This paper presents a variational level set method for simultaneous segmentation and bias field estimation of medical images with intensity inhomogeneity. In our model, the statistics of image intensities belonging to each different tissue in local regions are characterized by Gaussian distributions with different means and variances. According to maximum a posteriori probability (MAP) and Bayes’ rule, we first derive a local objective function for image intensities in a neighborhood around each pixel. Then this local objective function is integrated with respect to the neighborhood center over the entire image domain to give a global criterion. In level set framework, this global criterion defines an energy in terms of the level set functions that represent a partition of the image domain and a bias field that accounts for the intensity inhomogeneity of the image. Therefore, image segmentation and bias field estimation are simultaneously achieved via a level set evolution process. Experimental results for synthetic and real images show desirable performances of our method. 1. Introduction Image segmentation is an important and necessary step in various image processing and computer vision applications. However, due to the imperfection of the image acquisition process, intensity inhomogeneity (or bias field) is often seen in many real-world images, especially in medical images [1]. For example, the intensity inhomogeneity in magnetic resonance (MR) images usually manifests itself as a smooth intensity variation across the image [2]. Thus the resultant intensities of the same tissue vary with the locations of the tissue within the image. This can cause serious misclassifications when intensity-based segmentation algorithms are used. Therefore, intensity inhomogeneity has been challenging difficulty in image segmentation. The level set method, originally used as numerical technique for tracking interfaces and shapes [3], has been increasingly applied to image segmentation in the past decades [4, 5]. Compared with the classical image segmentation methods such as edge detection, thresholding, and region growing, level set methods have three desirable advantages. First, they can achieve subpixel accuracy of object boundaries [6]. Second, they allow incorporation of various prior knowledge, for example, shape and intensity distribution, so as to get more robust segmentation [7, 8]. Third, they can provide smooth and closed contours as segmentation results, which are necessary and can be readily used for further applications such as shape analysis and
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