Mathematical Morphology and Its Applications to Signal and Image Processing
13th International Symposium, ISMM 2017, Fontainebleau, France, May 15–17, 2017, Proceedings
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Santiago Velasco-Forero
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Chapter and Conference Paper
Group Equivariant Networks Using Morphological Operators
With the increase of interest upon rotation invariance and equivariance for Convolutional Neural Network (CNN), a fair amount of papers have been published on the subject and the literature keeps increasing. T...
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Chapter and Conference Paper
Counting Melanocytes with Trainable h-Maxima and Connected Component Layers
Bright objects on a dark background, such as cells in microscopy images, can sometimes be modeled as maxima of sufficient dynamic, called h-maxima. Such a model could be sufficient to count these objects in image...
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Chapter and Conference Paper
Can Generalised Divergences Help for Invariant Neural Networks?
We consider a framework including multiple augmentation regularisation by generalised divergences to induce invariance for non-group transformations during training of convolutional neural networks. Experiment...
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Chapter and Conference Paper
GenHarris-ResNet: A Rotation Invariant Neural Network Based on Elementary Symmetric Polynomials
In this paper, we propose a rotation invariant neural network based on Gaussian derivatives. The proposed network covers the main steps of the Harris corner detector in a generalized manner. More precisely, th...
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Chapter and Conference Paper
Near Out-of-Distribution Detection for Low-Resolution Radar Micro-doppler Signatures
Near out-of-distribution detection (OODD) aims at discriminating semantically similar data points without the supervision required for classification. This paper puts forward an OODD use case for radar targets...
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Article
Irregularity Index for Vector-Valued Morphological Operators
Mathematical morphology is a valuable theory of nonlinear operators widely used for image processing and analysis. Although initially conceived for binary images, mathematical morphology has been successfully ...
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Chapter and Conference Paper
Morphological Adjunctions Represented by Matrices in Max-Plus Algebra for Signal and Image Processing
In discrete signal and image processing, many dilations and erosions can be written as the max-plus and min-plus product of a matrix on a vector. Previous studies considered operators on symmetrical, unbounded...
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Chapter and Conference Paper
MorphoActivation: Generalizing ReLU Activation Function by Mathematical Morphology
This paper analyses both nonlinear activation functions and spatial max-pooling for Deep Convolutional Neural Networks (DCNNs) by means of the algebraic basis of mathematical morphology. Additionally, a genera...
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Chapter and Conference Paper
End-to-End Similarity Learning and Hierarchical Clustering for Unfixed Size Datasets
Hierarchical clustering (HC) is a powerful tool in data analysis since it allows discovering patterns in the observed data at different scales. Similarity-based HC methods take as input a fixed number of point...
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Chapter and Conference Paper
Scale Equivariant Neural Networks with Morphological Scale-Spaces
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings...
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Chapter and Conference Paper
Measuring the Irregularity of Vector-Valued Morphological Operators Using Wasserstein Metric
Mathematical morphology is a useful theory of nonlinear operators widely used for image processing and analysis. Despite the successful application of morphological operators for binary and gray-scale images, ...
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Chapter and Conference Paper
Max-Plus Operators Applied to Filter Selection and Model Pruning in Neural Networks
Following recent advances in morphological neural networks, we propose to study in more depth how Max-plus operators can be exploited to define morphological units and how they behave when incorporated in laye...
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Chapter and Conference Paper
Part-Based Approximations for Morphological Operators Using Asymmetric Auto-encoders
This paper addresses the issue of building a part-based representation of a dataset of images. More precisely, we look for a non-negative, sparse decomposition of the images on a reduced set of atoms, in order...
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Chapter and Conference Paper
Dealing with Topological Information Within a Fully Convolutional Neural Network
A fully convolutional neural network has a receptive field of limited size and therefore cannot exploit global information, such as topological information. A solution is proposed in this paper to solve this p...
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Book and Conference Proceedings
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Chapter and Conference Paper
Morphological Semigroups and Scale-Spaces on Ultrametric Spaces
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 pyram...
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Chapter and Conference Paper
Prior-Based Hierarchical Segmentation Highlighting Structures of Interest
Image segmentation is the process of partitioning an image into a set of meaningful regions according to some criteria. Hierarchical segmentation has emerged as a major trend in this regard as it favors the em...
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Chapter and Conference Paper
A Bayesian Approach to Linear Unmixing in the Presence of Highly Mixed Spectra
In this article, we present a Bayesian algorithm for endmember extraction and abundance estimation in situations where prior information is available for the abundances. The algorithm is considered within the ...
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Chapter and Conference Paper
Inner-Cheeger Opening and Applications
The aim of this paper is to study an optimal opening in the sense of minimize the relationship perimeter over area. We analyze theoretical properties of this opening by means of classical results from variatio...
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Chapter and Conference Paper
Nonlinear Operators on Graphs via Stacks
We consider a framework for nonlinear operators on functions evaluated on graphs via stacks of level sets. We investigate a family of transformations on functions evaluated on graph which includes adaptive fla...
