A Fast and Fully Automatic Method for Cerebrovascular Segmentation on Time-of-Flight (TOF) MRA Image

Abstract

The precise three-dimensional (3-D) segmentation of cerebral vessels from magnetic resonance angiography (MRA) images is essential for the detection of cerebrovascular diseases (e.g., occlusion, aneurysm). The complex 3-D structure of cerebral vessels and the low contrast of thin vessels in MRA images make precise segmentation difficult. We present a fast, fully automatic segmentation algorithm based on statistical model analysis and improved curve evolution for extracting the 3-D cerebral vessels from a time-of-flight (TOF) MRA dataset. Cerebral vessels and other tissue (brain tissue, CSF, and bone) in TOF MRA dataset are modeled by Gaussian distribution and combination of Rayleigh with several Gaussian distributions separately. The region distribution combined with gradient information is used in edge-strength of curve evolution as one novel mode. This edge-strength function is able to determine the boundary of thin vessels with low contrast around brain tissue accurately and robustly. Moreover, a fast level set method is developed to implement the curve evolution to assure high efficiency of the cerebrovascular segmentation. Quantitative comparisons with 10 sets of manual segmentation results showed that the average volume sensitivity, the average branch sensitivity, and average mean absolute distance error are 93.6%, 95.98%, and 0.333 mm, respectively. By applying the algorithm to 200 clinical datasets from three hospitals, it is demonstrated that the proposed algorithm can provide good quality segmentation capable of extracting a vessel with a one-voxel diameter in less than 2 min. Its accuracy and speed make this novel algorithm more suitable for a clinical computer-aided diagnosis system.

Appendix

Reasonable initialization of parameters will guarantee iterations of EM to consistently converge to a local minimum that proves empirically value. An automatic method for parameter initialization was developed. This initialization is based on the character of a normalized intensity histogram. The important procedure of the initialization is to estimate the parameters of the probability distributions corresponding to two distinct peaks with a long tail over a high-intensity region.

Let h(I) be the normalized intensity frequency corresponding to intensity I. The superscript 0 of the parameters presents initial value.

• (1) Peak1—Rayleigh distribution

$$ \sigma_0^0 = {I_{{\rm{peak}}1}},p_0^0 = \frac{{h\left( {\sigma_0^0} \right)}}{{{p_R}\left( {\sigma_0^0|\sigma_0^0} \right)}} $$

σ ₀ is parameter of Rayleigh distribution. P ₀ is the prior probability of Rayleigh distribution.

• (2) Peak2—Gaussian distribution

$\mu_{n - 1}^0 = {I_{{\rm{peak}}2}}$, $\sigma_{n - 1}^0$ is calculated using the maximum likelihood estimation (MLE) for Gaussian distribution in the region $\left[ {{I_{{\rm{peak}}2}} - 20,{I_{{\rm{peak}}2}} + 20} \right]\,{\hbox{of}}\,h(I),p_{n - 1}^0 = \frac{{h\left( {\sigma_{n - 1}^0} \right)}}{{{p_G}\left( {\sigma_{n - 1}^0|\left( {\sigma_{n - 1}^0,p_{n - 1}^0} \right)} \right)}}.$

μ _n−1 and σ _n−1 are parameters of the Gaussian distribution. P _n−1 is the prior probability of the Gaussian distribution.

• (3) Long tail—Gaussian distribution

Find intensity I _vessel that satisfies $\frac{{\sum\limits_{l = {I_{\rm{vessel}}}}^{{I_{\max }}} {h\left( {{I_l}} \right)} }}{{\sum\limits_{l = 1}^{{I_{\max }}} {h\left( {{I_l}} \right)} }} = 0.03$. That is, we rudely estimate the threshold of vessels from the last 3% of the high-intensity data of the observed histogram.

$\mu_n^0 = \frac{{{I_{\max }} - {I_{\rm{vessel}}}}}{2}$. $\sigma_n^0$ is calculated using the MLE 31 method for Gaussian distribution based on parameters $\mu_{13}^0$, I _vessel and I _max. $p_n^0 = 0.03$.

μ _n1 and σ _n are parameters of the Gaussian distribution relative to cerebral vessel. P _n is the prior probability of the Gaussian distribution.

The other Gaussian distributions equidistantly locate in the region $\left[ {{I_{{\rm{peak}}1}} + 12,{I_{{\rm{peak}}2}} - 12} \right].$