Optima on Hierarchies of Partitions

Serra, Jean; Kiran, Bangalore Ravi

doi:10.1007/978-3-642-38294-9_13

Cited by 6 publications

(12 citation statements)

References 11 publications

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“…Our framework does not have this limitation since we can use any criterion, as it is depicted in the variety and the diversity of the presented examples. As compared to the classical state-of-the-art approaches that consist of cutting a hierarchy of segmentations [3,2,14,4,17,18,20,19], each threshold of the extinction-based saliency map gives a segmentation result which is a priori different from any cut of the original hierarchy of segmentations. Actually, this process enlarges the set of possible partitions for a given hierarchy of segmentations.…”

Section: Resultsmentioning

confidence: 99%

“…They propose a new approach to find optimal cuts of H in one pass based on energy minimization. The interested reader can refer to [17,18,19] for more details.…”

Section: Cuts In a Hierarchymentioning

confidence: 99%

“…We focus on the comparison with two families of closely related work: shape-space filtering [6] in Section 3.1 and hierarchical cuts [2,17,18,19,20] in Section 3.2.…”

Section: Comparison With Related Workmentioning

confidence: 99%

“…The cut-based methods [2,17,18,19,20] reviewed in Section 2.2 consist of cutting the input hierarchy of segmentations horizontally or non-horizontally to obtain a partition. They do not change the structure of the input hierarchy of segmentations H in the sense that for each region in H, either all its child regions or none of these two regions belong to the final partition.…”

Section: Comparison With Hierarchical Cutsmentioning

confidence: 99%

“…Another advantage of our proposed framework is that it is not limited to the h-increasing attributes used in the state-of-the-art hierarchy transformation methods [3,2,14,4,17,18,19,37]. We can use any attribute in our proposed framework.…”

Section: Comparison With Hierarchical Cutsmentioning

confidence: 99%

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Hierarchical Segmentation Using Tree-Based Shape Spaces

Carlinet

Géraud

et al. 2017

IEEE Trans. Pattern Anal. Mach. Intell.

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Current trends in image segmentation are to compute a hierarchy of image segmentations from fine to coarse. A classical approach to obtain a single meaningful image partition from a given hierarchy is to cut it in an optimal way, following the seminal approach of the scale-set theory. While interesting in many cases, the resulting segmentation, being a non-horizontal cut, is limited by the structure of the hierarchy. In this paper, we propose a novel approach that acts by transforming an input hierarchy into a new saliency map. It relies on the notion of shape space: a graph representation of a set of regions extracted from the image. Each region is characterized with an attribute describing it. We weigh the boundaries of a subset of meaningful regions (local minima) in the shape space by extinction values based on the attribute. This extinction-based saliency map represents a new hierarchy of segmentations highlighting regions having some specific characteristics. Each threshold of this map represents a segmentation which is generally different from any cut of the original hierarchy. This new approach thus enlarges the set of possible partition results that can be extracted from a given hierarchy. Qualitative and quantitative illustrations demonstrate the usefulness of the proposed method.

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Section: Resultsmentioning

confidence: 99%

“…They propose a new approach to find optimal cuts of H in one pass based on energy minimization. The interested reader can refer to [17,18,19] for more details.…”

Section: Cuts In a Hierarchymentioning

confidence: 99%

“…We focus on the comparison with two families of closely related work: shape-space filtering [6] in Section 3.1 and hierarchical cuts [2,17,18,19,20] in Section 3.2.…”

Section: Comparison With Related Workmentioning

confidence: 99%

Section: Comparison With Hierarchical Cutsmentioning

confidence: 99%

Section: Comparison With Hierarchical Cutsmentioning

confidence: 99%

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Hierarchical Segmentation Using Tree-Based Shape Spaces

Carlinet

Géraud

et al. 2017

IEEE Trans. Pattern Anal. Mach. Intell.

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Ordering Partial Partitions for Image Segmentation and Filtering: Merging, Creating and Inflating Blocks

Ronse

2013

J Math Imaging Vis

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The refinement order on partitions corresponds to the operation of merging blocks in a partition, which is relevant to image segmentation and filtering methods. Its mathematical extension to partial partitions, that we call standard order, involves several operations, not only merging, but also creating new blocks or inflating existing ones, which are equally relevant to image segmentation and filtering techniques. These three operations correspond to three basic partial orders on partial partitions, the merging, inclusion and inflating orders. There are three possible combinations of these three basic orders, one of them is the standard order, the other two are the merging-inflating and inclusion-inflating orders. We study these orders in detail, giving in particular their minimal and maximal elements, covering relations and height functions. We interpret hierarchies of partitions and partial partitions in terms of an adjunction between (partial) partitions (possibly with connected blocks) and scalars. This gives a lattice-theoretical interpretation of edge saliency, hence a typology for the edges in partial partitions. The use of hierarchies in image filtering, in particular with component trees, is also discussed. Finally, we briefly mention further orders on partial partitions that can be useful for image segmentation. This work received funding from the Agence Nationale de la Recherche, contract ANR-2010-BLAN-0205-01.

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Efficient tree construction for multiscale image representation and processing

Havel

Merciol

Lefèvre

2016

J Real-Time Image Proc

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With the continuous growth of sensor performances, image analysis and processing algorithms have to cope with larger and larger data volumes. Besides, the informative components of an image might not be the pixels themselves, but rather the objects they belong to. This has led to a wide range of successful multiscale techniques in image analysis and computer vision. Hierarchical representations are thus of first importance, and require efficient algorithms to be computed in order to address real-life applications. Among these hierarchical models, we focus on morphological trees (e.g., min/max-tree, tree of shape, binary partition tree, αtree) that come with interesting properties and already led to appropriate techniques for image processing and analysis, with a growing interest from the image processing community. More precisely, we build upon two recent algorithms for efficient α-tree computation and introduce several improvements to achieve higher performance. We also discuss the impact of the data structure underlying the tree representation, and provide for the sake of illustration several applications where efficient multiscale image representation leads to fast but accurate techniques, e.g. in remote sensing image analysis or video segmentation.

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Optima on Hierarchies of Partitions

Cited by 6 publications

References 11 publications

Hierarchical Segmentation Using Tree-Based Shape Spaces

Hierarchical Segmentation Using Tree-Based Shape Spaces

Ordering Partial Partitions for Image Segmentation and Filtering: Merging, Creating and Inflating Blocks

Efficient tree construction for multiscale image representation and processing

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