Both parametric deformable models and geometrical deformable models (level sets) are powerful methods and have been used widely for the segmentation problems; however, they both tend to fail in the case of noise, poor image resolution, diffused boundaries or occluded shapes, and they dont take advantage of the a priori models. Yet, especially in the area of medical imaging, organs have well constrained forms within a family of shapes. Thus, additional constraints based on the shape of the objects are greatly needed besides the gray level information of these objects.
Our group has developed shape based segmentation approaches that works in high noise images. We have tested our algorithm on low-resolution abdomen images to segment the kidneys, and in brain MRI’s to segment the brain ventricles. The 2D results for the kidney segmentation have been validated by a radiologist and the 3D results of the ventricle segmentation have been validated with a geometrical phantom.
Research Team Aly A. Farag CVIP Director farag@cvip.louisville.edu Ayman El-Baz Research Assistant elbaz@cvip.louisville.edu Hongjian Shi Research Assistant hshi@cvip.louisville.edu Hossam Hassan Research Assistant hossam@cvip.louisville.edu Seniha Esen Yuksel Research Assistant esen@cvip.louisville.edu 
Methods
A novel shape based segmentation approach is proposed by modifying the external energy component of a deformable model. The proposed external energy component depends not only on the gray level of the images but also on the shape information which is obtained from the signed distance maps of objects in a given data set. The gray level distribution and the signed distance map of the points inside and outside the object of interest are accurately estimated using a novel statistical approach. This statistical approach is based on modelling the empirical density function (normalized histogram of occurrence) with a linear combination of discrete Gaussians (LCDG) with positive and negative components. The components of this linear combination are approximated with our novel modified Expectation-Maximization (EM) algorithm. Experimental results on the segmentation of the kidneys from low-contrast DCE-MRI (Fig 1.) and the segmentation of the ventricles from brain MRIs (Fig 2.) show how the approach is accurate in segmenting 2-D and 3-D data sets.
For ventricle segmentation from MRI, twenty data sets are not enough to get an accurate shape for the ventricles because the ventricles vibrate during the MRI or CT scans. Therefore, to cover all the shape variations of the brain ventricles for each subject, we performed linear elastic finite element analysis on the motion of the real brain ventricles. After finite element analysis, the 3D structure is re-sliced and 10 states of the ventricles are obtained resulting in 20 subjects * 10 states = 200 datasets. The four states of one subjects ventricles are shown in Fig. 2. Using the resulting 200 data sets for the ventricles, we followed our density estimation approach to estimate the density of the gray level distribution and the signed distance map inside and outside the ventricles.
For the accurate evaluation of our proposed approach, we used a mould ventricle phantom that resembles the geometrical structure of the real ventricles, scanned it with cone-beam CT, and used the scans for finite element simulation. Following the same procedure of the ventricle motion estimation, we captured all the variations of the motion of the phantom ventricles. Figure 3 shows the four states of this ventricle phantom. This shape change of the ventricles for the subject and the ventricle phantom are recorded in short videos that are given below.
Results
Fig 1. Segmentation results (shown in red to the right) w.r.t. the radiologists segmentation (to the left).
Fig 2. The four states of the real ventricles at t=0, 0.7s, 0.9s, 1.1s (final) from left to right.
Fig 3. The four states of the phantom ventricles at t=0, 0.4s, 0.7s, 1s (final) from left to right and top to bottom
Movies
Movie 1: The movement of the brain ventricles using finite element analysis Movie 2: The evaluation of our segmentation approach using a brain phantom
Acknowledgement / Sponsors
We would like to thank the University of Louisville for its sponsorship.
CVIP Lab 