A single image super-resolution reconstruction method based on a variational calculus model for multi-direction stencils is proposed in this study to enhance the accuracy of image super-resolution reconstruction and avoid distortion on the edges and areas with a rich texture caused by few stencil directions in classical interpolation. First

multi-direction stencils are built to reflect 28 directions used to calculate the contour directions of an input image. Then

the TV model is used to estimate image contours and to determine the optimized direction of the edge contours. Finally

image super-resolution reconstruction is realized through image interpolation based on the aforementioned multi-direction stencils. Compared with those in the classical high-resolution test image reconstruction method of image interpolation with contour stencils

the average peak signal-to-noise ratio and the average structural similarity obtained using the method presented in the current work are increased by 1.578 dB and 0.030 02 dB

respectively. The method proposed in the current work can effectively overcome the negative effects of traditional interpolation methods

such as blurred and jagged edges of images. Furthermore

this method can avoid distortion on the edges and areas with a rich texture caused by a few stencil directions. The effectiveness of this method has been verified via a large number of simulations.