Initialization of an Active Contour Algorithm for Mri Using Bayesian Wavelet Shrinkage and Multiscale Products

Magnetic resonance imaging (MRI) is generally regarded as one of the most powerful diagnostic techniques. Nevertheless, the incorporated noise during image acquisition or transmission degrades human interpretation or computer-aided analysis of the image. Thus, it appears sensible to reduce noise before performing image analysis. However, this preprocessing step should be performed with care in a way that enhances the diagnostically relevant image content. MRI magnitude images are generally modeled by a Rician distribution and the corresponding Rician noise is locally signal-dependent [1]. However, several authors have shown that in the wavelet domain the noise tends to an approximate Gaussian distribution. Also, in a number of recent publications [2, 3], we have shown that symmetric alpha-stable (SαS) distributions, a family of heavy-tailed densities, are sufficiently flexible and rich to appropriately model wavelet coefficients of images in various applications. This claim stands true for MRI as well. Consequently, in the undecimated wavelet domain, we apply a previously developed Bayesian estimator [2] that exploits these statistics to mitigate noise within each subband of interest. The use of an optimal Bayesian shrinkage technique guarantees that the edge information is not lost in the denoising process. The next step of our algorithm consists in further emphasizing this information. To achieve this, we make use of wavelet product scales. The motivation for doing so is that high amplitude coefficients (corresponding to edges) and low amplitude coefficients (corresponding to homogenous areas) tend to appear at the same spatial positions in different scales respectively [4]. In our implementation, we use a redundant wavelet transform [5] to avoid aliasing artifacts and to keep the same number of wavelet coefficients along scales. We form two product functions in the x and y directions that incorporate two adjacent scales. The corresponding modulus image is further processed by appropriate thresholding in order to form a binary edge map. Finally, the positions of the detected edges are used in the pixel domain in order to designate the initial contour of the boundary of interest toward which the snake algorithm should converge. The details of the complete algorithm are outlined in the following.