# Hierarchy Construction Schemes Within the Scale Set Framework

@article{Pruvot2007HierarchyCS, title={Hierarchy Construction Schemes Within the Scale Set Framework}, author={Jean-Hugues Pruvot and Luc Brun}, journal={ArXiv}, year={2007}, volume={abs/0712.1878} }

Segmentation algorithms based on an energy minimisation framework often depend on a scale parameter which balances a fit to data and a regularising term. Irregular pyramids are defined as a stack of graphs successively reduced. Within this framework, the scale is often defined implicitly as the height in the pyramid. However, each level of an irregular pyramid can not usually be readily associated to the global optimum of an energy or a global criterion on the base level graph. This last…

## 3 Citations

Fully deformable 3D digital partition model with topological control

- Mathematics, Computer SciencePattern Recognit. Lett.
- 2011

Hierarchical Matching Using Combinatorial Pyramid Framework

- Mathematics, Computer ScienceICISP
- 2008

A string matching approach to find a region correspondance between two images based on a cicular string matching algorithm which uses both the orientability of the plane and the hierarchical encoding of the two regions to reduce the computational cost of the matching and enforce its robustness.

Multi-Label Simple Points Definition for 3D Images Digital Deformable Model

- Computer Science, MathematicsDGCI
- 2009

The main contribution of this paper is the definition of multilabel simple points that ensures that the partition topology remains invariant during a deformable partition process. The definition is…

## References

SHOWING 1-10 OF 29 REFERENCES

Hierarchical Watersheds Within the Combinatorial Pyramid Framework

- Computer ScienceDGCI
- 2005

This paper presents a hierarchical watershed algorithm based on combinatorial pyramids which overcomes the problems connected to the presence of noise both within the basins and along the watershed contours.

Scale-Sets Image Analysis

- Mathematics, Computer ScienceInternational Journal of Computer Vision
- 2005

An exact and parameter-free algorithm to build scale-sets image descriptions whose sections constitute a monotone sequence of upward global minima of a multi-scale energy, which is called the “scale climbing” algorithm is introduced.

Building irregular pyramids by dual-graph contraction

- Mathematics
- 1995

Many image analysis tasks lead to, or make use of, graph structures that are related through the analysis process with the planar layout of a digital image. The author presents a theory that allows…

An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2004

The goal of this paper is to provide an experimental comparison of the efficiency of min-cut/max flow algorithms for applications in vision, comparing the running times of several standard algorithms, as well as a new algorithm that is recently developed.

Image segmentation using local variation

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

A new graph-theoretic approach to the problem of image segmentation that is able to preserve detail in low-variability regions while ignoring detail in high-Variability regions, which is illustrated with several examples on both real and synthetic images.

Constructing simple stable descriptions for image partitioning

- Mathematics, Computer ScienceInternational Journal of Computer Vision
- 2004

A new formulation of the image partitioning problem is presented: construct a complete and stable description of an image-in terms of a specified descriptive language-that is simplest in the sense of being shortest, which yields intuitively satisfying partitions for a wide class of images.

Constructing Stochastic Pyramids by MIDES - Maximal Independent Directed Edge Set

- Mathematics, Computer ScienceGbRPR
- 2003

The new method yields a higher reduction factor than the stochastic decimation algorithm (MIS) and maximal independent edge set (MIES), in all tests, which means the number of vertices in the subgraph induced by any set of contractible edges is reduced to half or less by a single parallel contraction.

Image Segmentation from Consensus Information

- Computer ScienceComput. Vis. Image Underst.
- 1997

A new approach toward image segmentation is proposed in which a set of slightly different segmentations is derived from the same input and the final result is based on the consensus among them, using the hierarchical, RAG pyramid technique.

Logarithmic Tapering Graph Pyramid

- Mathematics, Computer ScienceDAGM-Symposium
- 2002

A new method to determine contraction kernels for the construction of graph pyramids works with undirected graphs and yields a reduction factor of at least 2.0, better than the stochastic decimation algorithm, in all tests.