پردازش تصویر دیجیتال با روشهای درون یابی
Abstract
MSC
۱٫ Introduction
۲٫ The sampling Kantorovich algorithm for digital image processing
۳٫ The peak signal-to-noise ratio (PSNR)
۴٫ Some interpolation and quasi-interpolation methods for digital image processing
۵٫ Numerical examples
۶٫ Final remarks and conclusions
Acknowledgments
References
Abstract
In this paper we study the performance of the sampling Kantorovich (S–K) algorithm for image processing with other well-known interpolation and quasi-interpolation methods. The S-K algorithm has been implemented with three different families of kernels: central B-splines, Jackson type and Bochner–Riesz. The above method is compared, in term of PSNR (Peak Signal-to-Noise Ratio) and CPU time, with the bilinear and bicubic interpolation, the quasi FIR (Finite Impulse Response) and quasi IIR (Infinite Impulse Response) approximation. Experimental results show better performance of S-K algorithm than the considered other ones.
Introduction
The rescaling of an image is a widely studied problem in Digital Image Processing (D.I.P.). Typical methods developed to perform the above task are based on mathematical interpolation, see, e.g., [10,36]. For instance, bilinear and bicubic interpolation are among the most used interpolation methods for image rescaling, see e.g., [9,32]. The above methods are quite easy to implement and need of a small CPU time. On the other side, they provide not optimal results in terms of quality of the reconstruction, measured by the so-called PSNR (Peak Signal to Noise Ratio). To overcome this limit, recently quasi-interpolation methods have been successfully used. From the theoretical point of view, the better performance of the latter approximation methods than the interpolation ones, has been proved providing estimates concerning the order of approximation, see e.g., [7]. For instance, quasi Finite Impulse Response (quasi FIR) and Infinite Impulse Response (quasi IIR) have been reviewed to face the rescaling problem. Numerical results confirm the theoretical ones, e.g., in case of non trivial multiple image rotation (see [13] again). Concerning the quasi-interpolation methods for D.I.P., the so-called sampling Kantorovich (S-K) algorithm has been recently introduced (see [19]). The S–K algorithm is based on the theory of the sampling Kantorovich series Sw, w > 0, which are approximation operators particularly suitable for digital image reconstruction, in view of their mathematical expression, see e.g., [17,19].