The hierarchy of the cocoons of a graph and its application to image segmentation

Guigues, Laurent; Men, Hervé Le; Cocquerez, Jean-Pierre

doi:10.1016/s0167-8655(02)00252-0

Cited by 45 publications

(36 citation statements)

References 7 publications

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“…In [18] we proposed another way to obtain multi-scale segmentations from a dissimilarity-based grouping approach. We defined a cocoon of a valued graph as a connected set of nodes whose maximal internal dissimilarity is lower than the minimal dissimilarity with the exterior nodes.…”

Section: Ultrametric Distances and The Region/contour Dualitymentioning

confidence: 99%

“…We proved that the set of the cocoons of a graph is a hierarchy and released an associated ultrametrics. Cocoons hierarchies are related to complete-linkage clustering while the MST of a graph can be computed by single-linkage clustering [29,18].…”

Section: Ultrametric Distances and The Region/contour Dualitymentioning

confidence: 99%

“…The cut is extracted from a hierarchy of regions obtained by classical region-merging technique which has no particular affinity with the minimization problem. We also employed this method in an image segmentation algorithm based on minimizing a Minimum Description Length (MDL) criterion in a hierarchy of cocoons [18,17].…”

Section: Hierarchical Minimization Of Separable Energiesmentioning

confidence: 99%

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Scale-Sets Image Analysis

Guigues

Cocquerez

Men

2006

Int J Comput Vision

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197

198

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This paper introduces a multi-scale theory of piecewise image modelling, called the scale-sets theory, and which can be regarded as a region-oriented scale-space theory. The first part of the paper studies the general structure of a geometrically unbiased region-oriented multi-scale image description and introduces the scale-sets representation, a representation which allows to handle such a description exactly. The second part of the paper deals with the way scale-sets image analyses can be built according to an energy minimization principle. We consider a rather general formulation of the partitioning problem which involves minimizing a two-term-based energy, of the form λC+D, where D is a goodness-of-fit term and C is a regularization term. We describe the way such energies arise from basic principles of approximate modelling and we relate them to operational rate/distorsion problems involved in lossy compression problems. We then show that an important subset of these energies constitutes a class of multi-scale energies in that the minimal cut of a hierarchy gets coarser and coarser as parameter λ increases. This allows us to devise a fast dynamic-programming procedure to find the complete scale-sets representation of this family of minimal cuts. Considering then the construction of the hierarchy from which the minimal cuts are extracted, we end up with an exact and parameterfree 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. This algorithm can be viewed as a continuation method along the scale dimension or as a minimum pursuit along the operational rate/distorsion curve. Furthermore, the solution verifies a linear scale invariance property which allows to completely postpone the tuning of the scale parameter to a subsequent stage. For computational reasons, the scale climbing algorithm is approximated by a pair-wise region merging scheme: however the principal properties of the solutions are kept. Some results obtained with Mumford-Shah's piece-wise constant model and a variant are provided and different applications of the proposed multi-scale analyses are finally sketched.

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Section: Ultrametric Distances and The Region/contour Dualitymentioning

confidence: 99%

Section: Ultrametric Distances and The Region/contour Dualitymentioning

confidence: 99%

Section: Hierarchical Minimization Of Separable Energiesmentioning

confidence: 99%

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Scale-Sets Image Analysis

Guigues

Cocquerez

Men

2006

Int J Comput Vision

Self Cite

197

198

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“…General discussions on the ill-posedness of contrastbased (or discriminative) formulations of the segmentation problem can be found in [24], [25], [26], [4]. Ill-posedness of model-based (or generative model) formulations of the segmentation problem have been extensively discussed in the energy minimization-based segmentation community, see e.g.…”

Section: B Analysis Of Existing Evaluation Criteriamentioning

confidence: 99%

Multi-Scale Criteria for the Evaluation of Image Segmentation Algorithms

Philipp‐Foliguet¹,

Guigues²

2008

JMM

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Abstract-This paper deals with evaluation of image segmentation methods. We start with a state-of-the art of the evaluation criteria, involving a reference segmentation or not. Based on an analysis of the main existing criteria, we propose new criteria, when no ground-truth is available. These criteria, based on an energetic formalism, take into account both the complexity of the segmented image, through the boundary length and the goodness-offit of an underlying model with the initial data. The main interest is not to fix the level of detail expected by the evaluation criterion but to leave it to the user's choice, according to his purpose. These evaluation criteria are thus multi-scale criteria. Various forms of energy formulation are experimentally compared. Then after having chosen a particular energy, the performances of this new criterion is compared to the main existing criteria.

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“…Other methods for planar images [2], [3] use an adaptive criterion that depends on local properties rather than global ones. In contrast with the simple graph-based methods, cut-criterion methods capture the non-local cuts in a graph are designed to minimize the similarity between pixels that are being split [4] [5].…”

Section: Iintroduction and Related Workmentioning

confidence: 99%

Efficient Volumetric Segmentation Method

Burdescu¹,

Stănescu²,

Brezovan³

et al. 2014

Annals of Computer Science and Information Systems

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--In this paper we extend our previous work for planar images by adding a new step in the volumetric segmentation algorithm that allows us to determine regions closer to it. There are huge of papers for planar images and segmentation methods and most of them are graph-based for planar images and very few papers for volumetric segmentation methods. However, even if image segmentation is a heavily researched field, extending the algorithms to spatial has been proven not to be an easy task. A true volumetric segmentation remains a difficult problem to tackle due to the complex nature of the topology of spatial objects, the huge amount of data to be processed and the complexity of the algorithms that scale with the new added dimension. The problem of partitioning images into homogenous regions or semantic entities is a basic problem for identifying relevant objects. Visual segmentation is related to some semantic concepts because certain parts of a scene are pre-attentively distinctive and have a greater significance than other parts. A number of approaches to segmentation are based on finding compact regions in some feature space. A recent technique using feature space regions first transforms the data by smoothing it in a way that preserves boundaries between regions. The key to the whole own algorithm of volumetric segmentation is the honeycomb cells. The pre-processing module is used mainly to blur the initial RGB spatial image in order to reduce the image store and to make algorithms to be efficient. Then the volumetric segmentation module creates virtual cells of prisms with tree-hexagonal structure defined on the set of the image voxels of the input spatial image and a volumetric grid graph having tree-hexagons as cells of vertices. Early graph-based methods use fixed thresholds and local measures in finding a volumetric segmentation.Index terms-Volumetric Segmentation; Graph-based segmentation; Color segmentation; Syntactic segmentation I.INTRODUCTION AND RELATED WORKSHERE is a wide range of computational vision problems for planar images that could use of segmented images. The problem of partitioning images into homogenous regions or semantic entities is a basic problem for identifying relevant objects. Higher-level problems such as object recognition and image indexing can also make use of segmentation results in matching, to address problems such as figure-ground separation and recognition by parts. In both intermediate level and higher-level vision problems, contour detection of objects in real images is a fundamental problem. However the problems of planar image segmentation and grouping remain great challenges for computer vision. As a consequence we consider that a spatial segmentation method can detect visual objects from images if it can detect at least the most objects. We develop a visual feature-based method which uses a virtual spatial graph constructed on cells of prisms with treehexagonal structure containing half of the image voxels in order to determine a forest of spanning trees fo...

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The hierarchy of the cocoons of a graph and its application to image segmentation

Cited by 45 publications

References 7 publications

Scale-Sets Image Analysis

Scale-Sets Image Analysis

Multi-Scale Criteria for the Evaluation of Image Segmentation Algorithms

Efficient Volumetric Segmentation Method

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