978-1-4244-5997-1/10/$26.00 c ⃝2010 IEEE Multi-resolution Blur Effect Characterization: Comparative Study Amina Serir U.S.T.H.B, Facult´ e d’Electronique et Informatique, LTIR Algiers, Algeria 16111 Email: aserir@usthb.dz Azeddine Beghdadi Institut Galil´ ee, L2TI, Paris Cit´ e France, 93421 Email: azeddine.beghdadi@univ-paris13.fr Abstract—This paper investigates the best way to analyze blur effect in images. Many studies prove that using multi-resolution analysis improves the analysis efficiency by using edges per- sistence throughout multi-resolution representation. This paper turns on the best way to perform this multi-resolution analysis. Herein two multiresolution representations are considered: the linear Discrete Wavelet Transform DWT and the the non linear Multiplicative Multiresolution Decomposition MMD. Features are extracted in the both normalized transforms and are used to classify images into three classes (no blurred, blurred and very blurred images). These both approaches have been tested on LIVE Gblur Database. Results show clearly that blur effect is efficiently characterized by MMD’s features. I. I NTRODUCTION The blur is considered as one of the most studied distor- tion affecting image quality. It manifests itself as a loss of sharpness around edges and a decrease of visibility of fine details. To detect the blur in images, one could adopt one of two main approaches: modeling the blur effect or analyzing its annoying effect to Human Visual System HVS [4], [8]. The most popular techniques to characterize blur effect are either transform-based approaches or based on edge analysis. The ex- tensively used transform-based methods for blur identification are usually performed in some frequency domain: local DCT coefficients [6] and image wavelet coefficients [1], [3]. These approaches are motivated by the fact that blur is intrinsically due to the attenuation of spatial high frequencies, which commonly occurs during image filtering or data compression. It has been proven in many studies that multi-resolution representation offers an efficient tool for image analysis. Moreover, many of the proposed image quality measure are based on multiresolution analysis [7], [8]. Recently, in [7], the authors introduced a no linear multi- resolution decomposition to analyze and assess the blurriness effect in relation with image intrinsic information modeling by using a multiplicative multi-resolution analysis. This paper turns on seek the best way to assess blurriness effect in multi-resolution representation and try to response to the question ”What is the best way to represent blurriness us- ing either an additive model brought by DWT or multiplicative model by means of MMD. The rest of the paper is organized as follows : blurred transitions are modeled through polyphase components in section 2. Then section 3, introduces the normalized multi- resolution analysis by means of DWT and MMD, describes the extracted features to represent blurriness effect and the used classifier into three classes related to blur intensity. Section 4 presents the experimental results acquired of features efficiency related to blur assessment by using LIVE database (Gblur). Finally, the last section is devoted to conclude this work and gives some perspectives. II. BLUR ANALYSIS Herein, the blur effect model introduced in [7] is considered. This is done in the aim to apply this model to multi-resolution analysis by wavelet transform and by MMD. In [7], the authors have considered that in the space domain the blur manifests itself as a reduction of sharpness around edges and fine details and one way for estimating the blur effect in the spatial domain is then express the observed image using a deterministic model. One of the most used models is to consider the observed blurred image as the result of convolving the original unaltered version with the Impulse Response of a low pass filter [5]. The blur amount is then estimated through the filter parameters [2]. In [7], as an alternative to Gaussian filter, the authors use the binomial filter define through the finite impulse response (FIR), h(l)= 1 2 L ∑ L m=0 C m L δ(l +( L 2 - m)), where C m L = L! (L-m)!m! . Then, to analyze the blur effect in an image, they consider a transition between the positions 2n and 2n +1 of a line of the image I , then I (k, 2n - m)= v 1 and I (k, 2n +1+ m)= v 2 with m =0, 1,..., 2n. To analyze the blurring and sharpening independently from signal amplitude, the relative difference d(k,n) and the ratio r(k,n) are considered and are defined as follows: r(k,n)= I (k, 2n + 1) I (k, 2n) , d(k,l)=1 - r(k,n) (1) Thus the blurred transition could be characterized by: r L (k,n)= (A L + C L 2 L )r(k,n)+ A L A L r(k,n)+(A L + C L 2 L ) (2) and d L (k,n)=1 - r L (k,n); (3)