In this paper, we present a novel edge-directed upsampling method based on radial basis function (RBF) interpolation. In order to remove artifacts such as blurred edges or blocking effects, we suggest a nonlinear method capable of taking edge information into account. The resampling evaluation is determined according to the edge orientation. The proposed scheme is as simple to implement as linear methods but it demonstrates improved visual quality by preserving the edge features better than the classical linear interpolation methods. The algorithm is compared with some well-known linear schemes as well as recently developed nonlinear schemes. The resulting images demonstrate the new algorithm's ability to magnify an image while preserving the edge features.

In this paper, we study the convergence behavior of interpolants by smooth radial basis functions to polynomial interpolants in $\mathbb{R}^d$ as the radial basis functions are scaled to be increasingly flat. Larsson and Fornberg [Comput. Math. Appl., 49 (2005), pp. 103–130] conjectured a sufficient property for this convergence, and they also conjectured that Bessel radial functions do not satisfy this property. First, in the case of positive definite radial functions, we prove both conjectures by Larsson and Fornberg for the convergence of increasingly flat radial function interpolants. Next, we extend the results to the case of conditionally positive definite radial functions of order $m>0$.

A dramatic increase has been registered in the number of social media posts in photo form as well as in hashtag activism. Hashtags, which manifest thoughts and feelings clearly and concisely, originated on Twitter, where the length of a post is limited; their use, however, has expanded into other social media services, including Instagram. Hashtags, which make it easy to find and express support for posts of interest, have been widely used for online activism, although they have been criticized for fostering confirmation bias. Moreover, hashtag activism in photo form has been relatively understudied. This research analyzed Instagram photos with antivaccination hashtags as an example of hashtag activism through photos. In addition, we examined how the photo features were related to public response, which was manifested via engagement and comment sentiment. The results suggest that the photos which were categorized into “text” took the largest share. It was also found that the major way of claiming was to imprint key messages that persuade people not to vaccinate with remarks from professionals on photos and provide a source of supporting information in the post text with hashtags of antivaccine intention. Various photo features showed associations with engagement and comment sentiment, but the directions of correlation were usually the opposite: these results suggest that engagement and comment sentiment are separate domains that reveal different public responses.