Adaptive Directional Window Selection For Edge-Directed Interpolation Chi-Shing Wong Department of Electronic and Information Engineering Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong Wan-Chi Siu Department of Electronic and Information Engineering Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong Abstract— In this paper, we present an adaptive directional window selection for the edge-directed interpolation. The new window selection can solve the problem of covariance mismatch in high frequency and texture regions. It makes use of a practical directional elliptic window which works according to the edge direction sliding along an edge and then subsequently chooses the best window evaluated by choosing the elliptic window which has the lowest Means Square Error (MSE). Experimental results show that by the proposed technique can generate a high quality interpolated image which is better than other edge directed interpolation approaches. Experimental results also provided on different images to justify the value of this approach at the end of the paper. Keywords-component; Interpolation, edge-directed, sample window selection I. INTRODUCTION High Definition television (or HDTV) can produce a better visual quality than Standard Definition (or SDTV). It is because HDTV has a new digital television broadcasting system with a high-resolution display. However, not all the videos or movies produced with the high-resolution quality. Many videos or movies only contain a standard resolution (720×576) video sequence. Therefore, interpolation algorithms are demanding, such that standard resolution video sequence can be shown on high-resolution display units. It is well know that using a classical linear interpolation algorithm, such as bilinear and bicubic interpolation cannot produce a visual quality that is accepted by today customer, as it often suffers from the edge blurring effect or produce some artifacts around the edge area [1]. These artifacts will reduce substantially the visual quality of the video sequence, especially the artifacts that appear near the major edges. Therefore, many research studies [2]-[11] tried to improve the visual quality and lower the mean- squares errors and to make comparison with the linear interpolation algorithm. The New Edge-Directed Interpolation (NEDI) [12] method models natural images as a second-order locally stationary Gaussian process and predicts unknown pixels. The NEDI method uses a square window which is located at the center of the unknown pixels in order to model the statistics near the unknown pixels, so that the unknown pixels can be predicted. Recently, a Modified Edge-directed interpolation MEDI [13] was proposed in 2009, which suggested to use a multiple square training windows instead of a single square training window. However, we find that using multi-square windows do not always get the optimal result especially in the fine edge and texture regions. Therefore, we propose in this paper an Adaptive Directional Window Selection to overcome the exiting problem in the Edge-Directed Interpolation (EDI). II. PERVIOUS WORK In this section, let us review the basic principle of NEDI [12] and it’s window selection method. A. Basic Principle of NEDI Consider the interpolation of an image X with size H×W to a high-resolution image Y with size 2H×2W. The white dots in Fig.1 denote the original low-resolution pixels X i,j =Y 2i,2j and the gray dots denote the unknown pixel Y 2i+1,2j+1 which is to be estimated by the NEDI step one. The NEDI step one makes use of a fourth-order linear prediction to interpolate the unknown pixels Y 2i+1,2j+1 from the four neighboring pixels {Y 2i,2j , Y 2i+2,2j , Y 2i,2j+2 , Y 2i+2,2j+2 } as shown below: ∑∑ = = + + + + + = 1 0 1 0 ) ( 2 ), ( 2 2 1 2 , 1 2 k l l j k i l k j i Y Y α (1) According to Wiener filtering theory, the optimal Minimum Means Square Error (MMSE) prediction coefficients set α can be obtained as [12] y yy r R α 1 - = (2) where α = [α 0 , …. α 3 ], the auto-covariance R yy is a square matrix containing sixteen R kl with k, l = [0,…3] for the position in the sample points set, and the cross-covariance of r y contains four r l for l=[0,…3]. For example, r 0 is defined by E[Y 2i,2j Y 2i+1,2j+1 ] and R 02 is defined by E[Y 2i,2j Y 2i,2j+2 ] as shown in Fig. 1. The high-resolution cross-covariance r y is not available, because of the center pixel Y 2i+1,2j+1 is to be predicted. This difficulty can be overcome by the fact that the statistics of the pixels with respect to the low-resolution block and that of the high-resolution block are most likely to be similar. As a result, the auto-covariance and cross-covariance coefficients among the high-resolution block will be mostly alike that of the low- resolution block. Therefore, the low-resolution covariance R` yy and r` y will be used instead, for the calculation. 978-1-4244-7115-7/10/$26.00 ©2010 IEEE