Abstract—In this work, we improve a previously developed segmentation scheme aimed at extracting edge information from speckled images using a maximum likelihood edge detector. The scheme was based on finding a threshold for the probability density function of a new kernel defined as the arithmetic mean-to-geometric mean ratio field over a circular neighborhood set and, in a general context, is founded on a likelihood random field model (LRFM). The segmentation algorithm was applied to discriminated speckle areas obtained using simple elliptic discriminant functions based on measures of the signal-to-noise ratio with fractional order moments. A rigorous stochastic analysis was used to derive an exact expression for the cumulative density function of the probability density function of the random field. Based on this, an accurate probability of error was derived and the performance of the scheme was analysed. The improved segmentation scheme performed well for both simulated and real images and showed superior results to those previously obtained using the original LRFM scheme and standard edge detection methods. In particular, the false alarm probability was markedly lower than that of the original LRFM method with oversegmentation artifacts virtually eliminated. The importance of this work lies in the development of a stochastic-based segmentation, allowing an accurate quantification of the probability of false detection. Non visual quantification and misclassification in medical ultrasound speckled images is relatively new and is of interest to clinicians. Keywords—Discriminant function, false alarm, segmentation, signal-to-noise ratio, skewness, speckle. I. INTRODUCTION PECKLE noise is present in coherent imaging systems and is a form of object- or target-induced random noise. In the literature, segmentation algorithms applied to speckled images have not fully exploited the statistical nature of the underlying speckle formation process. Notable exceptions are [1 - 4]. A commonly used method employs the Laplacian of Gaussian edge detector. In this paper, we employ a novel statistical segmentation scheme for speckled images. This scheme is an improvement Manuscript submitted July 31, 2007. J. Daba is with the Electrical Engineering Department, University of Balamand, El Koura, Lebanon (e-mail: j.daba@balamand.edu.lb). J. Dubois is with the Electrical Engineering Department, University of Balamand, El Koura, Lebanon (e-mail: jeanpierre_dubois@hotmail.com). over a previously devised algorithm termed LRFM [5] by initially separating speckle areas from non speckle areas using simple elliptic discriminant functions. The segmentation algorithm is run on the discriminated speckle regions using an arithmetic mean-to-geometric mean ratio kernel applied to a circular window with a small radius. In the context of our work, segmentation can be considered as the first step of image analysis which aims at either a description of the image or a classification of the image content. II. SPECKLE MODEL The segmentation scheme is based on the physical and statistical model of coherent image formation, where the image intensities are exponentially distributed [6]: ( ) 1 exp , 0 I y p y y μ μ ⎛ ⎞ = − ≥ ⎜ ⎟ ⎝ ⎠ , (1) where μ is the mean intensity of a pixel. This is known as a single look speckle model. For the case of multilook model, the intensity of a single pixel is the non-coherent sum of L statistically independent looks of that pixel: 1 L L k k I i = = ∑ . (2) L I obeys a gamma distribution [6]: ( ) 1 1 , 0 ( -1)! L y L I L p y y e y L μ μ − − = ≥ . (3) The signal-to-noise ratio is increased by a factor of L , however the resolution is decreased by the same amount [1-4]. In this paper, we consider binary images composed of pixels with reflectivity levels of either 0 μ or 1 μ , and having a contrast ratio 1 μ = r / 1 0 > μ . Binary images in the context of this paper are reasonable since it has been shown in [7] that the mutual information extracted between the reflectivity and Improved Segmentation of Speckled Images Using an Arithmetic-to-Geometric Mean Ratio Kernel J. Daba, and J. Dubois S World Academy of Science, Engineering and Technology International Journal of Electrical and Computer Engineering Vol:1, No:10, 2007 1474 International Scholarly and Scientific Research & Innovation 1(10) 2007 scholar.waset.org/1307-6892/396 International Science Index, Electrical and Computer Engineering Vol:1, No:10, 2007 waset.org/Publication/396