This study emanates from a simple observation: as specified by Vapnik [37] in his study, an artificial neural network cannot generate a universal approximator if the aggregation function chosen to design the artificial neuron does not include non-linearity. The usual option is to follow a linear aggregation by a non-linear function, or so-called activation function. We wonder if this approach could be replaced by one using a natively non-linear aggregation function. Among all of the available non-linear aggregation functions, here we are interested in aggregations based on weighted minimum and weighted maximum operations [8] . As these operators were originally developed within a possibility theory and fuzzy rule framework, such operators cannot be easily integrated into a neural network because the values that are usually considered belong to [ 0 , 1 ] . For gradient descent based learning, a neuron must be an aggregation function derivable with respect to its inputs and synaptic weights, whose variables (synaptic weights, inputs and outputs) must all be signed real values. We thus propose an extension of weighted maximum based aggregation to enable this learning process. We show that such an aggregation can be seen as a combination of four Sugeno integrals. Finally, we compare this type of approach with the classical one.

This paper proposes a tentative and original survey of meeting points between Knowledge Representation and Reasoning (KRR) and Machine Learning (ML), two areas which have been developed quite separately in the last four decades. First, some common concerns are identified and discussed such as the types of representation used, the roles of knowledge and data, the lack or the excess of information, or the need for explanations and causal understanding. Then, the survey is organised in seven sections covering most of the territory where KRR and ML meet. We start with a section dealing with prototypical approaches from the literature on learning and reasoning: Inductive Logic Programming, Statistical Relational Learning, and Neurosymbolic AI, where ideas from rule-based reasoning are combined with ML. Then we focus on the use of various forms of background knowledge in learning, ranging from additional regularisation terms in loss functions, to the problem of aligning symbolic and vector space representations, or the use of knowledge graphs for learning. Then, the next section describes how KRR notions may benefit to learning tasks. For instance, constraints can be used as in declarative data mining for influencing the learned patterns; or semantic features are exploited in low-shot learning to compensate for the lack of data; or yet we can take advantage of analogies for learning purposes. Conversely, another section investigates how ML methods may serve KRR goals. For instance, one may learn special kinds of rules such as default rules, fuzzy rules or threshold rules, or special types of information such as constraints, or preferences. The section also covers formal concept analysis and rough sets-based methods. Yet another section reviews various interactions between Automated Reasoning and ML, such as the use of ML methods in SAT solving to make reasoning faster. Then a section deals with works related to model accountability, including explainability and interpretability, fairness and robustness. Finally, a section covers works on handling imperfect or incomplete data, including the problem of learning from uncertain or coarse data, the use of belief functions for regression, a revision-based view of the EM algorithm, the use of possibility theory in statistics, or the learning of imprecise models. This paper thus aims at a better mutual understanding of research in KRR and ML, and how they can cooperate. The paper is completed by an abundant bibliography.

The use of Micro-Aerial Vehicles (MAVs) equipped with odometry- and depth sensors has become predominant for a wide variety of challenging industrial applications such as the autonomous exploration (i.e., digital mapping), and inspection (i.e., online surface reconstruction) of unknown facilities. However, despite the ongoing attention these topics receive, autonomous exploration systems still lack common evaluation grounds to assess their relative performance in terms of data and experimental tools. We address this deficit by introducing FLYBO, the first unified benchmark environment that focuses on the performance of such flying robots in terms of autonomous exploration and online surface reconstruction. It includes (i) 11 challenging realistic indoor- and outdoor datasets of increasing complexity and size, with ground-truth, (ii) a comprehensive benchmark of 7 of the top-performing autonomous exploration algorithms including methods without publicly available code. (iii) A unified experimental system factorizes the routines shared by autonomous planners in order to fairly and accurately assess their exploration performance in a controlled environment.

We address the problem of autonomous exploration of unknown environments using a Micro Aerial Vehicle (MAV) equipped with an active depth sensor. As such, the task consists in mapping the gradually discovered environment while planning the envisioned trajectories in real-time, using on-board computation only. To do so, we present SplatPlanner, an end-to-end autonomous planner that is based on a novel Permutohedral Frontier Filtering (PFF) which relies on a combination of highly efficient operations stemming from bilateral filtering using permutohedral lattices to guide the entire exploration. In particular, our PFF is computationally linear in input size, nearly parameter-free, and aggregates spatial information about frontier-neighborhoods into density scores in one single step. Comparative experiments made on simulated environments of increasing complexity show our method consistently outperforms recent state-of-the-art methods in terms of computational efficiency, exploration speed and qualitative coverage of scenes. Finally, we also display the practical capabilities of our end-to-end system in a challenging real-flight scenario.

Convolution kernels are essential in signal processing. They are used to model sensors, to define filters, to ensure the interplay between continuous and discrete domains, etc. A classic shortcoming is the difficulty to define which kernel is suitable for a particular application. In previous articles, we relied on a simple analogy between positive convolution kernels and probability distributions to define the notion of maxitive kernel. A maxitive kernel aims at representing a convex set of positive convolution kernels. It therefore models imprecise information on the suitable kernel to be used. Though, in many applications, such as filtering, it may be necessary to use signed convolution kernels. In this article we propose to extend the notion of maxitive kernel domination over signed convolution kernels. This will lead us towards a concept little used until now that are signed - and thus non-monotonous - set functions.

Social skills training courses for managers and sales representatives are mainly realized today through role-playing sessions, which show several limits: realism, contextualization, evaluation objectivity. This paper describes a prototype of a Virtual Reality tool intended to answer these issues. This tool allows living role-playing sessions with virtual characters. We present the results of the first user tests we carried out. Users felt spatially present, involved, and socially present. Results also underline areas of improvement, such as nonverbal behaviors, scenario content and environment realism.

French Army infantrymen's are equipped today with a combat system called FELIN, which includes an infrared sighting device: the IR sight. One of the first manipulations learned by the soldier is the IR sight calibration. Currently, calibration training is a two-step process. The first step consists of practicing on a 2D WIMP software until making no mistakes. Then, the soldiers can apply his knowledge in the real situation on the shooting range. In this paper, we present an ad-hoc study of a learning method including a prototype in Virtual Reality for training on the FELIN IR sight calibration procedure. It has been experimented on real infantrymen learners in an infantry school. Results showed an attractive added value of Virtual Reality in this specific use case. It improved the learners' intrinsic motivation to repeat the training task as well as the learning efficiency. It also helped the training team to identify specific mistake types not detected by the traditional learning software.

In this paper, a new generic regularized reconstruction framework based on confidence interval constraints for tomographic reconstruction is presented. As opposed to usual state-of-the-art regularization methods that try to minimize a cost function expressed as the sum of a data-fitting term and a regularization term weighted by a scalar parameter, the proposed algorithm is a two-step process. The first step concentrates on finding a set of images that rely on the direct estimation of confidence intervals for each reconstructed value. Then, the second step uses confidence intervals as a constraint to choose the most appropriate candidate according to a regularization criterion. Two different constraints are proposed in this paper. The first one has the main advantage of strictly ensuring that the regularized solution will respect the interval-valued data-fitting constraint, thus preventing over-smoothing of the solution while offering interesting properties in terms of spatial and statistical bias/variance trade-off. Another regularization proposition based on the design of a smoother constraint also with appealing properties is proposed as an alternative. The competitiveness of the proposed framework is illustrated in comparison to other regularization schemes using analytical and GATE-based simulation and real PET acquisition.

The authentication of printed documents is an important problem these days. Numerous authentication techniques have been proposed in the relevant literature. One of the most promising solutions uses copy-sensitive graphical codes made of particular patterns. The two Level QR (2LQR) code uses specific textured patterns in order to ensure the sensitivity to duplication process. The authentication test of this code is based on comparing the correlation values between the original and the printed-and-scanned codes with a pre-determined threshold. The weakest feature of this technique is the rejection of authentic codes due to the small gap between correlation values for authentic and duplicated code. In this paper, we propose to reduce the number of false-negative results of the authentication test by using a very competitive Super-Resolution (SR) technique. The experimental results show the significant improvement of correlation values when using the images printed-and-scanned once, without increasing the correlation values of duplicated codes. Therefore, the 2LQR code copy sensitivity is not affected by the suggested quality improvement process.

This paper presents tomographic analysis using L-band NASA/JPL UAVSAR from AfriSAR data conducted over the Gabon Lope Park on February 2016. Prior to tomographic imaging, a phase residual correction methodology based on Sum Kronecker Product have been implemented. The estimated vertical structure of the forest extracted from the correct tomographic data is validated with small footprint light detection collected during the AfriSAR campaign on July 2015. The result demonstrates that L-band tomographic imaging can now be carried out even in the dense tropical forest.

Images that have been altered and more specifically spliced together have invaded the digital domain due to the ease with which we are able to copy and paste them. To detect such forgeries the digital image processing community is proposing new automatic algorithms designed to help human operators reveal manipulated images. In this paper, we focus on a local detection system, which considers which tampered areas produce local statistical effects that do not impact neighboring areas or the image as a whole. We propose to study how the definition of local blocks, considering their size and overlap, impacts final pixel detection. We also propose new features which are an original way to consider the noise of an image as a colored signal. Indeed, in a non-forged image, there is a high correlation of noise between the three color channels R, G and B. We show that an optimal configuration can be defined and in this case the proposed approach outperforms several previously proposed methods using the same tested dataset, in uncompressed and JPEG modes. Note, in this paper we only focus on feature extraction without using machine learning.

In this paper, we present a new regularization paradigm for inverse based regularized image reconstruction techniques. These methods usually attempt to minimize a cost function expressed as the sum of a data-fitting term and a regularization term. The trade-off between both terms is determined by a weighting parameter that has to be set by the user since this trade-off is data dependent. In the approach we present here, we first concentrate on finding a set of eligible candidates for the data fitting term minimization and then select the most appropriate candidate according to the regularization criterion. The main advantage of this method is that it does not require any weighting parameter, and guarantees that no over-regularization can occur. We illustrate this method with a super-resolution reconstruction technique to show its efficiency compared to other competitive methods. Comparisons are carried out with simulated and real data.

Augmented and Mixed Reality technologies bring often definitions understanding issues for novice users. In this paper, we introduce our work in progress, Immercity, regarding the development of a content curation application which manage the idea of communicating on these technologies by their use.

The most effective superresolution methods proposed in the literature require precise knowledge of the so-called point spread function of the imager, while in practice its accurate estimation is nearly impossible. This paper presents a new superresolution method, whose main feature is its ability to account for the scant knowledge of the imager point spread function. This ability is based on representing this imprecise knowledge via a non-additive neighborhood function. The superresolution reconstruction algorithm transfers this imprecise knowledge to output by producing an imprecise (interval-valued) high-resolution image. We propose some experiments illustrating the robustness of the proposed method with respect to the imager point spread function. These experiments also highlight its high performance compared with very competitive earlier approaches. Finally, we show that the imprecision of the high-resolution interval-valued reconstructed image is a reconstruction error marker.

The availability of high quality copy machines provides a large amount of printed document counterfeits. Numerous authentication techniques based on security printing, graphical codes, hashing or local hashing have been suggested earlier. In this paper, we propose a novel printed document authentication system based on sensitivity of a new two level QR (2LQR) code to copying process. This 2LQR code contains specific textured patterns, which are sensitive to printing and copying processes. Therefore, it can be used to detect unauthorized document duplication. Experimental results show the efficiency of this 2LQR code for copy detection.

The quick response (QR) code was designed for storage information and high-speed reading applications. In this paper, we present a new rich QR code that has two storage levels and can be used for document authentication. This new rich QR code, named two-level QR code, has public and private storage levels. The public level is the same as the standard QR code storage level; therefore, it is readable by any classical QR code application. The private level is constructed by replacing the black modules by specific textured patterns. It consists of information encoded using q-ary code with an error correction capacity. This allows us not only to increase the storage capacity of the QR code, but also to distinguish the original document from a copy. This authentication is due to the sensitivity of the used patterns to the print-and-scan (P&S) process. The pattern recognition method that we use to read the second-level information can be used both in a private message sharing and in an authentication scenario. It is based on maximizing the correlation values between P&S degraded patterns and reference patterns. The storage capacity can be significantly improved by increasing the code alphabet q or by increasing the textured pattern size. The experimental results show a perfect restoration of private information. It also highlights the possibility of using this new rich QR code for document authentication.

This paper presents a new iterative image super-resolution technique. Its main feature is its ability to account for a lack of knowledge of the so called Point Spread Function (PSF) of the imager. This ability is based on representing the ill-known PSF by mean of a maxitive kernel, i.e. an imprecise PSF. It also uses the nice properties of a fuzzy partition of the image plane for defining projection and back-projection operators whose particularity is to output interval-valued images instead of precise valued ones. Those operators transfer the imprecise knowledge on the PSF to the output imprecision. We propose some experiments illustrating the robustness of our approach with respect to the registration errors and its performance compared to very competitive earlier approaches.

This paper presents a new reconstruction operator to be used in a super-resolution scheme. Here, by reconstruction in super-resolution, we mean the back-projection operation, i.e. the way K low resolution (LR) images are aggregated to obtain a smooth high resolution (HR) image. Within this method, we replace the usual reconstruction procedure by a non-additive reconstruction operation based on the nice properties of fuzzy partitions. This non-additive reconstruction operator represents a convex family of usual additive reconstruction operators. The obtained reconstructed image is thus a convex family of usual reconstructed images. It allows the super-resolution method to be less sensitive to the choice of the reconstruction method. To make the reading of this method easier, it is presented with 1D signals. We present some experiments to illustrate the proved properties of this new operator.

This paper presents a theoretical and practical novel approach for computing the probability density function underlying a set of observations. The estimator we propose is an extension of the conventional Parzen Rosenblatt method that leads to a very specific interval-valued estimation of the density. Within this approach, we make use of the convenient representation of a set of usual (summative) kernels by a maxitive kernel (i.e. a possibility distribution) to derive an exact computation with a very low complexity of an interval-valued estimation. The considered set of kernels is particularly convenient since it contains kernels having comparable shapes and bandwidth. We prove that the obtained imprecise probability density function contains a set of precise density functions estimated using the standard method with kernels belonging to the considered set.

In this paper, we propose to show that a particular fuzzy extension of mathematical morphology coincides with a non-additive extension of linear filtering based on convolution kernels thus bridging the two approaches.

The way catadioptric images are acquired implies that they present radial distortions. Therefore, classical processing may not be suitable. This statement will be illustrated by considering edge detection matter. Classical edge detectors usually consist in three steps : gradient computation, maximization and thresholding. The two lasts steps use pixels neighborhood concept. On the opposite of perspective images where pixel neighborhood is intuitive, catadioptric images present radial resolution changes. Then, the size and shape of pixel neighborhood have to be depending on pixel location. This article presents a new gradient estimation approach based on non-additive kernels. This technique is adapted to catadioptric images and also provides a natural threshold discarding the arbitrary thresholding step.

In this paper, we propose a new method to perform the first derivative estimation of a discrete intensity distribution. This approach is based on a non-additive aggregation process and provides an estimate of the gradient as intervals instead of single values. These intervals are used to threshold a gradient-based edge detection and therefore discard spurious detections due to noise.

This article describes an original method to track 2D templates in a video sequence. This approach is based on robust modelling of the interaction between pattern movement and grey level variations in the image using fuzzy bimodal rules. Movement estimation is performed by inverting these rules and polling the results in a quasicontinuous histogram. Some experimental results are given to illustrate the performance of this algorithm

This paper describes morphological tools that have been adapted to omnidirectional catadioptric images.

This paper deals with main apparent motion estimation using a fuzzy representation of a pixel's gray level. Rough histograms and possibility theory are used to provide an accurate estimation of the motion. The use of these theories allows us to partly cope with the limitations of classical motion estimation methods. This article explains the estimation process in detail and also presents some illustrative examples.

Applied statistics are widely used in pattern recognition and other computing applications to find the most likely value of a parameter. The use of classical empirical statistics is based upon assumption about normality of underlying density distribution of data. When the data is corrupted by contaminated noise, then classical tools are usually not robust enough and the estimation of the mode is biased. In this article, we propose to estimate the main mode of a distribution by means of a rough histogram and we show that this estimation is robust to contamination.

The Hough transform is a popular method for detecting complex forms in digital images. However, the technique is not very robust since several parameters that determine the scope of the detection results, such as quantization thresholds and intervals, must first be defined. In the present paper, we propose to enhance shape detection with the Hough transform through fuzzy analysis. One chief drawback of the Hough transform, i.e. the uncertainty/precision duality, is thus reduced.

A solution to extract 3-D shapes from a structured light image is presented. The 2-D striped image is segmented into regions corresponding to quadratic surfaces. A fuzzy analysis of the stripe's properties allows one to locate discontinuities and to model stripe parts. These parts are tracked in consecutive images and matched in order to create regions. Segmentation results are presented which were obtained with a real scene consisting of multiple objects of arbitrary shapes.>