Edge-directional interpolation algorithm using structure tensor

The paper presents a new low complexity edge-directed image interpolation algorithm. The algorithm uses structure tensor analysis to distinguish edges from textured areas and to find local structure direction vectors. The vectors are quantized into 6 directions. Individual adaptive interpolation kernels are used for each direction. Experimental results show high performance of the proposed method without introducing artifacts. Introduction Development of a high-quality and detail-preserving image interpolation algorithm is a challenging problem. Linear methods [1] like bilinear and bicubic interpolation show great performance but they suffer from blur, ringing and staircase artifacts in the edge areas. Additional knowledge about image contents is used by more advanced image interpolation algorithms. For example, NEDI algorithm [2] uses the assumption of self-similarity between highand low-resolution images. Regularization-based image interpolation algorithms pose the image interpolation as a functional minimization problem [3, 4]. The functional contains the datafitting term and the stabilizer term. The data-fitting term restricts the high-resolution image to match the lowresolution image. The stabilizer term makes the highresolution image fit an a priori information. The similar approaches are MAP, POCS and PDE-based algorithms [5, 6, 7, 8, 9]. Learning-based algorithms construct the high-resolution image using a pre-built dictionary containing pairs of corresponding highand low-resolution patches [10, 11]. Regularization-based algorithms are time consuming as they perform the minimization of the regularization functional by iterative methods. Non-iterative edgedirectional image interpolation algorithms are developed for the performance critical applications. Great effectiveness has been shown by single-frame super-resolution algorithms which map low-resolution image patches into high-resolution ones. Deep convolutional neural networks [12, 13] and regression [14, 15] are used for high quality image interpolation. High effectiveness has been also shown by low complexity edge-directed image interpolation algorithms that consider the image resampling procedure as two consecuent problems [16, 17, 18, 19]. The first problem is finding the direction for each pixel corresponding to local image structure. The second problem is directional interpolation according to previously found directions. Existing algorithms use directional filtering [16], directional variation [17], second order derivatives [18] to find local structure direction. Existing algorithms also limit the number of possible directions to 2 or 4 to improve computational efficiency and to reduce the influence of discretization. For example, the algorithm [19] combines the results of applying directional cubic interpolation in two directions. Textured areas are a problem for edge-directed interpolation methods. Artifacts usually appear when edgedirected algorithm is applied to corners. Corners contain multiple directions and usually appear in textures areas. Using the structure tensor is an effective way to distinguish between edges, corners and flat areas. In this work, we propose fast and effective edgedirectional algorithm based on structure tensor and individual interpolation kernels for each direction. The main difference of the proposed algorithm with state-of-the-art algorithms is quantization of the direction vector into 6 directions and using optimal 4x4 kernels for each direction. The kernels are optimized by PSNR minimization over 29 reference images from LIVE database [20].