Within the framework of fuzzy algebras with fuzzy equality and a complete lattice for membership values, this paper introduces a novel fuzzified version of classical Green's relations on E -fuzzy semigroups, referred to as E -fuzzy Green's relations. We reveal several properties of E -fuzzy semigroups, including the properties of fuzzy unit elements within E -fuzzy cancellative semigroups. Additionally, we derive equivalent forms of these newly defined fuzzy relations and examine the properties of their associated cut-quotient structures in certain E -fuzzy semigroups. The E -fuzzy Green's relations on E -fuzzy semigroups are found to be compatible fuzzy equivalence relations (fuzzy equalities) on some E -fuzzy bands. Furthermore, we present two significant decomposition theorems related to the cut-quotient structures over fuzzy Green's relations, demonstrating that these structures have additional algebraic properties compared with the quotient structures over ordinary fuzzy equality E μ .

Frame sampling is a fundamental problem in video action recognition due to the essential redundancy in time and limited computation resources. The existing sampling strategy often employs a fixed frame selection and lacks the flexibility to deal with complex variations in videos. In this paper, we present a simple, sparse, and explainable frame sampler, termed as Motion-Guided Sampler (MGSampler). Our basic motivation is that motion is an important and universal signal that can drive us to adaptively select frames from videos. Accordingly, we propose two important properties in our MGSampler design: motion sensitive and motion uniform. First, we present two different motion representations to enable us to efficiently distinguish the motion-salient frames from the background. Then, we devise a motion-uniform sampling strategy based on the cumulative motion distribution to ensure the sampled frames evenly cover all the important segments with high motion salience. Our MGSampler yields a new principled and holistic sampling scheme, that could be incorporated into any existing video architecture. Experiments on five benchmarks demonstrate the effectiveness of our MGSampler over the previous fixed sampling strategies, and its generalization power across different backbones, video models, and datasets. The code is available at https://github.com/MCG-NJU/MGSampler.

In this paper, we propose a generalized linear model for video packet loss visibility that is applicable to different group-of-picture structures. We develop the model using three subjective experiment data sets that span various encoding standards (H.264 and MPEG-2), group-of-picture structures, and decoder error concealment choices. We consider factors not only within a packet, but also in its vicinity, to account for possible temporal and spatial masking effects. We discover that the factors of scene cuts, camera motion, and reference distance are highly significant to the packet loss visibility. We apply our visibility model to packet prioritization for a video stream; when the network gets congested at an intermediate router, the router is able to decide which packets to drop such that visual quality of the video is minimally impacted. To show the effectiveness of our visibility model and its corresponding packet prioritization method, experiments are done to compare our perceptual-quality-based packet prioritization approach with existing Drop-Tail and Hint-Track-inspired cumulative-MSE-based prioritization methods. The result shows that our prioritization method produces videos of higher perceptual quality for different network conditions and group-of-picture structures. Our model was developed using data from high encoding-rate videos, and designed for high-quality video transported over a mostly reliable network; however, the experiments show the model is applicable to different encoding rates.

Our work builds a general visibility model of video packets which is applicable to various types of GOP (group of pictures). The data used for analysis and building the model come from three subjective experiment sets with different encoding and decoding parameters on H.264 and MPEG-2 videos. We consider factors not only within a packet but also across its vicinity to account for possible temporal and spatial masking effects. This model can be useful for an intermediate router in a congested network to drop less visible packets to maintain overall video quality. Experiments are done to compare our perceptual-quality-based packet dropping approach with existing drop-tail and hint-track-inspired cumulative-MSE-based dropping methods. The result shows that our dropping method produces videos of higher perceptual quality for different network conditions and GOP structures.