ISMM 2017: 13TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL MORPHOLOGY
PROGRAM FOR MONDAY, MAY 15TH
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08:45-09:00 Session 1: Opening - Words of Welcome

MINES ParisTech Official Welcome - TBA

ISMM'2017 Organizing Committee Welcome - Jesus Angulo

09:00-10:00 Session 2: Keynote Lecture 1

Invited Speaker - Pierre Vandergheynst

09:00
TBA
10:00-11:30Coffee Break
10:30-12:10 Session 3: Oral Session - Theory
10:30
Morphological Perceptrons: Geometry and Training Algorithms
SPEAKER: unknown

ABSTRACT. Neural networks have traditionally relied on mostly linear models, such as the multiply-accumulate architecture of a linear perceptron that remains the dominant paradigm of neuronal computation. However, from a biological standpoint, neuron activity may as well involve inherently nonlinear and competitive operations. Mathematical morphology and minimax algebra provide the necessary background in the study of neural networks made up from these kinds of nonlinear units. This paper deals with such a model, called the morphological perceptron. We study some of its geometrical properties and introduce a training algorithm for binary classification. We point out the relationship between morphological classifiers and the emerging field of tropical geometry, which enables us to obtain a precise bound on the number of linear regions of the maxout unit, a popular choice for deep neural networks introduced recently. Finally, we present some relevant numerical results.

10:55
Morphological links between formal concepts and hypergraphs

ABSTRACT. Hypergraphs can be built from a formal context, and conversely formal contexts can be derived from a hypergraph. Establishing such links allows exploiting morphological operators developed in one framework to derive new operators in the other one. As an example, the combination of derivation operators on formal concepts leads to closing operators on hypergraphs which are not the composition of dilations and erosions. Several other examples are investigated in this paper, with the aim of processing formal contexts and hypergraphs, and navigating in such structures.

11:20
Morphological semigroups and scale-spaces on ultrametric spaces
SPEAKER: unknown

ABSTRACT. Ultrametric spaces are the natural mathematical structure to deal with data embedded into a hierarchical representation. This kind of representations is ubiquitous in morphological image processing, from pyramids of nested partitions to more abstract dendograms from minimum spanning trees. This paper is a formal study of morphological operators for functions defined on ultrametric spaces. First, the notion of ultrametric structuring function is introduced. Then, using as basic ingredient the convolution in (max,min)-algebra, the multi-scale ultrametric dilation and erosion are defined and their semigroup properties are stated. It is proven in particular that they are idempotent operators and consequently they are algebraically ultrametic closing and opening too. Some preliminary examples illustrate the behavior and practical interest of ultrametric dilation/erosion.

11:45
Introducing the Dahu Pseudo-Distance
SPEAKER: unknown

ABSTRACT. The minimum barrier (MB) distance is defined as the minimal interval of gray-level values in an image along a path between two points, where the image is considered as a vertex-valued graph. Yet this definition does not fit with the interpretation of an image as an elevation map, i.e. a somehow continuous landscape. In this paper, based on the discrete set-valued continuity setting, we present a new discrete definition for this distance, which is compatible with this interpretation, while being free from digital topology issues. Amazingly, we show that the proposed distance is related to the morphological tree of shapes, which in addition allows for a fast and exact computation of this distance. That contrasts with the classical definition of the MB distance, where its fast computation is only an approximation.

12:15-13:30Lunch Break
13:30-15:10 Session 4: Oral Session - Applications
13:30
An affinity score for grains merging and touching grains separation
SPEAKER: unknown

ABSTRACT. The physical properties of granular materials on a macroscopic scale derive from their microstructures. The segmentation of CT-images of this type of material is the first step towards simulation and modeling but it is not a trivial task. Non-spherical, elongated or non-convex objects fail to be separated with classical methods. Moreover, grains are commonly fragmented due to external conditions: aging, storage conditions, or even user-induced mechanical deformations. Grains are crushed into multiple fragments of different shape and volume; those fragments drift from one another in the binder phase. This paper focuses on reconstruction of grains from these fragments using scores that match the local thickness and the regularity of the interface between two objects from a given primary segmentation of the material. An affinity graph is built from those scores and optimized for a given application using a user-generated ground truth on a 2D slice of the tridimensional structures. A minimum spanning tree is generated, and a hierarchical cut is performed. This process allows to reassemble drifted fragments into whole grains and to solve the touching grains problem in tridimensional acquisitions.

13:55
Segmentation of collagen fiber bundles by waterfall on orientations
SPEAKER: unknown

ABSTRACT. The micro-structure of bovine leather samples is imaged three dimensionally using micro-computed tomography. We report on the first algorithm for automatic segmentation of typical'' elements of this multiscale structure based on the reconstructed 3D images. In spite of the scales being hardly separable, a coarse segmentation and a finer substructure can be derived in a consistent way. For preprocessing, an adapted morphological shock filter is suggested. The segmentation algorithm for the coarse fiber bundles exploits the watershed transform and the waterfall paradigm on orientation. The fine substructure is reconstructed from core parts within the bounds given by the coarse bundles.

14:20
Sparse Stereo Disparity Map Densification using Hierarchical Image Segmentation
SPEAKER: unknown

ABSTRACT. We describe a novel method for propagating disparity values using hierarchical segmentation by waterfall and robust regression models. High confidence disparity values obtained by state of the art stereo matching algorithms are interpolated using a coarse to fine approach. We start from a coarse segmentation of the image and try to fit each region’s disparities using robust regression models. If the fit is not satisfying, the process is repeated on a finer region’s segmentation. Erroneous values in the initial sparse disparity maps are generally excluded, as we use robust regressions algorithms and left-right consistency checks. Final disparity maps are therefore not only denser but can also be more accurate. The proposed method is general and independent from the sparse disparity map generation: it can therefore be used as a post-processing step for any stereo-matching algorithm.

14:45
Symmetric Counterparts of Classical 1D Haar Filters for Improved Image Reconstruction via Discrete Back-Projection
SPEAKER: unknown

ABSTRACT. A discrete 2D p:q lattice is comprised of known pixel values spaced at regular p:q intervals, where p, q are relatively prime integers. The lattice has zero values elsewhere. Sets of new symmetric convolution masks were constructed recently whose purpose is to interpolate values for all locations around each lattice point. These symmetric masks were found to outperform the traditional asymmetric masks that interpolate in proportion to the area each pixel shares within a p:q neighbourhood. The 1D projection of these new 2D symmetric masks can also be used when reconstructing images via filtered back-projection (FBP). Here the 1D symmetric filters are shown to outperform the traditional Haar filters that are built from the area-based masks. Images reconstructed using FBP with symmetric filters have errors up to 10% smaller than with Haar filters, and prove to be more robust under Poisson noise.

15:10-15:40Coffee Break
15:40-17:00 Session 5: Poster Session A
15:40
Morphological processing of Gaussian residuals for edge-preserving smoothing

ABSTRACT. The Gaussian filter thanks to its low-pass filtering properties removes the image noise and smooths the image surface. Smoothing influences remarkably the contours of image objects and consequently it does not preserve the original contrast at edges. This paper a method is described that introduces a correction of the result of Gaussian filtering thanks to which the original sharpness of edges is restored. This correction is based on the morphological reconstruction-based processing of the residual of the Gaussian filter. The final result of filtering using the proposed approach is an image consisting of smooth flat surfaces and sharp boundaries.

15:40
Quasi-flat zones for angular data simplification
SPEAKER: unknown

ABSTRACT. Quasi-flat zones are based on the constrained connectivity paradigm and they have proved to be effective tools in the context of image simplification and super-pixel creation. When stacked, they form successive levels of the alpha- or omega-tree powerful representations. In this paper we elaborate on their extension to angular data, whose periodicity prevents the direct application of grayscale quasi-flat zone definitions. Specifically we study two approaches in this regard, respectively based on reference angles and angular distance computations. The proposed methods are tested both qualitatively and quantitatively on a variety of angular data, such as hue images, texture orientation fields and optical flow images. The results indicate that quasi-flat zones constitute an effective means of simplifying angular data, and support future work on angular tree-based representations.

15:40
Connected Morphological Attribute Filters on Distributed Memory Parallel Machines
SPEAKER: unknown

ABSTRACT. We present a new algorithm for attribute filtering of extremely large images, using a forest of modified max-trees, suitable for distributed memory parallel machines. First, max-trees of tiles of the image are computed, after which messages are exchanged to modify the topology of the trees and update attribute data, such that filtering the modified trees on each tile gives exactly the same results as filtering a regular max-tree of the entire image. On a shared memory architecture, a speed-up of 23$\times$ is obtained on 32 cores, only about 10\% slower than the best shared memory algorithm.

15:40
Attribute Profiles from Partitioning Trees
SPEAKER: unknown

ABSTRACT. Morphological attribute profiles are among the most prominent spatial-spectral pixel description tools. They can be calculated efficiently through the multiscale tree based representation of their input. Although widely and successfully used with various inclusion trees, in this paper, we investigate their implementation through partitioning trees, and specifically alpha- and omega-trees. Our preliminary findings show that they are capable of comparable results to the state-of-the-art, while possessing additional properties rendering them suitable for the analysis of multivariate images.

15:40
Morphological Characterization of Graphene Plans Stacking
SPEAKER: unknown

ABSTRACT. The graphene is material obtained when carbon atoms form large planar molecules. Well organized, large graphene molecules stacked ontop each other convey to graphene particularly interesting properties useful in nuclear industry. Understanding how the organization on the molecular scale inﬂuences the mechanical properties of the material is a key element in the material manufacturing process. In this scope, features like local orientation and length have already been largely explored in the literature. This paper brings a new feature evaluating the number of plans stacked ontop each other and the length of this stacking. It allows obtaing other features such as the overall rate of organization or locality and preferential orientation. These informations, synthesized in the form of histograms provides a key information in the processus the material design. Experimental results obtained on images taken by an electronic scanning microscope are presented to illustrate the proposed method.

15:40
Morphological texture description from multispectral skin images in cosmetology
SPEAKER: unknown

ABSTRACT. In this paper, we propose methods to extract texture features from multispectral skin images. We first describe the acquisition protocol and corrections we applied on multispectral images. Then a morphological texture evaluation is proposed using either multivariate approach on multispectral dataset or marginal on a dataset whose dimensionality has been reduced by a multivariate analysis based on PCA.

15:40
Application of size distribution analysis to wrinkle evaluation of textile materials
SPEAKER: unknown

ABSTRACT. An application of size distribution analysis to the evaluation of wrinkle shape on fabrics is proposed. It calculates the size density function of the object indicating the region surrounded by a folded fabric in the standard experimental condition of the wrinkle/crease angle test. The characteristics of the size density function and the parameters of the linear and cubic function to the size density function indicate the fabric shape characteristics, which correspond to visual edge sharpness of pleat lines, as well as resilience and elasticity of the fabric.

15:40
Morphological Analysis of Brownian Motion for Physical Measurements
SPEAKER: unknown

ABSTRACT. Brownian motion is a well-known, apparently chaotic motion affecting microscopic objects in fluid media. The mathematical and physical basis of Brownian motion have been well studied but not often exploited. In this article we propose a particle tracking methodology based on mathematical morphology, suitable for Brownian motion analysis, which can provide difficult physical measurements such as the local temperature and viscosity. We illustrate our methodology on simulation and real data, showing that interesting phenomena and good precision can be achieved

18:30-19:45 Session : Social Event

Private and guided visit of the “Château de Fontainebleau”