Computerized Medical Imaging and Graphics 36 (2012) 501–513 Contents lists available at SciVerse ScienceDirect Computerized Medical Imaging and Graphics jo ur n al homep age : www.elsevier.com/locate/compmedimag Blind retrospective shading correction using a multi-objective minimization criterion M. Vlachos ∗ , E. Dermatas Department of Electrical Engineering & Computer Technology, University of Patras, Patras, Greece a r t i c l e i n f o Article history: Received 31 January 2011 Received in revised form 16 February 2012 Accepted 9 April 2012 Keywords: Blind retrospective shading correction Fully automatic Criterion minimization Linear image formation model Multiplicative and additive shading components Shading-free image a b s t r a c t In this paper, a fully automatic blind retrospective shading correction method based mainly on a min- imization of a multi-objective criterion is presented. The proposed method assumes that the acquired image has distorted from a multiplicative and an additive shading component and thus can be adequately described by the linear image formation model. The estimation of the shading-free image is based on parametric estimation of the multiplicative and the additive shading component and the consequent application of the inverse image formation model. First of all, an initial estimation of the shading-free image is performed by the minimization of the multi-objective function of an appropriate image criterion. Secondly, the multiplicative and the additive shading components are estimated, based on assumptions about their frequency content and then, they median filtered. Finally, an estimation of a shading-free image is obtained using the above estimations for the components and the application of the inverse image formation model. Qualitative and quantitative experiments were conducted in a variety of image modalities including artificial and real images of finger, retinal images, transmission electron microscopy (TEM) images, arm, palm and hand vein images and thorax X-ray images. In all cases of distorted images, the proposed method had successfully removed the majority of the shading effects and had not distorted the shading- free images satisfying the main goal of retrospective shading correction. The signal to noise ratio (SNR) or equivalently the reciprocal of the coefficient of variations is used as a quantitative measure of the reduction/increase of intensity variations within the objects of the same class after shading correction. In our experiments, for the purpose of evaluation the signal to noise ratio is calculated for two different classes (object and background). © 2012 Elsevier Ltd. All rights reserved. 1. Introduction The correction of shading and non-uniform illumination is an important preprocessing task which employed in a great number of image processing applications such as segmentation, registration or quantitative analysis. Although, a careful and accurate set up of the image acquisition system may degrade the importance of a brightness normalization algorithm, shading which appears due to the interaction of objects with illumination on the scene requires retrospective shading correction. The image formation process and the corresponding shading effects are described by a linear image formation model, which consists of a multiplicative and an additive shading component. The problem of shading and of presence of intensity inhomo- geneities is common in many image modalities. Although, this ∗ Corresponding author. Tel.: +30 2610996189. E-mail addresses: mvlachos@george.wcl2.ee.upatras.gr (M. Vlachos), dermatas@george.wcl2.ee.upatras.gr (E. Dermatas). problem has minor impact on visual image interpretation due to the fact that human perception has the ability to deduce the real image content from a distorted image its impact in automatic image processing or analysis cannot be deteriorated. Thus, the correction of shading and the compensation of non-uniform illumination is an important preprocessing step in many image processing tasks. In general, shading can be either object-independent or object- dependent. In the first case, an imperfect set up of the image acquisition system introduces shading and may be corrected by calibration methods, while in the latter shading produced from the interaction between the objects and illumination in the scene and can be corrected only retrospectively by using information from the acquired images. In case of infrared images shading is object-dependent and thus removing the non-uniform illumination effects can be achieved retrospectively. A retrospective shading correction method must correct the shading only when it is present and do not distort the shading-free images. The formation of an image Y is an interaction between objects and illumination in the scene. The relation between the acquired 0895-6111/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compmedimag.2012.04.002