Sébastien Pierard

Sébastien Piérard, Anthony Cioppa, Anaïs Halin et al.

Various tasks encountered in real-world surveillance can be addressed by determining posteriors (e.g. by Bayesian inference or machine learning), based on which critical decisions must be taken. However, the surveillance domain (acquisition device, operating conditions, etc.) is often unknown, which prevents any possibility of scene-specific optimization. In this paper, we define a probabilistic framework and present a formal proof of an algorithm for the unsupervised many-to-infinity domain adaptation of posteriors. Our proposed algorithm is applicable when the probability measure associated with the target domain is a convex combination of the probability measures of the source domains. It makes use of source models and a domain discriminator model trained off-line to compute posteriors adapted on the fly to the target domain. Finally, we show the effectiveness of our algorithm for the task of semantic segmentation in real-world surveillance. The code is publicly available at https://github.com/rvandeghen/MDA.

Anaïs Halin, Sébastien Piérard, Anthony Cioppa et al.

Properly understanding the performances of classifiers is essential in various scenarios. However, the literature often relies only on one or two standard scores to compare classifiers, which fails to capture the nuances of application-specific requirements. The Tile is a recently introduced visualization tool organizing an infinity of ranking scores into a 2D map. Thanks to the Tile, it is now possible to compare classifiers efficiently, displaying all possible application-specific preferences instead of having to rely on a pair of scores. This hitchhiker's guide to understanding the performances of two-class classifiers presents four scenarios showcasing different user profiles: a theoretical analyst, a method designer, a benchmarker, and an application developer. We introduce several interpretative flavors adapted to the user's needs by mapping different values on the Tile. We illustrate this guide by ranking and analyzing the performances of 74 state-of-the-art semantic segmentation models through the perspective of the four scenarios. Through these user profiles, we demonstrate that the Tile effectively captures the behavior of classifiers in a single visualization, while accommodating an infinite number of ranking scores. Code for mapping the different Tile flavors is available in supplementary material.

Sébastien Piérard, Anaïs Halin, Anthony Cioppa et al.

Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal theory for performance-based ranking. First, we introduce a rigorous framework built on top of both the probability and order theories. Our new framework encompasses the elements necessary to (1) manipulate performances as mathematical objects, (2) express which performances are worse than or equivalent to others, (3) model tasks through a variable called satisfaction, (4) consider properties of the evaluation, (5) define scores, and (6) specify application-specific preferences through a variable called importance. On top of this framework, we propose the first axiomatic definition of performance orderings and performance-based rankings. Then, we introduce a universal parametric family of scores, called ranking scores, that can be used to establish rankings satisfying our axioms, while considering application-specific preferences. Finally, we show, in the case of two-class classification, that the family of ranking scores encompasses well-known performance scores, including the accuracy, the true positive rate (recall, sensitivity), the true negative rate (specificity), the positive predictive value (precision), and F1. However, we also show that some other scores commonly used to compare classifiers are unsuitable to derive performance orderings satisfying the axioms.

Sébastien Piérard, Anaïs Halin, Anthony Cioppa et al.

In the computer vision and machine learning communities, as well as in many other research domains, rigorous evaluation of any new method, including classifiers, is essential. One key component of the evaluation process is the ability to compare and rank methods. However, ranking classifiers and accurately comparing their performances, especially when taking application-specific preferences into account, remains challenging. For instance, commonly used evaluation tools like Receiver Operating Characteristic (ROC) and Precision/Recall (PR) spaces display performances based on two scores. Hence, they are inherently limited in their ability to compare classifiers across a broader range of scores and lack the capability to establish a clear ranking among classifiers. In this paper, we present a novel versatile tool, named the Tile, that organizes an infinity of ranking scores in a single 2D map for two-class classifiers, including common evaluation scores such as the accuracy, the true positive rate, the positive predictive value, Jaccard's coefficient, and all F-beta scores. Furthermore, we study the properties of the underlying ranking scores, such as the influence of the priors or the correspondences with the ROC space, and depict how to characterize any other score by comparing them to the Tile. Overall, we demonstrate that the Tile is a powerful tool that effectively captures all the rankings in a single visualization and allows interpreting them.

Anaïs Halin, Sébastien Piérard, Renaud Vandeghen et al.

Characterizing domains is essential for models analyzing dynamic environments, as it allows them to adapt to evolving conditions or to hand the task over to backup systems when facing conditions outside their operational domain. Existing solutions typically characterize a domain by solving a regression or classification problem, which limits their applicability as they only provide a limited summarized description of the domain. In this paper, we present a novel approach to domain characterization by characterizing domains as probability distributions. Particularly, we develop a method to predict the likelihood of different weather conditions from images captured by vehicle-mounted cameras by estimating distributions of physical parameters using normalizing flows. To validate our proposed approach, we conduct experiments within the context of autonomous vehicles, focusing on predicting the distribution of weather parameters to characterize the operational domain. This domain is characterized by physical parameters (absolute characterization) and arbitrarily predefined domains (relative characterization). Finally, we evaluate whether a system can safely operate in a target domain by comparing it to multiple source domains where safety has already been established. This approach holds significant potential, as accurate weather prediction and effective domain adaptation are crucial for autonomous systems to adjust to dynamic environmental conditions.

Sébastien Piérard, Adrien Deliège, Marc Van Droogenbroeck

Ranking methods or models based on their performance is of prime importance but is tricky because performance is fundamentally multidimensional. In the case of classification, precision and recall are scores with probabilistic interpretations that are both important to consider and complementary. The rankings induced by these two scores are often in partial contradiction. In practice, therefore, it is extremely useful to establish a compromise between the two views to obtain a single, global ranking. Over the last fifty years or so,it has been proposed to take a weighted harmonic mean, known as the F-score, F-measure, or $F_β$. Generally speaking, by averaging basic scores, we obtain a score that is intermediate in terms of values. However, there is no guarantee that these scores lead to meaningful rankings and no guarantee that the rankings are good tradeoffs between these base scores. Given the ubiquity of $F_β$ scores in the literature, some clarification is in order. Concretely: (1) We establish that $F_β$-induced rankings are meaningful and define a shortest path between precision- and recall-induced rankings. (2) We frame the problem of finding a tradeoff between two scores as an optimization problem expressed with Kendall rank correlations. We show that $F_1$ and its skew-insensitive version are far from being optimal in that regard. (3) We provide theoretical tools and a closed-form expression to find the optimal value for $β$ for any distribution or set of performances, and we illustrate their use on six case studies.

Sébastien Piérard, Adrien Deliège, Anaïs Halin et al.

Frequently, multiple entities (methods, algorithms, procedures, solutions, etc.) can be developed for a common task and applied across various domains that differ in the distribution of scenarios encountered. For example, in computer vision, the input data provided to image analysis methods depend on the type of sensor used, its location, and the scene content. However, a crucial difficulty remains: can we predict which entities will perform best in a new domain based on assessments on known domains, without having to carry out new and costly evaluations? This paper presents an original methodology to address this question, in a leave-one-domain-out fashion, for various application-specific preferences. We illustrate its use with 30 strategies to predict the rankings of 40 entities (unsupervised background subtraction methods) on 53 domains (videos).

Sébastien Piérard, Marc Braham, Marc Van Droogenbroeck

Background subtraction (BGS) is a common choice for performing motion detection in video. Hundreds of BGS algorithms are released every year, but combining them to detect motion remains largely unexplored. We found that combination strategies allow to capitalize on this massive amount of available BGS algorithms, and offer significant space for performance improvement. In this paper, we explore sets of performances achievable by 6 strategies combining, pixelwise, the outputs of 26 unsupervised BGS algorithms, on the CDnet 2014 dataset, both in the ROC space and in terms of the F1 score. The chosen strategies are representative for a large panel of strategies, including both deterministic and non-deterministic ones, voting and learning. In our experiments, we compare our results with the state-of-the-art combinations IUTIS-5 and CNN-SFC, and report six conclusions, among which the existence of an important gap between the performances of the individual algorithms and the best performances achievable by combining them.