arXiv subjects

Santiago Velasco-Forero

Publications and source records attributed to Santiago Velasco-Forero.

At least 19 recordsLinked to original sources

arXiv2026

Graph neural networks for sampling-invariant embeddings of organized signal sets

Sensor networks and radars can deliver signals as organized sets, e.g. ordered signals, signals describing range cells within a grid or signals perceived as graph nodes. Within such sets, individual signals may be characterized by distinct sampling parameters. This paper investigates organized signal sets neural network encoders. In the context of this work, the purpose of such encoders is to project heterogeneously sampled signal sets into an arbitrary fixed-size vectors space. This new representation space is designed so that signal sets can be processed as vectors rid of sampling differences to allow for arbitrary topology-aware processing with no signal processing constraints. Within this representation space designed to reduce the influence of heterogeneous sampling parameters, the relevance of signal sets representations is evaluated by considering signal sets discrimination potential with a focus on waveforms separation. The encoding and embeddings discrimination experiments conducted rely exclusively on synthetic complex-valued radiofrequency signals.

cs.LG↗

arXiv2026

High-Resolution Range Profile Classifiers Require Aspect-Angle Awareness

We revisit High-Resolution Range Profile (HRRP) classification with aspect-angle conditioning. While prior work often assumes that aspect-angle information is incomplete during training or unavailable at inference, we study a setting where angles are available for all training samples and explicitly provided to the classifier. Using three datasets and a broad range of conditioning strategies and model architectures, we show that both single-profile and sequential classifiers benefit consistently from aspect-angle awareness, with an average accuracy gain of about 7% and improvements of up to 10%, depending on the model and dataset. In practice, aspect angles are not directly measured and must be estimated. We show that a causal Kalman filter can estimate them online with a median error of 5{\textdegree}, and that training and inference with estimated angles preserves most of the gains, supporting the proposed approach in realistic conditions.

eess.SP↗

arXiv2026

MFN Decomposition and Related Metrics for High-Resolution Range Profiles Generative Models

High-resolution range profile (HRRP ) data are in vogue in radar automatic target recognition (RATR). With the interest in classifying models using HRRP, filling gaps in datasets using generative models has recently received promising contributions. Evaluating generated data is a challenging topic, even for explicit data like face images. However, the evaluation methods used in the state-ofthe-art of HRRP generation rely on classification models. Such models, called ''black-box'', do not allow either explainability on generated data or multi-level evaluation. This work focuses on decomposing HRRP data into three components: the mask, the features, and the noise. Using this decomposition, we propose two metrics based on the physical interpretation of those data. We take profit from an expensive dataset to evaluate our metrics on a challenging task and demonstrate the discriminative ability of those.

cs.CV↗

arXiv2026

Conditional Generative Models for High-Resolution Range Profiles: Capturing Geometry-Driven Trends in a Large-Scale Maritime Dataset

High-resolution range profiles (HRRPs) enable fast onboard processing for radar automatic target recognition, but their strong sensitivity to acquisition conditions limits robustness across operational scenarios. Conditional HRRP generation can mitigate this issue, yet prior studies are constrained by small, highly specific datasets. We study HRRP synthesis on a largescale maritime database representative of coastal surveillance variability. Our analysis indicates that the fundamental scenario drivers are geometric: ship dimensions and the desired aspect angle. Conditioning on these variables, we train generative models and show that the synthesized signatures reproduce the expected line-of-sight geometric trend observed in real data. These results highlight the central role of acquisition geometry for robust HRRP generation.

cs.CV↗

arXiv2026

LmPT: Conditional Point Transformer for Anatomical Landmark Detection on 3D Point Clouds

Accurate identification of anatomical landmarks is crucial for various medical applications. Traditional manual landmarking is time-consuming and prone to inter-observer variability, while rule-based methods are often tailored to specific geometries or limited sets of landmarks. In recent years, anatomical surfaces have been effectively represented as point clouds, which are lightweight structures composed of spatial coordinates. Following this strategy and to overcome the limitations of existing landmarking techniques, we propose Landmark Point Transformer (LmPT), a method for automatic anatomical landmark detection on point clouds that can leverage homologous bones from different species for translational research. The LmPT model incorporates a conditioning mechanism that enables adaptability to different input types to conduct cross-species learning. We focus the evaluation of our approach on femoral landmarking using both human and newly annotated dog femurs, demonstrating its generalization and effectiveness across species. The code and dog femur dataset will be publicly available at: https://github.com/Pierreoo/LandmarkPointTransformer.

cs.CV↗

arXiv2025

Approximating Condorcet Ordering for Vector-valued Mathematical Morphology

Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and hyperspectral images, there is still no consensus on the most suitable vector ordering for constructing morphological operators. This paper addresses this issue by examining a reduced ordering approximating the Condorcet ranking derived from a set of vector orderings. Inspired by voting problems, the Condorcet ordering ranks elements from most to least voted, with voters representing different orderings. In this paper, we develop a machine learning approach that learns a reduced ordering that approximates the Condorcet ordering. Preliminary computational experiments confirm the effectiveness of learning the reduced mapping to define vector-valued morphological operators for color images.

cs.CV↗

arXiv2025

MorphoSkel3D: Morphological Skeletonization of 3D Point Clouds for Informed Sampling in Object Classification and Retrieval

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 levels of performance. With the integration of geometrical priors, the ability to learn and preserve the underlying structure can be enhanced when sampling. To shed light into the shape, a qualitative skeleton serves as an effective descriptor to guide sampling for both local and global geometries. In this paper, we introduce MorphoSkel3D as a new technique based on morphology to facilitate an efficient skeletonization of shapes. With its low computational cost, MorphoSkel3D is a unique, rule-based algorithm to benchmark its quality and performance on two large datasets, ModelNet and ShapeNet, under different sampling ratios. The results show that training with MorphoSkel3D leads to an informed and more accurate sampling in the practical application of object classification and point cloud retrieval.

cs.CV↗

arXiv2023

Adapting the Hypersphere Loss Function from Anomaly Detection to Anomaly Segmentation

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 Classifier (HSC). Both are compared on the MVTec Anomaly Detection Dataset (MVTec-AD) -- training images are flawless objects/textures and the goal is to segment unseen defects -- showing that consistent improvement is achieved by better designing the pixel-wise supervision.

cs.CV↗

arXiv2022

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 complete lattices, such as Cartesian powers of the completed real line. This paper focuses on adjunctions on closed hypercubes, which are the complete lattices used in practice to represent digital signals and images. We show that this constrains the representing matrices to be doubly-0-astic and we characterise the adjunctions that can be represented by them. A graph interpretation of the defined operators naturally arises from the adjacency relationship encoded by the matrices, as well as a max-plus spectral interpretation.

eess.SP↗

arXiv2022

Moving Frame Net: SE(3)-Equivariant Network for Volumes

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.Recently, a rotation and translation equivariant neural network for image data was proposed based on the moving frames approach. In this paper we significantly improve that approach by reducing the computation of moving frames to only one, at the input stage, instead of repeated computations at each layer. The equivariance of the resulting architecture is proved theoretically and we build a rotation and translation equivariant neural network to process volumes, i.e. signals on the 3D space. Our trained model overperforms the benchmarks in the medical volume classification of most of the tested datasets from MedMNIST3D.

cs.CV↗

arXiv2022

Scale Equivariant U-Net

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, convolutional layers equivariant to a semigroup of scalings and translations have been proposed. However, the equivariance of subsampling and upsampling has never been explicitly studied even though they are necessary building blocks in some segmentation architectures. The U-Net is a representative example of such architectures, which includes the basic elements used for state-of-the-art semantic segmentation. Therefore, this paper introduces the Scale Equivariant U-Net (SEU-Net), a U-Net that is made approximately equivariant to a semigroup of scales and translations through careful application of subsampling and upsampling layers and the use of aforementioned scale-equivariant layers. Moreover, a scale-dropout is proposed in order to improve generalization to different scales in approximately scale-equivariant architectures. The proposed SEU-Net is trained for semantic segmentation of the Oxford Pet IIIT and the DIC-C2DH-HeLa dataset for cell segmentation. The generalization metric to unseen scales is dramatically improved in comparison to the U-Net, even when the U-Net is trained with scale jittering, and to a scale-equivariant architecture that does not perform upsampling operators inside the equivariant pipeline. The scale-dropout induces better generalization on the scale-equivariant models in the Pet experiment, but not on the cell segmentation experiment.

stat.ML↗

arXiv2022

Differential invariants for SE(2)-equivariant networks

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 are equivariant operators computed from the partial derivatives of a function. In this paper we use differential invariants to define equivariant operators that form the layers of an equivariant neural network. Specifically, we derive invariants of the Special Euclidean Group SE(2), composed of rotations and translations, and apply them to construct a SE(2)-equivariant network, called SE(2) Differential Invariants Network (SE2DINNet). The network is subsequently tested in classification tasks which require a degree of equivariance or invariance to rotations. The results compare positively with the state-of-the-art, even though the proposed SE2DINNet has far less parameters than the compared models.

eess.IV↗

arXiv2022

Fully trainable Gaussian derivative convolutional layer

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 configurable layer based on anisotropic, oriented and shifted Gaussian derivative kernels which generalize notions encountered in previous related works while keeping their main advantage. The results show that the proposed layer has competitive performance compared to previous works and that it can be successfully included in common deep architectures such as VGG16 for image classification and U-net for image segmentation.

cs.NE↗

arXiv2022

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 general family of activation functions is proposed by considering both max-pooling and nonlinear operators in the context of morphological representations. Experimental section validates the goodness of our approach on classical benchmarks for supervised learning by DCNN.

cs.LG↗

arXiv2022

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 detection extensible to other kinds of sensors and detection scenarios. We emphasize the relevance of OODD and its specific supervision requirements for the detection of a multimodal, diverse targets class among other similar radar targets and clutter in real-life critical systems. We propose a comparison of deep and non-deep OODD methods on simulated low-resolution pulse radar micro-Doppler signatures, considering both a spectral and a covariance matrix input representation. The covariance representation aims at estimating whether dedicated second-order processing is appropriate to discriminate signatures. The potential contributions of labeled anomalies in training, self-supervised learning, contrastive learning insights and innovative training losses are discussed, and the impact of training set contamination caused by mislabelling is investigated.

eess.SP↗

arXiv2021

Paris-CARLA-3D: A Real and Synthetic Outdoor Point Cloud Dataset for Challenging Tasks in 3D Mapping

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 the advantages of this dataset is to have simulated the same LiDAR and camera platform in the open source CARLA simulator as the one used to produce the real data. In addition, manual annotation of the classes using the semantic tags of CARLA was performed on the real data, allowing the testing of transfer methods from the synthetic to the real data. The objective of this dataset is to provide a challenging dataset to evaluate and improve methods on difficult vision tasks for the 3D mapping of outdoor environments: semantic segmentation, instance segmentation, and scene completion. For each task, we describe the evaluation protocol as well as the experiments carried out to establish a baseline.

cs.CV↗

arXiv2021

ICLR 2021 Challenge for Computational Geometry & Topology: Design and Results

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 Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.CG↗

arXiv2021

Deep Random Projection Outlyingness for Unsupervised Anomaly Detection

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 handle multimodal normality. Theoretical and experimental arguments are presented to justify the choice of the anomaly score estimator. The performance of the proposed neural network approach is comparable to a state-of-the-art anomaly detection method. Experiments conducted on the MNIST, Fashion-MNIST and CIFAR-10 datasets show the relevance of the proposed approach.

eess.SP↗