# Energy-Based Geometric Multi-model Fitting

@article{Isack2011EnergyBasedGM, title={Energy-Based Geometric Multi-model Fitting}, author={Hossam N. Isack and Yuri Boykov}, journal={International Journal of Computer Vision}, year={2011}, volume={97}, pages={123-147} }

Geometric model fitting is a typical chicken-&-egg problem: data points should be clustered based on geometric proximity to models whose unknown parameters must be estimated at the same time. Most existing methods, including generalizations of RANSAC, greedily search for models with most inliers (within a threshold) ignoring overall classification of points. We formulate geometric multi-model fitting as an optimal labeling problem with a global energy function balancing geometric errors and…

## 306 Citations

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## References

SHOWING 1-10 OF 48 REFERENCES

### Fast Approximate Energy Minimization with Label Costs

- Computer Science2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- 2010

The main algorithmic contribution is an extension of α-expansion that also optimizes “label costs” with well-characterized optimality bounds, which has a natural interpretation as minimizing description length (MDL) and sheds light on classical algorithms like K-means and expectation-maximization (EM).

### Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography

- Computer ScienceCACM
- 1981

New results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form that provide the basis for an automatic system that can solve the Location Determination Problem under difficult viewing.

### Accelerated Hypothesis Generation for Multi-structure Robust Fitting

- Computer ScienceECCV
- 2010

This work proposes a fundamentally new approach to accelerate hypothesis sampling by guiding it with information derived from residual sorting that is naturally capable of handling data with multiple model instances and excels in applications which easily frustrate other techniques.

### A polynomial-time bound for matching and registration with outliers

- Computer Science2008 IEEE Conference on Computer Vision and Pattern Recognition
- 2008

This work presents a framework for computing optimal transformations, aligning one point set to another, in the presence of outliers, and develops several algorithms which make efficient use of convex programming.

### Fast approximate energy minimization via graph cuts

- Computer ScienceProceedings of the Seventh IEEE International Conference on Computer Vision
- 1999

This paper proposes two algorithms that use graph cuts to compute a local minimum even when very large moves are allowed, and generates a labeling such that there is no expansion move that decreases the energy.

### Two-view multibody structure-and-motion with outliers through model selection

- MathematicsIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2005

Multibody structure-and-motion (MSaM) is the problem in establishing the multiple-view geometry of several views of a 3D scene taken at different times, where the scene consists of multiple rigid…

### Two-View Motion Segmentation from Linear Programming Relaxation

- Computer Science2007 IEEE Conference on Computer Vision and Pattern Recognition
- 2007

A new mixture-of-fundamental-matrices model is proposed to describe the multibody motions from two views that can be naturally formulated as a linear programming (LP) problem and can be solved efficiently by linear program relaxation.

### Optimal consensus set for digital line and plane fitting

- Computer Science, MathematicsInt. J. Imaging Syst. Technol.
- 2011

By using a digital model instead of a continuous one, it is shown that it can generate all possible consensus sets for model fitting and efficiently searches the optimal solution with time complexity O(Nd log N) for dimension d.

### MLESAC: A New Robust Estimator with Application to Estimating Image Geometry

- Computer ScienceComput. Vis. Image Underst.
- 2000

A new robust estimator MLESAC is presented which is a generalization of the RANSAC estimator which adopts the same sampling strategy as RANSac to generate putative solutions, but chooses the solution that maximizes the likelihood rather than just the number of inliers.

### Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation

- Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1996

A novel statistical and variational approach to image segmentation based on a new algorithm, named region competition, derived by minimizing a generalized Bayes/minimum description length (MDL) criterion using the variational principle is presented.