2d-Ar Model
STRUCTURE PRESERVING IMAGE INTERPOLATION VIA ADAPTIVE 2D AUTOREGRESSIVE MODELING Xiangjun Zhang and Xiaolin Wu Department of Electrical & Computer Engineering, McMaster University Hamilton, ON, Canada L8S 4K1; zhangxj@grads.ece.mcmaster.ca/xwu@ece.mcmaster.ca
ABSTRACT The performance of image interpolation depends on an image model that can adapt to nonstationary statistics of natural images when estimating the missing pixels. However, the construction of such an adaptive model needs the knowledge of every pixels that are absent. We resolve this dilemma by a new piecewise 2D autoregressive technique that builds the model and estimates the missing pixels jointly. This task is formulated as a non-linear optimization problem. Although computationally demanding, the new non-linear approach produces superior results than current methods in both PSNR and subjective visual quality. Moreover, in quest for a practical solution, we break the non-linear optimization problem into two subproblems of linear least-squares estimation. This linear approach proves very effective in our experiments. Index Terms— Image interpolation, autoregressive process, optimization, soft decision. 1. INTRODUCTION With ever increasing computation power in image and video processing, more sophisticated adaptive image interpolation methods were proposed in recent years. To preserve directional information, Li and Orchard proposed a technique of estimating the covariance of high resolution image from the covariance of the low resolution image, and a Wiener-filtering like interpolation scheme based on the estimated covariance [1]. Muresan and Parks [2] cast the method of [1] into the light of adaptive optimal recovery, and proposed a general approach to image interpolation. The reproduction quality of any image interpolation algorithm primarily depends on its adaptability to varying pixel structures across an image, which is the central theme of this paper. In fact, modeling of non-stationarity of
ABSTRACT The performance of image interpolation depends on an image model that can adapt to nonstationary statistics of natural images when estimating the missing pixels. However, the construction of such an adaptive model needs the knowledge of every pixels that are absent. We resolve this dilemma by a new piecewise 2D autoregressive technique that builds the model and estimates the missing pixels jointly. This task is formulated as a non-linear optimization problem. Although computationally demanding, the new non-linear approach produces superior results than current methods in both PSNR and subjective visual quality. Moreover, in quest for a practical solution, we break the non-linear optimization problem into two subproblems of linear least-squares estimation. This linear approach proves very effective in our experiments. Index Terms— Image interpolation, autoregressive process, optimization, soft decision. 1. INTRODUCTION With ever increasing computation power in image and video processing, more sophisticated adaptive image interpolation methods were proposed in recent years. To preserve directional information, Li and Orchard proposed a technique of estimating the covariance of high resolution image from the covariance of the low resolution image, and a Wiener-filtering like interpolation scheme based on the estimated covariance [1]. Muresan and Parks [2] cast the method of [1] into the light of adaptive optimal recovery, and proposed a general approach to image interpolation. The reproduction quality of any image interpolation algorithm primarily depends on its adaptability to varying pixel structures across an image, which is the central theme of this paper. In fact, modeling of non-stationarity of
References: [1] X. Li and M. T. Orchard, “New edge-directed interpolation,” IEEE Trans. Image Processing, pp. 1521–1527, Oct. 2001. [2] D. D. Muresan and T. W. Parks, “Adaptively quadratic (aqua) image interpolation,” IEEE Trans. on Image Processing, vol. 13, pp. 690–698, May 2004. [3] X. Wu, K. U. Barthel, and W. Zhang, “Piecewise 2d autoregression for predictive image coding.” in IEEE ICIP’98, vol. 3, Oct. 1998, pp. 901–904. [4] B. Meyer and P. Tischer, “Tmw – a new method for lossless image compression,” in Proceed. of PCS’97, Oct. 1997. [5] I. Matsuda, H. Mori, J. Maeda, and S. Itoh, “Design and evaluation of minimum-rate predictors for lossless image coding,” Trans. IEICE (DII), vol. J85-D-II, pp. 448–456, Mar. 2002. [6] R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoustic, Speech and Signal Processing, vol. 29, pp. 1153–1160, 1981. [7] K. Jensen and D. Anastassiou, “Subpixel edge localization and the interpolation of still images,” IEEE Trans. Image Processing, vol. 4, pp. 285–295, Mar. 1995. (g) Proposed LLS method (h) Proposed LLS method (i) Proposed nonlinear method (j) Proposed nonlinear method Fig. 5. Parts of original and reconstructed Lena and Bike images. IV - 196