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LINE-BASED SINGLE VIEW METHODS FOR ESTIMATING 3D CAMERA ORIENTATION IN URBAN SCENES. Ron Tal York University. Outline. Introduction Previous works Approach Results Conclusion. Motivation. Vanishing point. Manhattan Assumption.
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LINE-BASED SINGLE VIEW METHODS FOR ESTIMATING 3D CAMERA ORIENTATION IN URBAN SCENES Ron Tal York University
Outline • Introduction • Previous works • Approach • Results • Conclusion
Motivation Vanishing point
Manhattan Assumption • Recovering this ‘Manhattan frame’ is an important first stage of any single-view reconstruction system • Each direction points towards a vanishing point • In urban imagery, linear features belong to one of 3 mutually orthogonal 3D directions
Outline • Introduction • Previous works • Approach • Results • Conclusion
Early Works • Coexter(1955): Mathematical formulation • Haralick (1980): Application to scene analysis • Barnard (1983): Gauss sphere representation • Collins & Weiss (1991): Least-square formulation
Early Works: Limitations • Assumes strong linear cues are found • Assumes data association is known • No unified framework for estimating the Manhattan frame
Unified Framework: Manhattan World’s • Coughlan & Yuille (1999, 2003) • For gradient observation and frame parameters • Define a probabilistic mixture model • Maximum-likelihood estimate of parameters
Edge-Based Methods • Denis et al. (2008) • Argues less is more • Sparse edge-based probabilistic framework • Accuracy improves by a factor of 2.5 • Begs the question: can we do even better with even sparser lines?
Contributions • More accurate mapping of edges to lines • Artifact free line selection • Line-based framework for recovering the Manhattan frame • Evaluation of line-based methods with the state of the art
YorkUrbanDB • Contains 102 images taken using a calibrated camera • Introduced by Denis et al. (2008) • Hand labeled ground-truth lines and Manhattan frames
Outline • From edges to lines • Line selection • Probabilistic framework • Maximum-likelihood optimization • Introduction • Previous works • Approach • Results • Conclusion
Hough Transform • Lines are detected using the Hough transform, Duda and Hart (1972): • Parametric representation of a line y x
Hough Transform • Discretization of Hough map is a trade-off between accuracy and tolerance for false positives • Observation uncertainty needs to be explicitly considered
Probabilistic Hough Transforms • Kiryati & Bruckstein (2000) • Li and Xie (2003) • Fernandes & Oliveira (2008) • Barinoval et al. (2010) • My solution: a Kernel voting scheme that accurately propagates edge-observation uncertainty onto the Hough domain
Observation Uncertainty • Edge observation uncertainty can be modeled
Propagation of Uncertainty • Linear propagation of uncertainty is used to map observation uncertainty: where
Propagation of Uncertainty • Thus • Recall: and therefore
Kernel Voting • Hough map is the accumulation of BVN kernels that correspond to edge observations
Kernel Voting • Each kernel is computed according to the distribution defined by
Outline • From edges to lines • Line selection • Probabilistic framework • Maximum-likelihood optimization • Introduction • Previous works • Approach • Results • Conclusion
Line Selection • Classical approaches to peak selection: • Sorted list of local maxima • Hough map smoothing • Greedy global maxima selection, followed by NMS • Problem: • Sampling error is unavoidable
Line Selection • Solution: a greedy iterative selection technique that subtracts contributions of edges that belong to detected lines
Outline • From edges to lines • Line selection • Probabilistic framework • Maximum-likelihood optimization • Introduction • Previous works • Approach • Results • Conclusion
Probabilistic Framework • Given a Manhattan frame, the probability of a line is defined as: Determined Via error model Cause prior Learned via training
Error Model • Gauss sphere representation for extended lines: • On the image plane for point features:
Probability of a Line • More specifically: • Where:
Outline • From edges to lines • Line selection • Probabilistic framework • Maximum-likelihood optimization • Introduction • Previous works • Approach • Results • Conclusion
Maximum-Likelihood Optimization • Given a set of line observations we can find the frame that maximizes the likelihood • The rotation parameter is described by the Euler angles that map the camera frame onto the Manhattan frame
A set of three rotations about the axes of the frame: Maximum-Likelihood Optimization 29
Outline • Introduction • Previous works • Approach • Results • Conclusion
Comparison with traditional Hough Quantitative Evaluation 31
Comparison with traditional Hough Quantitative Evaluation 32
Quantitative Evaluation 33 • Previous edge- and gradient-based methods
Run-Time 34
Qualitative Comparison 35 Edge-based Line-based
Outline • Introduction • Previous works • Approach • Results • Conclusion
Conclusion Accurate method for line extraction Improved framework for Manhattan line extraction Method presented outperforms the state of the art by over a factor of 2 37