1,708 research outputs found
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
On the equivalence between hierarchical segmentations and ultrametric watersheds
We study hierarchical segmentation in the framework of edge-weighted graphs.
We define ultrametric watersheds as topological watersheds null on the minima.
We prove that there exists a bijection between the set of ultrametric
watersheds and the set of hierarchical segmentations. We end this paper by
showing how to use the proposed framework in practice in the example of
constrained connectivity; in particular it allows to compute such a hierarchy
following a classical watershed-based morphological scheme, which provides an
efficient algorithm to compute the whole hierarchy.Comment: 19 pages, double-colum
New characterizations of minimum spanning trees and of saliency maps based on quasi-flat zones
We study three representations of hierarchies of partitions: dendrograms
(direct representations), saliency maps, and minimum spanning trees. We provide
a new bijection between saliency maps and hierarchies based on quasi-flat zones
as used in image processing and characterize saliency maps and minimum spanning
trees as solutions to constrained minimization problems where the constraint is
quasi-flat zones preservation. In practice, these results form a toolkit for
new hierarchical methods where one can choose the most convenient
representation. They also invite us to process non-image data with
morphological hierarchies
Cell Segmentation in 3D Confocal Images using Supervoxel Merge-Forests with CNN-based Hypothesis Selection
Automated segmentation approaches are crucial to quantitatively analyze
large-scale 3D microscopy images. Particularly in deep tissue regions,
automatic methods still fail to provide error-free segmentations. To improve
the segmentation quality throughout imaged samples, we present a new
supervoxel-based 3D segmentation approach that outperforms current methods and
reduces the manual correction effort. The algorithm consists of gentle
preprocessing and a conservative super-voxel generation method followed by
supervoxel agglomeration based on local signal properties and a postprocessing
step to fix under-segmentation errors using a Convolutional Neural Network. We
validate the functionality of the algorithm on manually labeled 3D confocal
images of the plant Arabidopis thaliana and compare the results to a
state-of-the-art meristem segmentation algorithm.Comment: 5 pages, 3 figures, 1 tabl
The Spine of the Cosmic Web
We present the SpineWeb framework for the topological analysis of the Cosmic
Web and the identification of its walls, filaments and cluster nodes. Based on
the watershed segmentation of the cosmic density field, the SpineWeb method
invokes the local adjacency properties of the boundaries between the watershed
basins to trace the critical points in the density field and the separatrices
defined by them. The separatrices are classified into walls and the spine, the
network of filaments and nodes in the matter distribution. Testing the method
with a heuristic Voronoi model yields outstanding results. Following the
discussion of the test results, we apply the SpineWeb method to a set of
cosmological N-body simulations. The latter illustrates the potential for
studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version:
http://skysrv.pha.jhu.edu/~miguel/SpineWeb
Analyses of the Watershed Transform
International audienceIn the framework of mathematical morphology, watershed transform (WT) represents a key step in image segmentation procedure. In this paper, we present a thorough analysis of some existing watershed approaches in the discrete case: WT based on flooding, WT based on path-cost minimization, watershed based on topology preservation, WT based on local condition and WT based on minimum spanning forest. For each approach, we present detailed description of processing procedure followed by mathematical foundations and algorithm of reference. Recent publications based on some approaches are also presented and discussed. Our study concludes with a classification of different watershed transform algorithms according to solution uniqueness, topology preservation, prerequisites minima computing and linearity
Weighted fusion graphs: merging properties and watersheds
International audienc
Discrete region merging and watersheds
incollectionThis paper summarizes some results of the authors concerning watershed divides and their use in region merging schemes.The first aspect deals with properties of watershed divides that can be used in particular for hierarchical region merging schemes. We introduce the mosaic to retrieve the altitude of points along the divide set. A desirable property is that, when two minima are separated by a crest in the original image, they are still separated by a crest of the same altitude in the mosaic. Our main result states that this is the case if and only if the mosaic is obtained through a topological thinning.The second aspect is closely related to the thinness of watershed divides. We present fusion graphs, a class of graphs in which any region can be always merged without any problem. This class is equivalent to the one in which watershed divides are thin. Topological thinnings do not always produce thin divides, even on fusion graphs. We also present the class of perfect fusion graphs, in which any pair of neighbouring regions can be merged through their common neighborhood. An important theorem states that the divides of any ultimate topological thinning are thin on any perfect fusion graph
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