# Global optimization using embedded graphs

@inproceedings{Geiger2000GlobalOU, title={Global optimization using embedded graphs}, author={Davi Geiger and Hiroshi Ishikawa}, year={2000} }

One of the challenges of computer vision is that the information we seek to extract from images is not even defined for most images. Because of this, we cannot hope to find a simple process that produces the information directly from a given image. Instead, we need a search, or an optimization, in the space of parameters that we are trying to estimate.
In this thesis, I introduce two new optimization methods that use graph algorithms. They are characterized by their ability to find a global…

## Figures from this paper

## 41 Citations

Fast Approximate Energy Minimization via Graph Cuts

- Computer Science, MathematicsIEEE Trans. Pattern Anal. Mach. Intell.
- 2001

This work presents two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves that allow important cases of discontinuity preserving energies.

Stereo Matching and Graph Cuts

- Mathematics
- 2008

The stereo matching aims to find corresponding entities between two (or more) images, i.e. entities that are projections of the same 3D object in the scene. Constraints used in stereo matching can be…

Fast approximate energy minimization via graph cuts

- Computer Science, MathematicsProceedings 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.

21 Stereo Matching and Graph Cuts

- 2014

The stereo matching aims to find corresponding entities between two (or more) images, i.e. entities that are projections of the same 3D object in the scene. Constraints used in stereo matching can be…

A Surface Reconstruction Method Using Global Graph Cut Optimization

- Mathematics, Computer ScienceInternational Journal of Computer Vision
- 2005

This work proposes a direct surface reconstruction approach which starts from a continuous geometric functional that is minimized up to a discretization by a global graph-cut algorithm operating on a 3D embedded graph.

Extraction of Three-dimensional Information from Images - Application to Computer Graphics. (Extraction d'informations tridimensionnelles à partir d'images - Application à l'informatique graphique)

- Computer Science, Art
- 2004

This dissertation focuses on the creation of the information used in Computer Graphics and shows how the appearance of a human face is retrieved from a single image and how the extracted data are used to render the original face under a new lighting environment.

Unsupervised Image Partitioning with Semidefinite Programming

- Computer ScienceDAGM-Symposium
- 2002

This work applies a novel optimization technique, semidefinite programming, to the unsupervised partitioning of images, and proves that, from the optimization point of view, this approach cannot perform worse than spectral relaxation approaches which, conversely, may completely fail for the un supervised choice of the eigenvector threshold.

Greedy approach for image restoration based on energy minimization

- 2009

Image restoration can be seen as a problem of finding a function (restored image) that minimizes an energy that models the noise. This global optimization problem can be mapped to a problem of…

An Algorithm for Dense Disparity Mapping by Using Graph Cuts

- Computer Science
- 2005

An improved global optimal algorithm for dense disparity mapping using graph cuts is presented and performance of the proposed algorithm is improved and it will take a shorter time to compute an accuracy dense disparities mapping.

A Volumetric Reconstruction Method from Multiple Calibrated Views using Global Graph Cut Optimization

- Mathematics
- 2003

In this paper, a new formulation and solution to volumetric reconstruction from multiple calibrated images is presented. This problem has been previously formulated either as a continuous geometric…

## References

SHOWING 1-10 OF 78 REFERENCES

Segmentation by grouping junctions

- Mathematics, Computer ScienceProceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231)
- 1998

For a convex smoothing penalty, the global optimal solution for an energy function that fits the data can be obtained in a polynomial time, by a novel use of the maximum-flow algorithm.

"Ratio regions": a technique for image segmentation

- Computer Science, MathematicsProceedings of 13th International Conference on Pattern Recognition
- 1996

A image segmentation algorithm in which the segmented region has both an exterior boundary cost and an interior benefit associated with it, and how to efficiently compute an approximation to common snakes under the additional constraint that it enclose a given point is shown.

A Computational Approach to Edge Detection

- Mathematics, Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1986

There is a natural uncertainty principle between detection and localization performance, which are the two main goals, and with this principle a single operator shape is derived which is optimal at any scale.

Globally optimal regions and boundaries

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

A new form of energy functional for the segmentation of regions in images, and an efficient method for finding its global optima, which can have contributions from both the region and its boundary, is proposed.

Normalized cuts and image segmentation

- Mathematics, Computer ScienceProceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition
- 1997

This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.

Complete Dense Stereovision Using Level Set Methods

- Computer ScienceECCV
- 1998

A novel geometric approach for solving the stereo problem for an arbitrary number of images based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images is presented.

Fast Approximate Maximum a Posteriori Restoration of Multicolour Images

- Mathematics
- 1995

We propose a new algorithm for the approximation of the maximum a posteriori (MAP) restoration of noisy images. The image restoration problem is considered in a Bayesian setting. We assume as prior…

Using Dynamic Programming For Minimizing The Energy Of Active Contours In The Presence Of Hard Constraints

- Mathematics, Computer Science[1988 Proceedings] Second International Conference on Computer Vision
- 1988

The optimization problem is set up as a discrete multi-stage decision process and is solved by a “time-delayed” discrete dynamic programming algorithm, which leads to a stable behavior for the active contours over iterations, in addition to allowing for hard constraints to be enforced on the behavior of the solution.

Dynamic Programming for Detecting, Tracking, and Matching Deformable Contours

- Mathematics, Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1995

The information provided by the user's selected points is explored and an optimal method to detect contours which allows a segmentation of the image is applied, based on dynamic programming (DP), and applies to a wide variety of shapes.

Trace Inference, Curvature Consistency, and Curve Detection

- Mathematics, Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1989

It is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time, and that tangent and curvature information are sufficient, which make it possible to specify powerful constraints between estimated tangents to a curve.