A Fuzzy C-Means Based Spatial Pixel and Membership Relationships for Image Segmentation
Fuzzy C-Means (FCM) is a well-known method for image segmentation. However, since the pixels themselves are considered independent of each other, the segmentation result is sensitive to noise. Fuzzy clustering with spatial constraints provides a powerful way to account for the spatial dependencies between the neighboring pixels, in order to reduce the sensitivity of the segmentation result to noise. In this paper, we propose a new FCM algorithm that incorporates the spatial relationship between neighboring pixels. Different from above methods that depend on parameters $\alpha$, $\lambda_s$, $\lambda_g$, or $\beta$ to keep a balance between sensitivity with respect to noise and the preservation of salient details, the proposed method does not require any such parameters. Moreover, we introduce a new way to incorporate both the spatial pixel relationship and the spatial membership relationship into the algorithm. To estimate parameters that are to minimize the objective function, we propose a method based on the Lagrange technique. The proposed method is tested on synthetic and real world images and the performance is compared with other methods based on FCM models, demonstrating its robustness with respect to noise and accuracy of image segmentation.