Santiago Velasco-Forero

• Ph.D.
• Professor (Assistant) at Mines Paris, PSL University

Point clouds are a set of data points in space to represent the 3D geometry of objects. A fundamental step in the processing is to identify a subset of points to represent the shape. While traditional sampling methods often ignore to incorporate geometrical information, recent developments in learning-based sampling models have achieved significant...

Image segmentation is a common intermediate operation in many image processing applications. On automated systems it is important to evaluate how well it, or its subsystems are performing without access to the Ground Truth. In Deep Learning based image segmentation there are very few methods to evaluate the output quality without using a ground tru...

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 images, provided we know the dynamic threshold that tells apart actual objects from irrelevant maxima. In this paper we introduce a neural arch...

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. This paper aims to fill the lack of morphological approaches on the matter. We propose a set of group equivariant layers using morphological o...

We consider a framework including multiple augmentation regularisation by generalised divergences to induce invariance for non-group transformations during training of convolutional neural networks. Experiments on supervised classification of images at different scales not considered during training illustrate that our proposed method performs bett...

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, the Harris corner response function is a combination of the elementary symmetric polynomials of the integrated dyadic (outer) product of the gr...

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 detection extensible to other kinds of sensors and detection scenarios. We emphasize the relevance of OODD and its specific supervision requ...

We propose an incremental improvement to Fully Convolutional Data Description (FCDD), an adaptation of the one-class classification approach from anomaly detection to image anomaly segmentation (a.k.a. anomaly localization). We analyze its original loss function and propose a substitute that better resembles its predecessor, the Hypersphere Classif...

Cell counting is an important step in many biological experiments. Itcan be challenging, due to the large variability in contrast and shapeof the cells, especially when their density is so high that the cellsare closely packed together. Automation is needed to increase thespeed and quality of the detection. In this study, a cell countingmethod is d...

Equivariance of neural networks to transformations helps to improve their performance and reduce generalization error in computer vision tasks, as they apply to datasets presenting symmetries (e.g. scalings, rotations, translations). The method of moving frames is classical for deriving operators invariant to the action of a Lie group in a manifold...

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 general family of activation functions is proposed by considering both max-pooling and nonlinear operators in the context of morphological represen...

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 complete lattices, such as Cartesian powers of the completed real line. This paper focuses on adjunctions on closed hypercubes, which are th...

In neural networks, the property of being equivariant to transformations improves generalization when the corresponding symmetry is present in the data. In particular, scale-equivariant networks are suited to computer vision tasks where the same classes of objects appear at different scales, like in most semantic segmentation tasks. Recently, convo...

In the field of composite materials, mesoscale modelings based on X-ray computed tomography are becoming ever more widespread. This tool, aiming to increase the fidelity of the descriptive modeling of textile geometry for Finite Elements Analysis (FEA), requires image processing to identify the different objects within the material. In the present...

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 complete lattices, such as Cartesian powers of the completed real line. This paper focuses on adjunctions on closed hypercubes, which are th...

The Gaussian kernel and its derivatives have already been employed for Convolutional Neural Networks in several previous works. Most of these papers proposed to compute filters by linearly combining one or several bases of fixed or slightly trainable Gaussian kernels with or without their derivatives. In this article, we propose a high-level config...

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 general family of activation functions is proposed by considering both max-pooling and nonlinear operators in the context of morphological represen...

Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled with equivariance of neural networks can improve their generalization to new samples. Differential invariants...

Near out-of-distribution detection (OOD) aims at discriminating semantically similar data points without the supervision required for classification. This paper puts forward an OOD use case for radar targets detection extensible to other kinds of sensors and detection scenarios. We emphasize the relevance of OOD and its specific supervision require...

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 extended to vector-valued images using several approaches. Vector-valued morphological operators based on total orders are particularly promi...

The algorithm presented in this paper is an application of a general framework for morphological processing of signals on weighted graphs. Here we apply it to images by defining what we call a co-circularity graph. In this graph, the vertices are the pixels and the weighted edges depend on a consistency criterion (co-circularity) between local orie...

Paris-CARLA-3D is a dataset of several dense colored point clouds of outdoor environments built by a mobile LiDAR and camera system. The data are composed of two sets with synthetic data from the open source CARLA simulator (700 million points) and real data acquired in the city of Paris (60 million points), hence the name Paris-CARLA-3D. One of th...

Paris-CARLA-3D is a dataset of several dense colored point clouds of outdoor environments built by a mobile LiDAR and camera system. The data are composed of two sets with synthetic data from the open source CARLA simulator (700 million points) and real data acquired in the city of Paris (60 million points), hence the name Paris-CARLA-3D. One of th...

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstat...

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topolog-ical Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomsta...

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 points and the matrix of pairwise similarities and output the dendrogram representing the nested partition. However, in some cases, the entire dat...

Responding to the challenge of detecting unusual radar targets in a well identified environment, innovative anomaly and novelty detection methods keep emerging in the literature. This work aims at presenting a benchmark gathering common and recently introduced unsupervised anomaly detection (AD) methods, the results being generated using high-resol...

Random projection is a common technique for designing algorithms in a variety of areas, including information retrieval, compressive sensing and measuring of outlyingness. In this work, the original random projection outlyingness measure is modified and associated with a neural network to obtain an unsupervised anomaly detection method able to hand...

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon as we know a priori that transformed versions of the same objects appear in the data. The semigroup cross-cor...

The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon as we know a priori that transformed versions of the same objects appear in the data. The semigroup cross-cor...

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 to unveil a morphological and explainable structure of the data. Additionally, we want this decomposition to be computed online for any new...

This paper presents the methods that have participated in the SHREC’20 contest on retrieval of surface patches with similar geometric reliefs and the analysis of their performance over the benchmark created for this challenge. The goal of the context is to verify the possibility of retrieving 3D models only based on the reliefs that are present on...

The minimum spanning tree (MST) is one the most popular data structure used to extract hierarchical information from images. This work addresses MST construction in streaming for images. First, we focus on the problem of computing a MST of the union of two graphs with a non-empty intersection. Then we show how our solution can be applied to streami...

Point cloud datasets for perception tasks in the context of autonomous driving often rely on high resolution 64-layer Light Detection and Ranging (LIDAR) scanners. They are expensive to deploy on real-world autonomous driving sensor architectures which usually employ 16/32 layer LIDARs. We evaluate the effect of subsampling image based representati...

We propose a framework for image characterization using hierarchies of segmentations. For this purpose, we structure the space of hierarchies using the Gromov–Hausdorff distance. We propose different ways of combining hierarchies and study their properties thanks to the GH distance. We then expose how to leverage the combinatorial space of hierarch...

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 emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of struc...

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 layers of conventional neural networks. Besides showing that they can be easily implemented with modern machine learning frameworks, we confirm a...

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 to unveil a morphological and interpretable structure of the data. Additionally, we want this decomposition to be computed online for any ne...

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 to unveil a morphological and interpretable structure of the data. Additionally, we want this decomposition to be computed online for any ne...

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 layers of conventional neural networks. Besides showing that they can be easily implemented with modern machine learning frameworks, we confirm a...

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 emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of struc...

This paper presents the results of the SHREC'18 track: Retrieval of gray patterns depicted on 3D models. The task proposed in the contest challenges the possibility of retrieving surfaces with the same texture pattern of a given query model. This task, which can be seen as a simplified version of many real world applications, requires a characteriz...

This track of the SHREC 2018 originally aimed at recognizing relief patterns over a set of triangle meshes from laser scan acquisitions of archaeological fragments. This track approaches a lively and very challenging problem that remains open after the end of the track. In this report we discuss the challenges to face to successfully address geomet...

Sparse modeling involves constructing a succinct representation of initial data as a linear combination of a few typical atoms of a dictionary. This paper deals with the use of sparse representations to introduce new nonlinear image filters which efficiently approximate morphological operators. Reasons why non-negative matrix factorization (NMF) is...

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 dendrograms from minimum spanning trees. This paper is a formal study of morphological operators fo...

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 emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of struc...

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 emergence of important regions at different scales. On the other hand, many methods allow us to have prior information on the position of struc...

This book contains the refereed proceedings of the 13th International Symposium on Mathematical Morphology, ISMM 2017, held in Fontainebleau, France, in May 2017. The 36 revised full papers presented together with 4 short papers were carefully reviewed and selected from 53 submissions. The papers are organized in topical sections on algebraic theor...

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 framework of the linear mixing model. The novelty of this work lies in the introduction of bound parameters which allow us to introduce prior...

The segmentation, seen as the association of a partition with an image, is a difficult task. It can be decomposed in two steps: at first, a family of contours associated with a series of nested partitions (or hierarchy) is created and organized, then pertinent contours are extracted. A coarser partition is obtained by merging adjacent regions of a...

The segmentation, seen as the association of a partition with an image, is a difficult task. It can be decomposed in two steps: at first, a family of contours associated with a series of nested partitions (or hierarchy) is created and organized, then pertinent contours are extracted. A coarser partition is obtained by merging adjacent regions of a...

In this paper we report the results of the SHREC 2016 contest on "Retrieval of human subjects from depth sensor data". The proposed task was created in order to verify the possibility of retrieving models of query human subjects from single shots of depth sensors, using shape information only. Depth acquisition of different subjects were realized u...

This paper presents a comparative study of six methods for the retrieval and classification of textured 3D models, which have been selected as representative of the state of the art. To better analyse and control how methods deal with specific classes of geometric and texture deformations, we built a collection of 572 synthetic textured mesh models...

Covariance matrix estimation is fundamental for anomaly detection, especially for the Reed and Xiaoli Yu (RX) detector. Anomaly detection is challenging in hyperspectral images because the data has a high correlation among dimensions, heavy tailed distributions and multiple clusters. This paper comparatively evaluates modern techniques of covarianc...

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 variational calculus. Firstly, we explore the optimal radius as attribute in morphological attribute filtering for grey scale images. Secondly, an ap...

Recent works on image co-segmentation aim to segment common objects among image sets. These methods can co-segment simple images well, but their performance may degrade significantly on more cluttered images. In order to co-segment both simple and complex images well, this paper proposes a novel paradigm to rank images and to propagate the segmentat...

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 flat and non-flat erosions and dilations in the sense of mathematical morphology. Additionally, the connection to mean motion curvature on graph...

This paper introduces mathematical morphology operators for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonical quadratic structuring function by the Riemannian distance used for the adjoint dilation/erosion. We then extend the canonical case to a most gen...

Anomaly Detection methods are used when there is not enough information about the target to detect. These methods search for pixels in the image with spectral characteristics that differ from the background. The most widespread detection test, the RX-detector, is based on the Mahalanobis distance and on the background statistical characterization t...

This chapter illustrates the suitability of recent multivariate ordering approaches to morphological analysis of colour and multispectral imagesworking on their vector representation. On the one hand, supervised ordering renders machine learning notions and image processing techniques, through a learning stage to provide a total ordering in the col...

We propose a regularised version of the classical singular value decomposition for simultaneous outliers and associated important band detection. The proposed optimisations are twofold: First, they exploit sequential optimisation techniques in L0 formulation to obtain sparse solution of classical principal component analysis. Second, we have develo...

Mathematical morphology is a nonlinear image processing methodology based on the application of complete lattice theory to spatial structures. Let us consider an image model where at each pixel is given a univariate Gaussian distribution. This model is interesting to represent for each pixel the measured mean intensity as well as the variance (or u...

We study a class of mathematical morphology filters to operate conditionally according to a set of pixels marked by a binary mask. The main contribution of this paper is to provide a general framework for several applications including edge enhancement and image denoising, when it is affected by salt-and-pepper noise. We achieve this goal by revisi...

Connective segmentation based on the definition of a dissimilarity measure on pairs of adjacent pixels is an appealing framework to develop new hierarchical segmentation methods. Usually, the dissimilarity is fully determined by the intensity values of the considered pair of adjacent pixels, so that it is independent of the values of the other imag...

This paper reports the results of the SHREC'14 track: Retrieval and classification on textured 3D models, whose goal is to evaluate the performance of retrieval algorithms when models vary either by geometric shape or texture, or both. The collection to search in is made of 572 textured mesh models, having a two-level classification based on geomet...

This paper explore the problem of unsupervised hierarchical segmentation for hyperspectral images using a multivariate version of the structure tensor [1] and morphological seg-mentation methods based on a pixel dissimilarity measures [2]. This spatial structure tensor fusions the edge information along the spectral dimension of the gradient by usi...

This paper introduces a probabilistic framework for adaptive morphological dilation and erosion. More precisely our probabilistic formalization is based on using random walk simulations for a stochastic estimation of adaptive and robust morphological operators. Hence, we propose a theoretically sound morphological counterpart of Monte Carlo stochas...

In this paper, nonlocal mathematical morphology operators are introduced as a natural extension of nonlocal-means in the max-plus algebra. Firstly, we show that nonlocal morphology is a particular case of adaptive morphology. Secondly, we present the necessary properties to have algebraic properties on the associated pair of transformations. Finall...

This paper introduces mathematical morphology for real-valued images whose support space is a Riemannian manifold. The starting point consists in replacing the Euclidean distance in the canonic quadratic structuring function by the Riemannian distance. Besides the definition of Riemannian dilation/erosion and Riemannian opening/closing, their prope...

This contribution reports the results of the SHREC 2013 track: Retrieval on Textured 3D Models, whose goal is to evaluate the performance of retrieval algorithms when models vary either by geometric shape or texture, or both. The collection to search in is made of 240 textured mesh models, divided into 10 classes. Each model has been used in turn a...

Pixel-wise classification in high-dimensional multivariate images is investigated. The proposed method deals with the joint use of spectral and spatial information provided in hyperspectral images. Additive morphological decomposition (AMD) based on morphological operators is proposed. AMD defines a scale-space decomposition for multivariate images...

Mathematical morphology is a nonlinear image processing methodology based on computing min/max operators in local neighbourhoods. In the case of tensor-valued images, the space of SPD matrices should be endowed with a partial ordering and a complete lattice structure. Structure tensor describes robustly the local orientation and anisotropy of image...

Mathematical morphology is a nonlinear image processing methodology based on the application of complete lattice theory to spatial structures. Let us consider an image model where at each pixel is given a univariate Gaussian distribution. This model is interesting to represent for each pixel the measured mean intensity as well as the variance (or u...

The open problem of the generalization of mathematical morphology to vector images is handled in this paper using the paradigm of depth functions. Statistical depth functions provide from the “deepest” point a “center-outward ordering” of a multidimensional data distribution and they can be therefore used to construct morphological operators. The f...

Edges are crucial descriptors for image analysis and rely mostly on local spectral distances. In this paper, local spectral changes are assimilated to the local statistical dependences which are measured by the local mutual information. This metric is shown to be invariant to unknown bijective transforms which makes it a good candidate for analyzin...