3
1st step : Thanks to the segments, compute the carrier lines2nd step : H points are computed : OH and Segments should make a 90° angle3rd step : A circle is found passing through the H points
12. Extract circles
RanSac method
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O
2. Compute the circle which intersect the 2 points and O1. Two points H are chosen randomly among all3. Create a band of epsilon size and count the number of H points inside4. Repeat steps 1 to 3 many times5. Keep in memory the 2 H points and captured points
-> Remove them from the beginning ensemble and iterate
13. Compute the P coordinates
• XP = 2 x Xc
• YP = 2 x Yc
• We could compute uncertainty with the variance-covariance matrix
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O
P
C
14. Results
• On 100 different images :
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Pourcentage of correct
detection of the vertical
vanishing point
100%
Pourcentage of correct
detection of the horizontal
vanishing points
92%
Good performance
15. Results
• Issues :
– Segments near to the origin -> the H point
position will change a lot the circle
– Noisy image : edge detection not precise
– Complex architectures whith many curves
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18. Bibliography
• Automatic detection of vanishing points and
their uncertainty based on projective
geometry, M. Kalantari, F. Jung, JP. Guédon, N.
Paparoditis
• Détéction entièrement automatique de points
de fuite dans des scènes architecturales
urbaines, M. Kalantari, F. Jung
• A new Approach to Vanishing Point Detection
in Architectural Environments, Carsten Rother
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19. Conclusion
• Interesting and contemporary subject
• What’s next : Smartphone applications etc.
SOME QUESTIONS ?
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