Approximations of Fuzzy Numbers by Using r-s Piecewise Linear Fuzzy Numbers Based on Weighted Metric

Using simple fuzzy numbers to approximate general fuzzy numbers is an important research aspect of fuzzy number theory and application. The existing results in this field are basically based on the unweighted metric to establish the best approximation method for solving general fuzzy numbers. In order to obtain more objective and reasonable best approximation, in this paper, we use the weighted distance as the evaluation standard to establish a method to solve the best approximation of general fuzzy numbers. Firstly, the conceptions of I-nearest r-s piecewise linear approximation (in short, PLA) and the II-nearest r-s piecewise linear approximation (in short, PLA) are introduced for a general fuzzy number. Then, most importantly, taking weighted metric as a criterion, we obtain a group of formulas to get the I-nearest r-s PLA and the II-nearest r-s PLA. Finally, we also present specific examples to show the effectiveness and usability of the methods proposed in this paper.

A spatial approach to rainfall in Sertão do Pajeú – Pernambuco

Changes in precipitation have implications for the hydrological cycle and water resources. Climate change is expected to alter average temperature and precipitation values, increasing the variability of these events, which could cause more intense and frequent floods and droughts. The objective of this study was to characterize the rainfall in the microregion of Pajeú, in Pernambuco, as well as to provide subsidies for public policies aimed at water scarcity. For this, rainfall data were used at stations belonging to the micro-region and its surroundings, for the period from January 1980 to December 2019. In addition, to mitigate the influences caused by temporal heterogeneity, stations with large discontinuity of information. The Inverse Weighted Distance was used to perform the interpolation of data and preparation of maps with isolines of rainfall. The results show the places with the highest annual rainfall during the study period were Serra Talhada and Triunfo, and the lowest rainfall occurred in the vicinity of Ingazeira and Tabira.

Remote Sensing Image Retrieval Using Convolutional Neural Network Features and Weighted Distance

Remote sensing image retrieval (RSIR) may be a fundamental task in remote sensing. Most content-based image retrieval (CBRSIR) approaches take an easy distance as similarity criteria. A retrieval method supported weighted distance and basic features of Convolutional Neural Network (CNN) is proposed during this letter. the strategy contains two stages. First, in offline stage, the pretrained CNN will be fine-tuned by some labelled images from our target data set, then accustomed extract CNN features, and labelled the pictures within the retrieval data set. Second, in online stage, we extract features of the query image by using fine-tuned CNN model and calculate the load of every image class and apply them to calculate the space between the query image and also the retrieved images. Experiments and methods are conducted on two Remote Sensing Image Retrieval data sets. Compared with the state-of the-art methods, the proposed method significantly improves retrieval performance.

WDTISeg: One-Stage Interactive Segmentation for Breast Ultrasound Image Using Weighted Distance Transform and Shape-Aware Compound Loss

Accurate tumor segmentation is important for aided diagnosis using breast ultrasound. Interactive segmentation methods can obtain highly accurate results by continuously optimizing the segmentation result via user interactions. However, traditional interactive segmentation methods usually require a large number of interactions to make the result meet the requirements due to the performance limitations of the underlying model. With greater ability in extracting image information, convolutional neural network (CNN)-based interactive segmentation methods have been shown to effectively reduce the number of user interactions. In this paper, we proposed a one-stage interactive segmentation framework (interactive segmentation using weighted distance transform, WDTISeg) for breast ultrasound image using weighted distance transform and shape-aware compound loss. First, we used a pre-trained CNN to attain an initial automatic segmentation, based on which the user provided interaction points of mis-segmented areas. Then, we combined Euclidean distance transform and geodesic distance transform to convert interaction points into weighted distance maps to transfer segmentation guidance information to the model. The same CNN accepted the input image, the initial segmentation, and weighted distance maps as a concatenation input and provided a refined result, without another additional segmentation network. In addition, a shape-aware compound loss function using prior knowledge was designed to reduce the number of user interactions. In the testing phase on 200 cases, our method achieved a dice of 82.86 ± 16.22 (%) for automatic segmentation task and a dice of 94.45 ± 3.26 (%) for interactive segmentation task after 8 interactions. The results of comparative experiments proved that our method could obtain higher accuracy with fewer simple interactions than other interactive segmentation methods.

CoolMoves

Current Virtual Reality (VR) systems are bereft of stylization and embellishment of the user's motion - concepts that have been well explored in animations for games and movies. We present CooIMoves, a system for expressive and accentuated full-body motion synthesis of a user's virtual avatar in real-time, from the limited input cues afforded by current consumer-grade VR systems, specifically headset and hand positions. We make use of existing motion capture databases as a template motion repository to draw from. We match similar spatio-temporal motions present in the database and then interpolate between them using a weighted distance metric. Joint prediction probability is then used to temporally smooth the synthesized motion, using human motion dynamics as a prior. This allows our system to work well even with very sparse motion databases (e.g., with only 3-5 motions per action). We validate our system with four experiments: a technical evaluation of our quantitative pose reconstruction and three additional user studies to evaluate the motion quality, embodiment and agency.