# Image Interpolation with Regional Gradient Estimation
###### Abstract  
This paper proposes an image interpolation method with regional gradient estimation (GEI) to solve the problem of the nonlinear interpolation method not sufficiently considering non-edge pixels. First, the approach presented in this paper expanded on the edge diffusion idea used in CGI and proposed a regional gradient estimation strategy to improve the problem of gradient calculation in the CGI method. Next, the gradient value was used to determine whether a pixel was an edge pixel. Then, a 1D directional filter was employed to process edge pixels while interpolating non-edge pixels using a 2D directionless filter. Finally, we experimented with various representative interpolation methods for grayscale and color images, including the one presented in this paper, and compared them in terms of subjective results, objective criteria, and computational complexity. The experimental results showed that GEI performed better than the other methods in an experiment concerning the visual effect, objective criteria, and computational complexity. image interpolation; image enhancement; bicubic interpolation; nonlinear interpolation; image gradient; edge diffusion; regional gradient estimation +
Footnote †: journal:  
image interpolation method is used to interpolate the frequency domain coefficients; then, threshold processing is performed to obtain the required interpolation image. This method effectively combines the interpolation method and the band-pass filtering feature of the wavelet transform; thus, it can effectively maintain high-frequency detail in the image and improve the visual effect of image interpolation. The approach based on edge information uses a non-directional interpolation method to process non-edge pixels, while for edge pixels, a directional interpolation method is used according to the direction of the edge. This paper mainly studies the interpolation method based on edge information. In general, image edges are regions where the gray level changes dramatically and its derivative exceeds a threshold, usually by only one or two pixels in width. Such pixels are used in 1D directional interpolation along the edge direction. Meanwhile, non-edge pixels are processed using linear interpolation. However, for non-edge pixels near the edge, if the neighborhood involved in their interpolation crosses the border, the boundaries are blurred after interpolation. This paper proposes a nonlinear interpolation method called \"image interpolation with regional gradient estimation\". Compared to existing nonlinear interpretation methods, the GEI method can distinguish the edge pixels and non-edge pixels of an image more effectively. Specifically, the proposed method employs a regional gradient estimation strategy to reduce the error generated by the CGI method when judging the gradient of unknown pixels, thereby enhancing the image's interpolation effect. First, the proposed method utilizes the CGI method's concept of edge diffusion to diffuse the image edges and determine the properties of the diffused image pixel. Second, the gradients of unknown pixels in high-resolution (HR) images are estimated using bicubic interpolation with regional gradients. The estimated gradient is then applied to determine the properties of the unknown pixel. According to the properties, different interpolation methods are selected, including 2D directionless interpolation for non-edge pixels and 1D directional interpolation for edge pixels. We experimented with various representative interpolation methods for grayscale and color images, including the one presented in this paper, and compared them in terms of subjective results, objective criteria, and computational complexity. The experimental results showed that GEI performed better than the other methods in an experiment concerning the visual effect, objective criteria, and computational complexity. The structure of this paper is as follows. Section 1 is the introduction. Section 2 briefly describes the image interpolation problem and the idea of edge diffusion.