Hierarchical Queues: general description and implementation in MAMBA Image library

This paper describes thoroughly the hierarchical queues (HQ) which are implemented in the MAMBA image library. The use of these HQ to realize watershed transforms and geodesic reconstructions is fully explained. The extension of these morphological operators to 32-bit images is also described

Fast implementation of large erosions and dilations in Mamba

This document explains how to implement fast erosions and dilations when large structuring elements are needed. These structuring elements can be squares, hexagons, octogons or dodecagons. This implementation, realized in the Mamba library brings a dramatic increase of the computation speed. This increase is all the more important as the size of the structuring element is large

Towards a unification of waterfalls, standard and P algorithms

This document is an extension of the paper: "P algorithm, a dramatic enhancement of the waterfall transformation". It has mainly two purposes. Firstly, it comes back to the waterfalls, standard and P algorithms to propose a general segmentation scheme which covers and unifies these different processes. Secondly, it contains the source code for the implementation of these waterfalls, standard and P operators with the MAMBA Image software library

Basic Morphological Operators Applied on Partitions

This document describes morphological operators designed for partitions (mosaic) images. Two approaches are addressed. Either each cell of the partition is processed independently of the other cells or the partition is considered as an image representation of a graph where some basic morphological operators (erosion and dilation) can be defined. An implementation of these operators in the Mamba image library is also given

Algorithmic description of erosions and dilations in Mamba

This note describes the implementation of the basic structuring elements in the Mamba-Image library. These structuring elements are composed of those which are defined on the elementary neighborhood of a point (hexagon on an hexagonal grid, square on a square one) but also of the octogonal (square grid) and dodecagonal (hexagonal grid) ones

Critical Balls

Presentation available at http://cmm.ensmp.fr/~beucher/publi/ICS13-Critical%20Balls.pdfProceedings of international congresses organised under the auspices of ISS are available either as reprints or as CD-ROM. Contact the secretary for more information : [email protected] audienceThis paper introduces the concept of critical ball. Critical balls are maximal balls which are necessary and sufficient to describe and rebuild sets, contrary to maximal balls where some redundancy exists. A general definition of a critical ball is given in continuous spaces and some of its main properties are depicted. Thanks to a slight modification of their definition, critical balls can also be used in digital spaces. Then, we explain how to extract them rapidly through the use of two residual transformations. Finally, some examples of use of critical balls for shape description and image segmentation are briefly presented

Sur un problème de définition de l'érosion géodésique

Cette note est destinée à éclaircir la définition de l'érosion géodésique numérique et la façon dont cette définition est inférée à partir de la définition de la dilatation géodésique. On montre que la définition de l'érosion géodésique numérique n'est pas une extension de l'érosion géodésique ensembliste. On explique la raison de cette différence qui induit quelques difficultés lors de l'utilisation de cet opérateur

How to simulate a volume-controlled flooding with mathematical morphology operators?

This note discusses some ideas for simulating a (real) flood on a (real) topographic surface by means of morphological tools. This work has been initiated following exchanges with some partners of the THESEUS project (Innovative technologies for safer European coasts in a changing climate) regarding the use of mathematical morphology tools for flooding simulations (note that the CMM does not belong to the THESEUS consortium, this contribution has no other motive than promoting morphological tools in this research domain!)

The Watershed Transformation Applied to Image Segmentation

Image segmentation by mathematical morphology is a methodology based upon the notions of watershed and homotopy modification.This paper aims at introducing this methodology through various examples of segmentation in materials sciences, electron microscopy and scene analysis. First, we defined our basic tool, the watershed transform. We showed that this transformation can be built by implementing a flooding process on a greytone image. This flooding process can be performed by using elementary morphological operations such as geodesic skeleton and reconstruction. Other algorithms are also briefly presented (arrows representation). Then, the use of this transformation for image segmentation purposes is discussed. The application of the watershed transform to gradient images and the problems raised by over-segmentation are emphasized. This leads, into the third part, to the introduction of a general methodology for segmentation, based on the definition of markers and on a transformation called homotopy modification. This complex tool is defined in detail and various types of implementations are given. Many examples of segmentation are presented. These examples are taken from various fields: transmission electron microscopy, scanning electron microscopy (SEM), 3D holographic pictures, radiography, non destructive control and so on. The final part of this paper is devoted to the use of the watershed transformation for hierarchical segmentation. This tool is particularly efficient for defining different levels of segmentation starting from a graph representation of the images based on the mosaic image transform. This approach will be explained by means of examples in industrial vision and scene analysis

A pairwise likelihood approach for the empirical estimation of the underlyingvariograms in the plurigaussian models

The plurigaussian model is particularly suited to describe categorical regionalized variables. Starting from a simple principle, the thresh-olding of one or several Gaussian random fields (GRFs) to obtain categories, the plurigaussian model is well adapted for a wide range ofsituations. By acting on the form of the thresholding rule and/or the threshold values (which can vary along space) and the variograms ofthe underlying GRFs, one can generate many spatial configurations for the categorical variables. One difficulty is to choose variogrammodel for the underlying GRFs. Indeed, these latter are hidden by the truncation and we only observe the simple and cross-variogramsof the category indicators. In this paper, we propose a semiparametric method based on the pairwise likelihood to estimate the empiricalvariogram of the GRFs. It provides an exploratory tool in order to choose a suitable model for each GRF and later to estimate its param-eters. We illustrate the efficiency of the method with a Monte-Carlo simulation study .The method presented in this paper is implemented in the R packageRGeostats.Comment: To be submitted to Spatial Statistic