The problem of evacuating two robots from the disk in the face-to-face model was first introduced in [16], and extensively studied (along with many variations) ever since with respect to worst case analysis. We initiate the study of the same problem with respect to average case analysis, which is also equivalent to designing randomized algorithms for the problem. First we observe that algorithm B2 of [16] with worst case cost Wrs (B2) := 5.73906 has average case cost Avg (B2) := 5.1172. Then we verify that none of the algorithms that induced worst case cost improvements in subsequent publications has better average case cost, hence concluding that our problem requires the invention of new algorithms. Then, we observe that a remarkable simple algorithm, B1, has very small average case cost Avg (B1) := 1 + π, but very high worst case cost Wrs (B1) := 1 + 2π. Motivated by the above, we introduce constrained optimization problem 2 EVAC w F 2F , in which one is trying to minimize the average case cost of the evacuation algorithm given that the worst case cost does not exceed w. The problem is of special interest with respect to practical applications, since a common objective in search-and-rescue operations is to minimize the average completion time, given that a certain worst case threshold is not exceeded, e.g. for safety or limited energy reasons. Our main contribution is the design and analysis of families of new evacuation parameterized algorithms A (p) which can solve 2 EVAC w F 2F , for every w ∈ [Wrs (B1) , Wrs (B2)]. In particular, by letting parameter(s) p vary, we obtain parametric curve (Avg (A (p)) , Wrs (A (p))) that induces a continuous and strictly decreasing function in the mean-worst case space, and whose endpoints are (Avg (B1) , Wrs (B1)) , (Avg (B2) , Wrs (B2)). Notably, the worst case analysis of the problem, since it's introduction, has been relying on technical numerical, computerassisted, calculations, following tedious robots trajectories' analysis. Part of our contribution is a novel systematic procedure, which, given any evacuation algorithm, can derive it's worst and average case performance in a clean and unified way.

The digital image proves critical evidence in the fields like forensic investigation, criminal investigation, intelligence systems, medical imaging, insurance claims, and journalism to name a few. Images are an authentic source of information on the internet and social media. But, using easily available software or editing tools such as Photoshop, Corel Paint Shop, PhotoScape, PhotoPlus, GIMP, Pixelmator, etc. images can be altered or utilized maliciously for personal benefits. Various active, passive and other new deep learning technology like GAN approaches have made photo-realistic images difficult to distinguish from real images. Digital image tamper detection now focuses on determining the authenticity and consistency of digital photos. The major research problems use generic solutions and strategies, such as standardized data sets, benchmarks, evaluation criteria and generalized approaches.This paper overviews the evaluation of various image tamper detection methods. A brief discussion of image datasets and a comparative study of image criminological (forensic) methods are included in this paper. Furthermore, recently developed deep learning techniques along with their limitations have also been addressed. This study aims to comprehensively analyze image forgery detection methods using conventional and advanced deep learning approaches.

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The problem of evacuating two robots from the disk in the face-to-face model was first introduced by Czyzowicz et al. [DISC’2014], and has been extensively studied (along with many variations) ever since with respect to worst-case analysis. We initiate the study of the same problem with respect to average-case analysis, which is also equivalent to designing randomized algorithms for the problem. In particular, we introduce constrained optimization problem 2EvacF2F, in which one is trying to minimize the average-case cost of the evacuation algorithm given that the worst-case cost does not exceed w. The problem is of special interest with respect to practical applications, since a common objective in search-and-rescue operations is to minimize the average completion time, given that a certain worst-case threshold is not exceeded, e.g., for safety or limited energy reasons. Our main contribution is the design and analysis of families of new evacuation parameterized algorithms which can solve 2EvacF2F, for every w for which the problem is feasible. Notably, the worst-case analysis of the problem, since its introduction, has been relying on technical numerical, computer-assisted calculations, following tedious robot trajectory analysis. Part of our contribution is a novel systematic procedure, which given any evacuation algorithm, can derive its worst- and average-case performance in a clean and unified way.

Anomaly detection in video systems has been popular over several years. It is still challenging to detect anomalies in a static object. To manage this objective, we focus on changes in the position of a stationary object in videos. In a normal scenario, the pixel values of the static object are fixed while in abnormal motion the fixed values change.We introduce a new concept to determine anomalies based on manual annotations in each video frame, only over a part of a static object in a frame such that it can be taken as a reference for the whole. Through color channel splitting we determine mask image, from which handcrafted features such as scratch area, perimeter, equivalent diameter and density are calculated. In the next step, we analyze frame-wise changes in feature values using a linear regression model, feature values are constant when the object remains stationary while there is a rise or fall in values when an object changes location. We classify feature values through anomaly scores and thresholds. In this model, we are evaluating our proposed framework on 12 real-time video datasets. Results are compared with existing techniques which are outperforming in terms of accuracy, mean square error and area under the curve.

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Anomalous event recognition has a complicated definition in the complex background due to the sparse occurrence of anomalies. In this paper, we form a framework for classifying multiple anomalies present in video frames that happen in a context such as the sudden moment of people in various directions and anomalous vehicles in the pedestrian park. An attention U-net model on video frames is utilized to create a binary segmented anomalous image that classifies each anomalous object in the video. White pixels indicate the anomaly, and black pixels serve as the background image. For better segmentation, we have assigned a border to every anomalous object in a binary image. Further to distinguish each anomaly a watershed algorithm is utilized that develops multi-level gray image masks for every anomalous class. This forms a multi-class problem, where each anomalous instance is represented by a different gray color level. We use pixel values, Optical Intensity, entropy values, and Gaussian filter with sigma 5, and 7 to form a feature extraction module for training video images along with their multi-instance gray-level masks. Pixel-level localization and identification of unusual items are done using the feature vectors acquired from the feature extraction module and multi-class stack classifier model. The proposed methodology is evaluated on UCSD Ped1, Ped2 and UMN datasets that obtain pixel-level average accuracy results of 81.15%,87.26% and 82.67% respectively.

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