Image Segmentation Using a Trimmed Likelihood Estimator in the Asymmetric Mixture Model Based on Generalized Gamma and Gaussian Distributions

Abstract

Finite mixture model (FMM) is being increasingly used for unsupervised image segmentation. In this paper, a new finite mixture model based on a combination of generalized Gamma and Gaussian distributions using a trimmed likelihood estimator (GGMM-TLE) is proposed. GGMM-TLE combines the effectiveness of Gaussian distribution with the asymmetric capability of generalized Gamma distribution to provide superior flexibility for describing different shapes of observation data. Another advantage is that we consider the spatial information among neighbouring pixels by introducing Markov random field (MRF); thus, the proposed mixture model remains sufficiently robust with respect to different types and levels of noise. Moreover, this paper presents a new component-based confidence level ordering trimmed likelihood estimator, with a simple form, allowing GGMM-TLE to estimate the parameters after discarding the outliers. Thus, the proposed algorithm can effectively eliminate the disturbance of outliers. Furthermore, the paper proves the identifiability of the proposed mixture model in theory to guarantee that the parameter estimation procedures are well defined. Finally, an expectation maximization (EM) algorithm is included to estimate the parameters of GGMM-TLE by maximizing the log-likelihood function. Experiments on multiple public datasets demonstrate that GGMM-TLE achieves a superior performance compared with several existing methods in image segmentation tasks.

Segmentation of Brain MR Images by Using Fully Convolutional Network and Gaussian Mixture Model with Spatial Constraints

“…For experimentation purposes, all MR images from the IBSR 18 dataset are preprocessed by removing blank images and extracting the main brain parts from the skull. [31]), (g) CBCLO (see [32]), and (h) ground truth. Thus, there are 1000 images of size 255 × 255 that are selected from ten random subjects for training, and 300 images are adopted from other three subjects for testing.…”

“…In addition, we observe, regardless of which slices are used, that the proposed model can obtain rich details. In the next experiment, the performance of GMMD-U is compared to that of FCM, GMM, K-means, SMM-SC (see [31]), CBCLO (see [32]), and classical U-net by using the brain MRI (slice 70 of one patient) in ISBR 18, and the results are provided in Figure 12. The classical U-net algorithm used here is divided into three parts for dealing with the segmentation task, which contains CSF, GM, and WM.…”

“…The experiment determines the performance of five algorithms on the testing set. Figure 13 shows the Dice coefficient of the segmentation performance of FCM, K-means, GMM, SMM-SC (see [31]), CBCLO (see [32]), classical U-net, and GMMD-U on the brain MRI of one patient (ISBR 18). It is clear from this figure that GMMD-U shows the highest Dice coefficient values among all algorithms and the smallest fluctuation range in each part of tissues.…”

An Improved Multithreshold Segmentation Algorithm Based on Graph Cuts Applicable for Irregular Image

“…where (•) is the gray value of pixel points, (•) is the spatial position of pixel points, ‖ • ‖ 2 2 is the two norm, and are positive scale factors, and is positive integer, representing the range of pixel points involved in calculating the weight. The weight function is visualized for several values of ∈ [1,5] in Figure 3.…”

“…Image threshold segmentation refers to dividing an image into two parts: background and foreground under a certain gray value, and target object can be easily recognized by distinguishing between foreground and background [1,2]. At present, target recognition based on image segmentation is widely used in medical care, military, geology, agriculture, and many other fields [3][4][5][6].…”