Modified Numerical Scheme for Perona-Malik Model in Image Restoration
This paper proposes a difference scheme based on nonlinear diffusion Perona-Malik model for numerical calculation in image restoration. Our scheme can adapt to determine the tangent directions to the isophote lines based on two mutually orthogonal directi
- PDF / 2,341,926 Bytes
- 10 Pages / 439.37 x 666.142 pts Page_size
- 51 Downloads / 234 Views
Abstract. This paper proposes a difference scheme based on nonlinear diffusion Perona-Malik model for numerical calculation in image restoration. Our scheme can adapt to determine the tangent directions to the isophote lines based on two mutually orthogonal directional derivatives, which results that diffusion is along the edges as much as possible. One of typical edge stopping functions for Perona-Malik model is modified in order to improve robust calculation and satisfy the compatibility, stability and convergence for our numerical scheme. Computer experimental results indicate that the algorithm corresponding to our numerical scheme is very efficient for noise removal in regardless whether the noise is serious or not. Keywords: Image restoration · Difference scheme tion · Perona-Malik model · Nonlinear diffusion
1
· Numerical calcula-
Introduction
Historically, image restoration is not only one of the oldest concerns but also one of the most important and fundamental tasks [1]. Removing the noise while preserving image edges is difficult but much desired. Nowadays, for this aim there emerge three main directions: stochastic modeling, wavelets and partial differential equation (PDE) approaches [2][3]. For PDE-based methods, Perona-Malik (P-M) model (ref. [4]) is considered to be the most classic equation so that it has attracted much attention in recent decades; see [5], [6] and [7], etc. However, P-M model is pathological [5][8]. In other words, robust calculation of diffusion coefficient is a severe challenge for the model when the noise of the initial image is sharp oscillation. A classical method to overcome this disadvantage is the smooth version of P-M model proposed by Catt´e et al. in [5]. As two-dimensional Gaussian kernel Gσ is introduced into edge stopping function, their model can smooth the flat and edge regions adaptively. However, it’s difficult to choose proper scale parameter σ. In order to further improve the cases depending seriously on the gradient values of an image, Guo et al. proposed an adaptive P-M model by variable exponent term 2 |∇u|α(|∇Gσ ∗u| ) (Edge indicator function must satisfy 0 ≤ α(·) ≤ 2.) replacing c Springer-Verlag Berlin Heidelberg 2015 H. Zha et al. (Eds.): CCCV 2015, Part I, CCIS 546, pp. 366–375, 2015. DOI: 10.1007/978-3-662-48558-3 37
Modified Numerical Scheme for Perona-Malik Model in Image Restoration
367
|∇u|2 for edge stopping function in [7]. When the model is applied to image processing, experimental results show that it can achieve higher quality images for peak signal to noise ratio (PSNR) and image edge has been preserved better. A similar model was mentioned by Maiseli et al. [9] with different edge indicator function from [7]. This paper improves robust calculation of P-M model by modifying one of typical edge stopping functions. Meanwhile, we present a new numerical scheme for P-M model. P-M model is recalled in Sect. 2.1 and our scheme is deduced from the aspect of numerical analysis in Sect. 2.2. According to the product of two mutually orthogonal directional derivati
Data Loading...
