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# How to detect vanishing points on architectural scenes ?

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Presents you one concept (without details, only principles) of how to compute vanishing points using geommetry and computer vision.

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### How to detect vanishing points on architectural scenes ?

1. 1. Project PresentationHow to detect vanishing pointson architectural scenesPERNEY Benjamin - 20121
2. 2. Contents• Why compute vanishing points ?• Application on architectural scenes• What is a vanishing point ?• Chasles-Steiner theorem• Algorithm• Results• Summary & conclusionPERNEY Benjamin - 20122
3. 3. Vanishing points :Why ?PERNEY Benjamin - 201232D image : 3D information LOST• Real life : Parallel lines• Environments created by humans contains many parallel lines
4. 4. Vanishing points :Why ?• Providing strong information about 3Dstructure of a scene (Best way)• Applications :– Camera calibration– Augmented Reality– Create 3D map– Help land surveyor toalign buildingsPERNEY Benjamin - 20124
5. 5. • Compute the photo orientationVertical of the scene• Minimize the errorHigh numbers of segmentsPurpose :Application on architectural scenePERNEY Benjamin - 20125Allows to :
6. 6. Vanishing points :What is it ?PERNEY Benjamin - 201262D image : Converging linesReal life : Parallel linesVanishing pointVanishing line
7. 7. Related works• Different methods were proposed :– Gaussian sphere : more accurate but complex– Projective Geometry approach• Chasles-Steiner theorem :PERNEY Benjamin - 20127« An homography between twobundles of converging lines definea conic section, and reciprocally »
8. 8. Algorithm stepsPERNEY Benjamin - 201281. Extract segments• Based on Canny-Deriche detection2. Transform segments in points• Apply the Chasles-Steiner theorem3. Extract circles among previous points found• RanSac method adapted4. Compute coordinates of the vanishing points
9. 9. 2 steps :-Smoothing- Calculation of magnitude and gradient direction- Non-maximum suppression- Hysteresis thresholdingExtract segmentsCanny-DerichedetectionLocal maximadetectionPolygonizationPERNEY Benjamin - 20129
10. 10. 4th step : Thanks to the circle parameters (especially, center coordinates),We can determine the vanishing points as the opposite point of the image originChasles-Steiner Theorem• Applied to vanishing points computing :PERNEY Benjamin - 201210OPCImageH1H2H3S1S2S31st 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
11. 11. Chasles-Steiner TheoremPERNEY Benjamin - 201211
12. 12. Extract circlesRanSac methodPERNEY Benjamin - 201212O2. 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. 13. Compute the P coordinates• XP = 2 x Xc• YP = 2 x Yc• We could compute uncertainty with the variance-covariance matrixPERNEY Benjamin - 201213OPC
14. 14. Results• On 100 different images :PERNEY Benjamin - 201214Pourcentage of correctdetection of the verticalvanishing point100%Pourcentage of correctdetection of the horizontalvanishing points92%Good performance
15. 15. Results• Issues :– Segments near to the origin -> the H pointposition will change a lot the circle– Noisy image : edge detection not precise– Complex architectures whith many curvesPERNEY Benjamin - 201215
16. 16. Results & improvementsPERNEY Benjamin - 201216
17. 17. SummaryPERNEY Benjamin - 201217(a) (b)(c) (d)
18. 18. Bibliography• Automatic detection of vanishing points andtheir uncertainty based on projectivegeometry, M. Kalantari, F. Jung, JP. Guédon, N.Paparoditis• Détéction entièrement automatique de pointsde fuite dans des scènes architecturalesurbaines, M. Kalantari, F. Jung• A new Approach to Vanishing Point Detectionin Architectural Environments, Carsten RotherPERNEY Benjamin - 201218
19. 19. Conclusion• Interesting and contemporary subject• What’s next : Smartphone applications etc.SOME QUESTIONS ?PERNEY Benjamin - 201219