Some improvements for image filtering using peer group techniques Joan-Gerard Camarena a , Valentín Gregori a , Samuel Morillas b, * , Almanzor Sapena a a Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino Vera, s/n 46022 Valencia, Spain b Centro de Investigación en Tecnologías Gráficas, Universidad Politécnica de Valencia, Camino Vera, s/n 46022 Valencia, Spain article info Article history: Received 8 January 2008 Received in revised form 3 March 2009 Accepted 11 July 2009 Keywords: Adaptive filter Color image denoising Peer group filter Switching filter Vector filter abstract An image pixel peer group is defined as the set of its neighbor pixels which are similar to it according to an appropriate distance or similarity measure. This concept has been successfully used to devise algorithms for detection and suppression of impulsive noise in gray-scale and color images. In this paper, we present a novel peer group-based approach intended to improve the trade-off between computational efficiency and filtering quality of previous peer group-based methods. We improve the computational efficiency by using a modification of a recent approach that can only be applied when the distance or similarity mea- sure used fulfills the so-called triangular inequality property. The improvement of the filtering quality is achieved by the inclusion of a refinement stage in the noise detection. The proposed method performs according to the following steps: First, we partition the image into disjoint blocks and we perform a fast classification of the pixels into three types: non-corrupted, non-diagnosed and corrupted; second, we refine the initial findings by analyzing the non-diagnosed pixels and finally every pixel is classified either as cor- rupted or non-corrupted. Then, only corrupted pixels are replaced so that uncorrupted image data is pre- served. Experimental results suggest that the proposed method is able to outperform state-of-the-art methods both in filtering quality and computational efficiency. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction Vector median-based filters [1–5] are widely used methods for impulsive noise reduction in color and multichannel images be- cause of two main reasons: (i) they are able to perform a robust fil- tering since they are based on the theory of robust statistics and (ii) the existing correlation among the image channels is necessarily taken into account because the images are treated as vector fields. However, since in these classical methods the filtering operation is applied on every image pixel regardless whether it is noisy or not they tend to blur image edges and details and so to degrade the im- age quality. Also, because of its nonlinear nature, these methods are quite computationally demanding. In order to overcome these drawbacks, a series of nonlinear filters have been proposed. These filters can be classified into the following categories: switching fil- ters [6–26], filters using weighting coefficients [35–41], fuzzy fil- ters [42–49], neuro-fuzzy filters [50–52], and partition-based filters [53–55]. The filtering method proposed in this paper belongs to the fam- ily of switching filters [6–26]. These filters follow a detect and re- place approach so that the filtering operation is only applied to the pixels detected as noisy and, consequently, the noise-free image structures are preserved. Indeed, when the images are corrupted by impulsive noise, the switching approaches can be successfully applied because of their sufficient performance and low computa- tional complexity. The filters within this family differ mainly in their impulse noise detection technique and, in some cases, also in the restoration operation applied to the noisy pixels: The meth- od in [6] use boundaries to distinguish between noise-free and noisy data. In [7], a multi-normal distribution of the color vectors is assumed and the confidence limit of the color vector under pro- cessing is checked. Quaternion rotation theory is used in [8]. The work in [9] use a fuzzy inference system which takes as inputs some statistical measures of the pixel under processing and its neighborhood. The method in [10] checks the difference between the input vector and the mean of several lowest ranked vectors. The method in [11] performs the detection by using the input vec- tor, the vector median, the vector mean and their aggregated dis- tances to other vectors inside the filter window. The work in [12] extends the former work in [11] by utilizing the variance approxi- mation in the multivariate case. The filter in [13] evaluates the rank of the processed pixel in different orderings and the tech- niques in [14,15] use robust estimators. The solution presented in [16] uses center weighting coefficients and the methods in [17–22] use a similarity based vector ordering to increase the importance of the pixel under consideration in the impulse detec- tion process. The methods in [23,24] use the observed differences between the pixel and its neighbors aligned in four main directions and the usage of the observed differences for the pixel with respect 0262-8856/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.imavis.2009.07.005 * Corresponding author. Tel.: +34 963879518. E-mail address: smorillas@mat.upv.es (S. Morillas). Image and Vision Computing 28 (2010) 188–201 Contents lists available at ScienceDirect Image and Vision Computing journal homepage: www.elsevier.com/locate/imavis