Abstract
The primary goal of the research on image segmentation is to produce better segmentation algorithms. In spite of almost 50 years of research and development in this Held, the general problem of splitting in image into meaningful regions remains unsolved. New and emerging techniques are constantly being applied with reduced Success. The design of each of these new segmentation algorithms requires spending careful attention judging the effectiveness of the technique. This paper demonstrates how the proposed methodology is well suited to perform a quantitative comparison between image segmentation algorithms using I ground-truth segmentation. It consists of a general framework already partially proposed in the literature, but dispersed over several works. The framework is based on the principle of eliminating the minimum number of elements Such that a specified condition is met. This rule translates directly into a global optimization procedure and the intersection-graph between two partitions emerges as the natural tool to solve it. The objective of this paper is to summarize, aggregate and extend the dispersed work. The principle is clarified, presented striped of unnecessary supports and extended to sequences of images. Our Study shows that the proposed framework for segmentation performance evaluation is simple, general and mathematically sound.

Abstract
Deep learning has recently gained popularity in the field of video anomaly detection, with the development of various methods for identifying abnormal events in visual data. The growing need for automated systems to monitor video streams for anomalies, such as security breaches and violent behaviours in public areas, requires the development of robust and reliable methods. As a result, there is a need to provide tools to objectively evaluate and compare the real-world performance of different deep learning methods to identify the most effective approach for video anomaly detection. Current state-of-the-art metrics favour weakly-supervised strategies stating these as the best-performing approaches for the task. However, the area under the ROC curve, used to justify this statement, has been shown to be an unreliable metric for highly unbalanced data distributions, as is the case with anomaly detection datasets. This paper provides a new perspective and insights on the performance of video anomaly detection methods. It reports the results of a benchmark study with state-of-the-art methods using a novel proposed framework for evaluating and comparing the different models. The results of this benchmark demonstrate that using the currently employed set of reference metrics led to the misconception that weakly-supervised methods consistently outperform semi-supervised ones. © 2023 The Authors

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