CEREBROVASCULAR SEGMENTATION FROM MRA IMAGES

Abstract

There is provided a method of processing a cerebrovascular medical image, the method comprising receiving magnetic resonance angiography (MRA) image associated with a cerebrovascular tissue comprising blood vessels and brain tissues other than blood vessels; segmenting MRA image using a prior appearance model for generating first prior appearance features representing a first-order prior appearance model and second appearance features representing a second-order prior appearance model of the cerebrovascular tissue, wherein current appearance model comprises a 3D Markov-Gibbs Random Field (MGRF) having a 2D rotational and translational symmetry such that MGRF model is 2D rotation and translation invariant; segmenting MRA image using current appearance model for generating current appearance features distinguishing blood vessels from other brain tissues; adjusting MRA image using first and second prior appearance features and current appearance futures; and generating an enhanced MRA image based on said adjustment. There is also provided a system for doing the same.

Claims

1. A method of processing a cerebrovascular medical image, the method comprising: receiving a magnetic resonance angiography (MRA) image associated with a cerebrovascular tissue comprising blood vessels and brain tissues other than blood vessels; segmenting the MRA image using a prior appearance model for generating first prior appearance features representing a first-order prior appearance model and second appearance features representing a second-order prior appearance model of the cerebrovascular tissue, wherein the current appearance model comprises a 3D Markov-Gibbs Random Field (MGRF) having a 2D rotational and translational symmetry such that the MGRF model is 2D rotation and translation invariant; segmenting the MRA image using a current appearance model for generating current appearance features distinguishing the blood vessels from the other brain tissues; adjusting the MRA image using the first and second prior appearance features and the current appearance futures; and generating an enhanced MRA image based on said adjustment.

2. The method of processing a cerebrovascular medical image according to claim 1, wherein said prior appearance model uses interaction parameters analytically estimated from a set of MRA training data.

3. The method of processing a cerebrovascular medical image according to claim 2, wherein the first prior appearance features representing a first-order prior appearance model and the second appearance features representing a second-order prior appearance model are respectively provided by energies of the training data according to the following equations: $E_0\left(z\right)=\underset{q=0}{\overset{Q-1}{.Math.}}.Math.F_{0,\mathrm{vasc}}\left(q,z\right)\left[F_{0,\mathrm{vasc}}\left(q;z\right)-\underset{\_}{1}\right]$ $E_v\left(z\right)=\underset{q=0}{\overset{Q-1}{.Math.}}.Math.\underset{q^{}=0}{\overset{Q-1}{.Math.}}.Math.F_{v,\mathrm{vasc}}\left(q,q^{};z\right)\left[F_{v,\mathrm{vasc}}\left(q,q^{};z\right)-\underset{\_}{1}\right]$ wherein: E.sub.0: variance of a co-occurrence distribution representing the first order prior appearance model; E.sub.: variance of a co-occurrence distribution representing the second order prior appearance model; F.sub.0,vasc: marginal empirical distributions of gray levels; F.sub.v,vasc: gray level co-occurrences.

4. The method of processing a cerebrovascular medical image according to claim 3, wherein said prior appearance model excludes alignment of the training data.

5. The method of processing a cerebrovascular medical image according to claim 4, wherein said current appearance model comprises a Linear combination of Discrete Gaussians (LCDG) model and an EM-based model for linear combination of Gaussian approximation.

6. The method of processing a cerebrovascular medical image according to claim 5, wherein said generating current appearance features comprises estimating first Gibbs probability densities of voxels to be blood vessels (P (q Vessels)) and estimating second Gibbs probability densities of voxels to be brain tissues other than blood vessels (P (q Brain)) according to the following equations respectively and making probabilistic decisions based on said first and second calculated Gibbs probability densities: $P\left(q|\mathrm{Brain}\right)=\frac{1}{}.Math.\underset{r=1}{\overset{2}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right)$ $P\left(\mathrm{qVessels}\right)=\frac{1}{1-}.Math.\underset{r=3}{\overset{C_p}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right)$ $\mathrm{Where}.Math..Math.=\frac{\mathrm{wp},1+\mathrm{wp},2}{\underset{r}{\overset{}{.Math.}}.Math.w_{p,r}}$ and wherein C.sub.p, C.sub.n, w.sub.p, w.sub.n, .sub.p, .sub.n denotes parameters of the LCDG.

7. The method of processing a cerebrovascular medical image according to claim 6, further comprising applying bias correction and skull stripping to the MRA image prior to the segmentations.

8. The method of processing a cerebrovascular medical image according to claim 7, wherein the adjusting of the MRA image comprises analysing the MRA image using a 3D connectivity analysis based on the first and second prior appearance features and the current appearance futures.

9. The method of processing a cerebrovascular medical image according to claim 8, wherein the adjusting the MRA image is conducted using a Random Forest model.

10. The method of processing a cerebrovascular medical image according to claim 1, wherein the blood vessels comprise small and large blood vessels.

11. The method of processing a cerebrovascular medical image according to claim 1, wherein said MRA image of a cerebrovascular tissue is related to a mammalian.

12. The method of processing a cerebrovascular medical image according to claim 11, wherein said mammalian is a human.

13. A system for processing a cerebrovascular medical image, the system comprising: a data input interface for receiving a magnetic resonance angiography (MRA) image associated with a cerebrovascular tissue comprising blood vessels and brain tissues other than blood vessels; at least one processor for processing the received MRA image, the MRA image processing comprising: segmenting the MRA image using a prior appearance model for generating first prior appearance features representing a first-order prior appearance model and second appearance features representing a second-order prior appearance model of the cerebrovascular tissue, wherein the current appearance model comprises a 3D Markov-Gibbs Random Field (MGRF) having a 2D rotational and translational symmetry such that the MGRF model is 2D rotation and translation invariant; segmenting the MRA image using a current appearance model for generating current appearance features distinguishing the blood vessels from the other brain tissues; adjusting the MRA image using the first and second prior appearance features and the current appearance futures; and generating an enhanced MRA image based on said adjustment.

14. The system for processing a cerebrovascular medical image according to claim 13, wherein said prior appearance model uses interaction parameters analytically estimated from a set of MRA training data.

15. The system for processing a cerebrovascular medical image according to claim 14, wherein the first prior appearance features representing a first-order prior appearance model and the second appearance features representing a second-order prior appearance model are respectively provided by energies of the training data according to the following equations: $E_0\left(z\right)=\underset{q=0}{\overset{Q-1}{.Math.}}.Math.F_{0,\mathrm{vasc}}\left(q,z\right)\left[F_{0,\mathrm{vasc}}\left(q;z\right)-\underset{\_}{1}\right]$ $E_v\left(z\right)=\underset{q=0}{\overset{Q-1}{.Math.}}.Math.\underset{q^{}=0}{\overset{Q-1}{.Math.}}.Math.F_{v,\mathrm{vasc}}\left(q,q^{};z\right)\left[F_{v,\mathrm{vasc}}\left(q,q^{};z\right)-\underset{\_}{1}\right]$ wherein: E.sub.0: variance of a co-occurrence distribution representing the first order prior appearance model; E.sub.: variance of a co-occurrence distribution representing the second order prior appearance model; F.sub.0,vasc: marginal empirical distributions of gray levels; F.sub.v,vasc: gray level co-occurrences.

16. The system for processing a cerebrovascular medical image according to claim 15, wherein said prior appearance model excludes alignment of the training data.

17. The system for processing a cerebrovascular medical image according to claim 16, wherein said current appearance model comprises a Linear combination of Discrete Gaussians (LCDG) model and an EM-based model for linear combination of Gaussian approximation.

18. The system for processing a cerebrovascular medical image according to claim 17, wherein said generating current appearance features comprises estimating first Gibbs probability densities of voxels to be blood vessels (P (q Vessels)) and estimating second Gibbs probability densities of voxels to be brain tissues other than blood vessels (P (q Brain)) according to the following equations respectively and making probabilistic decisions based on said first and second calculated Gibbs probability densities: $P\left(q|\mathrm{Brain}\right)=\frac{1}{}.Math.\underset{r=1}{\overset{2}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right)$ $P\left(\mathrm{qVessels}\right)=\frac{1}{1-}.Math.\underset{r=3}{\overset{C_p}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right).Math.\underset{l=1}{\overset{C_n}{.Math.}}.Math.-w_{n,l}.Math.\left(q|{}_{n,l}\right)$ $\mathrm{Where}.Math..Math.=\frac{\mathrm{wp},1+\mathrm{wp},2}{\underset{r}{\overset{}{.Math.}}.Math.w_{p,r}}$ and wherein C.sub.p, C.sub.n, w.sub.p, w.sub.n, .sub.p, .sub.n denotes the parameters of the LCDG.

19. The system for processing a cerebrovascular medical image according to claim 18, wherein the MRA image processing further comprising applying bias correction and skull stripping to the MRA image prior to the segmentations.

20. The system for processing a cerebrovascular medical image according to claim 19, wherein the adjusting of the MRA image comprises analysing the MRA image using a 3D connectivity analysis based on the first and second prior appearance features and the current appearance futures.

21. The system for processing a cerebrovascular medical image according to claim 20, wherein the adjusting the MRA image is conducted using a Random Forest model.

22. The system for processing a cerebrovascular medical image according to claim 1, further comprising a display for displaying the enhanced MRA image to a user.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The invention will now be described with reference to the accompanying drawings, which illustrate a preferred embodiment of the present invention without restricting the scope of the invention's concept, and in which:

[0038] FIG. 1. illustrates the proposed segmentation system;

[0039] FIG. 2. 2D and 3D illustration of the proposed rotational and translational invariance neighbourhood system;

[0040] FIG. 3. Illustration of the evaluation metrics (DS) and HD;

[0041] FIG. 4. Illustrates evaluation metrics (DS) and HD (Average Vessel Volume Difference (AVVD)); and

[0042] FIG. 5A. 5B. Illustration of the T1-weighted MRI axial views for (a) adult and (b) infant brains.

DETAILED DESCRIPTION

[0043] In accordance with the present invention, a method to extract both micro and macro brain blood vessels from MRA images is proposed. Segmentation of the cerebrovascular structure is crucial since it helps in the diagnoses process, surgery planning, research, and monitoring. Moreover, the benefits of the segmentation of the cerebrovascular structure lay in its ability to improve the simulation of the blood flow and the visualization of the vessels in which each developed method solves a problem faced previously or triggers a specific region of the brain. This present invention proposes a statistical approach, as demonstrated in FIG. 1, that utilizes a voxel-wise classification based on determining probability models of voxel intensities, in order to separate blood vessels from the background of each TOFMRA slice. This is done by approximating the marginal empirical distribution of intensity probabilities with LCDG with alternate signs and utilizing EM-based techniques for linear combination of Gaussian approximation that are adapted for dealing with LCDGs.

[0044] The present invention proposes a fully automated method the steps of bias correction and skull stripping, enhancement of vascular contrast and homogeneity, modelling vascular prior appearance using a pairwise, rotation and translation invariant, Markov-Gibbs random field (MGRF), the interaction parameters of which have been analytically estimated from a set of MRA training data, modelling the current appearance using our prior model and a Linear combination of Discrete Gaussians (LCDG) approach, initial classification of vascular tissue using Random Forest, final extraction of the brain vascular system based on 3D connectivity analysis.

[0045] The proposed framework performs well in the presence of inhomogeneities that may exist in MRA images. This is due to its encoding local spatial information using the MGRF model to identify vascular tissue irrespective of large-scale variation in absolute signal intensities. Details of the proposed approach are outlined in the following sections. [0046] Let (x, y, z) denote Cartesian coordinates of points in a finite arithmetic lattice R={(x, y, z): x=0, . . . , X1; y=0, . . . , Y1, z=0, . . . , Z1}. [0047] Q={0, . . . , Q1} denotes a set of gray levels. [0048] g: R.fwdarw.Q is a 3D grayscale image.

[0049] Bias Correction and Skull Stripping:

[0050] Considering bias correction and skull stripping in accordance with an embodiment of the present invention, illumination non-uniformity of infant brain MRIs, which is known as bias field, limits the accuracy of the existing brain extraction approaches. Therefore, to accurately extract the brain it is important to account for the low frequency intensity non-uniformity or inhomogeneity.

[0051] Homogeneity Enhancement:

[0052] The present invention deals with bias correction and skull stripping. Illumination non-uniformity of infant brain MRIs, which is known as bias field, limits the accuracy of the existing brain extraction approaches. Therefore, to accurately extract the brain it is important to account for the low frequency intensity non-uniformity or inhomogeneity.

[0053] To enhance the vascular homogeneity, the present invention developed a new 3D generalized Gauss-Markov random field (GGMRF) model with 2D rotational and translational invariance that will be applied after the bias correction and skull striping step. The main idea of the model is to reduce the signals inconsistencies of the MRA data by estimating the new grey level that minimize the Gibbs energy between the voxel of interest and its neighbor. To ensure the proposed GGMRF is invariant under rotations and translations, they selected the neighborhood system to be central-symmetric around the voxel of interest (e.g., spherical-neighborhood system) as demonstrated in FIG. 2. To GGMRF model, let the gray level values of volume g be considered as samples from a 3D GGMRF model with spherically symmetric neighborhood system (n.sub.1; n.sub.2). The maximum a posteriori (MAP) estimates and voxel-wise stochastic relaxation (iterative conditional mode (ICM) of voxel values at each location sR are as follows:

[00005]$\begin{array}{cc}q\left(s\right)=\mathrm{argmin}.Math.{.Math.g\left(s\right)-q.Math.}^{}+{}^{}.Math.{}^{}.Math.\underset{r{n}_1}{.Math.}.Math.{}_1\left(r\right).Math.g\left(s+r\right)-q.Math.{|}^{}.Math.+{}^{}.Math.{}^{}.Math.\underset{r.Math.n_2}{.Math.}.Math.{}_2\left(r\right).Math.{.Math.g\left(s+r\right)-q.Math.}^{}& \left(1\right)\end{array}$

[0054] The neighborhood n.sub.1 is located at a unit distance from the central voxel. Similarly, n.sub.2 is the neighborhood located at a double unit distance from the central voxel. .sub.1 and .sub.2 are the corresponding GGMRF potentials, and and are scaling factors. The parameter [1.01, 2.0] controls the level of smoothing (e.g., =2 for smooth vs. =1.01 for relatively abrupt edges). The parameter 1, 2 determines the Gaussian, =2, or Laplace, =1, prior distribution of the estimator.

To enhance the contrast of MRA images, we are proposing to use our former, unsupervised first-order appearance model to estimate the marginal grey level distributions of blood vessels and other brain tissues. The discrete Gaussian (DG) distribution on Q with parameter vector =(, .sup.2) is defined by its probability mass function.

[00006]$\begin{array}{cc}\left(q|\right)=\{\begin{array}{c}.Math.\frac{-0.5-}{},q=0\\ .Math.\frac{\left(-q-+0.5\right)}{}-.Math.\frac{\left(-q--0.5\right)}{},0<q<Q-1\\ 1-.Math.\frac{\left(Q--1.5\right)}{},q=Q-1\end{array}& \left(2\right)\end{array}$

where is the standard normal distribution function. An LCDG model with K of dominant modes is given by a sum of C.sub.p positively weighted and C.sub.n negatively weighted discrete Gaussian components with C.sub.pK:

[00007]$\begin{array}{cc}P\left(q\right)=\underset{r=1}{\overset{C_p}{.Math.}}.Math.w_{p,r}.Math.\left(q|{}_{p,r}\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right)& \left(3\right)\end{array}$

where the weights are constrained to be nonnegative and satisfy

[00008]$\begin{array}{cc}\underset{r=1}{\overset{C_p}{.Math.}}.Math.w_{p,r}-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_n,l=1& \left(4\right)\end{array}$

[0055] In the case of TOF-MRA images, K=3, corresponding to grey matter, white matter, and blood vessels. Given the observed voxel intensities within the brain in one slice of an MRA volume, the parameters of the LCDG (C.sub.p, C.sub.n, w.sub.p, w.sub.n, .sub.p, .sub.n) were estimated using the modified expectation-maximization algorithm in [?]. Assuming the positively weighted DG components are ordered such that .sub.p,1.sub.p,2 . . . .sub.p,Cp, the marginal distribution of grey levels within brain tissue (grey/white matter) and within blood vessels were calculated as:

[00009]$\begin{array}{cc}P\left(q|\mathrm{Brain}\right)=\frac{1}{}.Math.\underset{r=1}{\overset{2}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right).Math..Math.P\left(\mathrm{qVessels}\right)=\frac{1}{1-}.Math.\underset{r=3}{\overset{C_p}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right).Math..Math.\mathrm{Where}.Math..Math.=\frac{\mathrm{wp},1+\mathrm{wp},2}{\underset{r}{\overset{}{.Math.}}.Math.w_{p,r}}& \left(5\right)\end{array}$

Given these preliminaries, we employed the following algorithm to improve the homogeneity and contrast of MRA images as follows: [0056] 1) Choose >0 [0057] 2) For each MRA volume g: R.fwdarw.Q [0058] a) For each slice g.sub.ig [0059] i) Estimate parameters of the LCDG model using modified EM algorithm. [0060] ii) Calculate the empirical marginal distri-butions of brain tissue P.sub.i(q Brain) and blood vessels P.sub.i (q Vessel) using equation 5

.fwdarw.R [0061] b) Initialize contrast-enhanced image E: R [0062] c) For each sR [0063] i) Solve equation 1 for q(s) using gradient descent [0064] ii) P.sub.vP.sub.i([q(s)+0.5]| Vessel), where [] denotes the greatest integer function. [0065] iii) P.sub.oP.sub.i[(q(s)+0.5]|Brain) [0066] iv) If P.sub.vP.sub.i

E(s)q{circumflex over ()}(s)+

Else

E(s)q{circumflex over ()}(s)

Note that is a small value controlling the degree of contrast enhancement; in all our experiments we used =1.

[0067] Rotation and Translation Invariant MGRF-Based Prior Cerebral Vasculature Appearance Model:

[0068] To develop the proposed learnable MGRF model in away that it does not require any alignment stage in order to use it to extract cerebral vasculature. The appearance of cerebral vasculature is modeled 3D MGRF, having 2D rotational and translational symmetry, with neighborhood system N. As illustrated in Fig.?, N is specified by a set of characteristic voxel neighborhoods of the origin, {n.sub.: =1, 2, . . . , N} and their corresponding Gibbs potentials V.sub.. A characteristic neighborhood n.sub. is spherically symmetric if and only if it comprises all voxels whose distance from the origin falls within a half-open interval, n.sub.={r: d.sub.min,r<d.sub.max,}.

[0069] Since the MRA appearance of the cerebral vasculature changes from large vessels (bright) to microvessels (less bright), we have to take this effect into account in order to accurately segment cerebral vasculature. To accomplish this we developed the 3D interaction system to be a function in the z (inferior-superior) direction. That is, for each axial slice of the MRA volume there is a corresponding set of Gibbs interaction potentials V.sub. (q, q.sup.J; z), as well as a gray level potential V.sub.0(q, q.sup.J; z)=V.sub.0(q; z). Note that V.sub.0 represents the estimated potential for the first order prior appearance of the cerebral vasculature and V.sub. is the pairwise, or second order, prior appearance of the cerebral vasculature.

[0070] To identify/learn the proposed MGRF model, we have to estimate the potentials V.sub. and V.sub.0. Thus, consider a training set of MRA volumes g=g.sub.1 . . . g.sub.T and the families of voxel pairs (s, s) where s R, s.sup.J=s+r, and r n.sub.. Let F.sub.,t(q, q.sup.J; z) be a joint empirical probability distribution of gray level co-occurrences in the training nodules from the image g.sub.t. Also define F.sub.0,t(q, q.sup.J; z)=F.sub.0,t(q; z) the empirical distribution of gray levels.

[0071] The MGRF model of the t-th object is specified by the joint Gibbs probability distribution on the sublattice R.sub.t={sR|g.sub.t(s) is vasculature}.

[00010]$\begin{array}{cc}{P}_t\left(q,q^J\right)=\frac{1}{Z_t}.Math.\exp [|R_t.Math.\underset{v=0}{\overset{N}{.Math.}}.Math.\left(.Math..Math.v,t.Math.\underset{Z=1}{\overset{Z_t-1}{.Math.}}.Math.V_{v,t}\left(q,q^J;z.Math..Math.F_{v,t}\left(q,q^J;z\right)\right)\right]& \left(6\right)\end{array}$

where .sub.,t is the average cardinality of the neighborhood n.sub. with respect to the sublattice R.sub.t. We make the simplifying assumption that different vascular trees have approximately the same total volume, R.sub.t=R.sub.vasc, and the same neigh-borhood sizes, .sub.,t=.sub.. For independent samples, the joint probability distribution of gray values for all the training cerebral vasculature is as follows:

[00011]$\begin{array}{cc}{P}_S=\frac{1}{Z}.Math.\exp [{\mathrm{TR}}_{\mathrm{vasc}}.Math.\underset{v=0}{\overset{N}{.Math.}}.Math.\left[{}_v.Math.\underset{z=1}{\overset{Z-1}{.Math.}}.Math.V_{v,\mathrm{vasc}}\left(q,q^J;z\right).Math.F_{v,\mathrm{vasc}}\left(q,q^J;z\right)\right]& \left(7\right)\end{array}$

Where the marginal empirical distributions of gray levels F.sub.0,vasc and gray level co-occurrences F.sub.,vasc describe now all the cerebral vasculature from the training set. Using the analytical approach similar to that in previous work, the potentials are approximated with the scaled centered empirical probabilities:

[00012]$\begin{array}{cc}{V}_0,\mathrm{vasc}\left(q;z\right)=F_0,\mathrm{vasc}\left(q;z\right)-1/Q.Math..Math.V_{v,\mathrm{vasc}}\left(q,q^J;z\right)=F_{v,\mathrm{vasc}}\left(q,q^J;z\right)-\frac{1}{Q^2}& \left(8\right)\end{array}$

For computing MGRF energies E.sub.0 and E.sub. of the spherically symmetric pairwise voxel interactions in the training data, note that the energies are equal to the variances of the co-occurrence distributions:

[00013]$\begin{array}{cc}{E}_0\left(z\right)=\underset{v=0}{\overset{Q-1}{.Math.}}.Math.F_{0,\mathrm{vasc}}\left(q,z\right)\left[F_{0,\mathrm{vasc}}\left(q;z\right)-\underset{\_}{1}\right]& \left(9\right)\\ E_v\left(z\right)=\underset{q=0}{\overset{Q-1}{.Math.}}.Math.\underset{q^{}=0}{\overset{Q-1}{.Math.}}.Math.F_{0,\mathrm{vasc}}\left(q,z\right)\left[F_{0,\mathrm{vasc}}\left(q;z\right)-\underset{\_}{1}\right]& \left(10\right)\end{array}$

The calculated Energies from Eqs (9 and 10) will be used as a discriminatory features that represent the first-order and second-order prior appearance model of cerebral vasculature.

[0072] LCDG-Based Current Appearance Model:

[0073] The visual appearance of cerebral vasculature in each current data set g to be segmented typically differ from the appearance of the training cerebral vasculature due to nonlinear intensity variations from different data acquisition systems and changes in patient tissue characteristics, scanner type, and scanning parameters. This is why, in addition to the appearance prior learned from the normalized training data sets, we model the marginal gray level distribution with a dynamic mixture of two distributions for brain blood vessels and other brain tissues, respectively by using the LCDG model in Eq. 5 to estimate the marginal density of blood vessels and other brain tissues.

[0074] Extraction of the Cerebral Vasculature:

[0075] To highlight the advantages that the extracted features by using the proposed segmentation approach are separable and it can be accurately classified/segmented by any classifier algorithm, they will feed the extracted prior appearance features and current appearance features to different classifier such as Support Vector Machine, Neural Network, auto-encoder network followed by Softmax decision network, and decision tree. Finally, to extract the cerebral vasculature Matlab toolbox will be used to extract the largest connected 3D component from the initially classified 3D data. To summarize, the whole segmentation approach is as follows; 1) Read TOF MRA volume, 2) Apply bias correction algorithm followed by skull stripping algorithm 3) Use Eqs. 9 and 10 to estimate the energy of the first-order and second-order prior appearance. 3) Use Eq. 5 to estimate the probability density for any voxel to be blood vessels (P (q Vessels)) and probability to be other brain tissues (P (q Brain)), 4) Feed the estimated current and prior features to your classifier. 5) Extract Cerebral Vasculature by Using Matlab tool-box to extract the largest connected component.

[0076] Evaluation Metrics:

[0077] The segmentation results of the proposed blood vessels segmentation framework are evaluated using two types of metrics: area-based similarity metrics and a distance based error. The area-based similarity indicates the overlap between the segmented area and the gold standard. This type of metrics are crucial for studying areal measurements, e.g., total volumes of blood vessels. The distance-based error measures how close edges of the segmented vessels are to the ground truth. In this present invention, the Dice coefficient (DC) and absolute vessels volume difference (AVVD) are used to describe the area-based similarity, while the 95-percentile bidirectional Hausdorff distance (BHD) is used to characterize the distance-based error metric. FIG. 3 is an illustration of the evaluation metrics (DS) and HD and FIG. 4 is the evaluation metrics (DS) and HD.

[0078] Dice Coefficient (DC):

[0079] The Dice coefficient (DC) is used first to evaluate the segmentation accuracy. DC is the most commonly used similarity metric for segmentation evaluation by characterizing the agreement between the segmented (S) and the gold standard (G) regions based on the determination of true positive (TP) value, true negative (TN) value, false negative (FN) value, and false positive (FP) value. The TP is defined as the number of positively labelled voxels that are correct; the FP is the number of positively labelled voxels that are incorrect; the TN is the number of negatively labelled voxels that are correct; and the FN is the number of negatively labelled voxels that are incorrect.

[00014]$\begin{array}{cc}D.Math..Math.C=\frac{2.Math.\mathrm{TP}}{2.Math.\mathrm{TP}+\mathrm{FP}+\mathrm{FN}}& \left(11\right)\end{array}$

The calculated value of the DC can have a percentage value in the range 0% to 100%, where 0% means strong dis-similarity and 100% means that there is a perfect similarity. To obtain the gold standard that used in the segmentation evaluation process, an MRA expert delineated the brain vessels.

[0080] Another area-based metric that is used in this paper for the evaluation of segmentation, in addition to the DSC, is the absolute Vessels volume difference (AVVD). The AVVD is the volume difference, (percentage), between the output of the segmentation framework, S, and the gold standard, G, as follow:

[00015]$\begin{array}{cc}\mathrm{AVVD}\left(G,S\right)=\frac{.Math.G-S.Math.}{.Math.G.Math.}& \left(12\right)\end{array}$

where |GS| is the absolute difference between the number of voxels in G and S, |G| is the number of voxels in G

[0081] Bidirectional Hausdorff Distance (BHD):

[0082] In addition to the DSC and AVVD, the distances between G and S borders are used as an additional metric to measure the accuracy of the segmentation framework. To measure the distance error between the borders of G and S, we used the bidirectional Hausdorff distance (BHD). The HD from the boarder points of G to the boarder points of S is defined as the maximum distance from the border of G to the nearest point on the border of S.

HD(G,S)=max{min{d(g,s)}}gG sS(13) [0083] where g and s denote points of set G and S respectively
The bidirectional Haussdorf distance (BHD) between the segmented region S and its ground truth G is defined as:

BHD(G,S)=max{HD(G,S),HD(S,G)}(14)

In this present invention, they use the 95th-percentile bidirectional Haussdorf distance (BHD) as a metric that measures the segmentation accuracy.

[0084] In order to evaluate the performance of the proposed cerebral vasculature segmentation system, it was applied to 270 ToF-MRA data sets which were obtained from the University of Pittsburgh. An MR expert assessed the results qualitatively. The ToF-MRA data were acquired using a 3T Trio TIM scanner with a 12-channel phased-array head coil, resulting in 3-D multislab high-resolution images (160 slices), with a thickness of 0.5 mm, matrix size of 384 448, a flip angle of 15 degrees, repetition time of 21 ms, and echo time of 3.8 ms. In addition, the accuracy of the proposed approach was quantitatively validated using 30 data sets with a known manually segmented ground truth that were obtained by an MR expert. To highlight the role of each step in the proposed segmentation system, the output of each step for a selected axial cross-section of one subject was demonstrated. The homogeneity and contrast is enhanced by using the proposed GGMRF model. Also, to highlight the role of using the current and learned prior appearance model, we displayed the voxel-wise energies for each voxels in ToF-MRA image. It is very clear that the combined energy of each voxel (current and prior appearance) in the cerebral vasculature is higher than the energy of the brain tissues which confirms good guidance for any classifier that we plan to use. Another way to visualize the role of each model for the whole ToF-MRA volume is to use the Maximum Intensity Projection (MIP). FIG. 5 denotes T1-weighted MRI axial views for adult and infant brains.

[0085] In conclusion, the cerebral vascular diseases are threatening the life of millions around the world. The diagnosis of such diseases has been a challenge over the years and most physicians would agree that the most important step of recovery is having the right diagnosis. If the illness is precisely identified, most likely proper treatment will be done. Therefore, segmentation of the cerebrovascular structure is crucial since it helps in the diagnoses process, surgery planning, research, and monitoring. Moreover, the benefits of the segmentation of the cerebrovascular structure lay in its ability to improve the simulation of the blood flow and the visualization of the vessels in which each developed method solves a problem faced previously or triggers a specific region of the brain. This invention proposes a statistical approach that utilizes a voxel-wise classification based on determining probability models of voxel intensities, in order to separate blood vessels from the background of each TOFMRA slice. This is done by approximating the marginal empirical distribution of intensity probabilities with LCDG.

[0086] It is an object of the present invention to develop a method of processing a cerebrovascular medical image, the method comprising receiving a magnetic resonance angiography (MRA) image associated with a cerebrovascular tissue comprising blood vessels and brain tissues other than blood vessels, segmenting the MRA image using a prior appearance model for generating first prior appearance features representing a first-order prior appearance model and second appearance features representing a second-order prior appearance model of the cerebrovascular tissue, wherein the current appearance model comprises a 3D Markov-Gibbs Random Field (MGRF) having a 2D rotational and translational symmetry such that the MGRF model is 2D rotation and translation invariant, segmenting the MRA image using a current appearance model for generating current appearance features distinguishing the blood vessels from the other brain tissues, adjusting the MRA image using the first and second prior appearance features and the current appearance futures and generating an enhanced MRA image based on said adjustment.

[0087] It is also an object of the present invention to provide a method of processing a cerebrovascular medical image, wherein said prior appearance model uses interaction parameters analytically estimated from a set of MRA training data.

[0088] In an embodiment, the method of processing a cerebrovascular medical image, wherein the first prior appearance features representing a first-order prior appearance model and the second appearance features representing a second-order prior appearance model are respectively provided by energies of the training data according to the following equations:

[00016]$E_0\left(z\right)=\underset{q=0}{\overset{Q-1}{.Math.}}.Math.F_{0,\mathrm{vasc}}\left(q,z\right)\left[F_{0,\mathrm{vasc}}\left(q;z\right)-\underset{\_}{1}\right]$$E_v\left(z\right)=\underset{q=0}{\overset{Q-1}{.Math.}}.Math.\underset{q^{}=0}{\overset{Q-1}{.Math.}}.Math.F_{v,\mathrm{vasc}}\left(q,q^{};z\right)\left[F_{v,\mathrm{vasc}}\left(q,q^{};z\right)-\underset{\_}{1}\right]$

wherein,
E.sub.0 and E.sub.: variances of the co-occurrence distributions and will be used as a discriminatory features that represent the first order and second-order prior appearance model of cerebral vasculature
F.sub.0,vasc: marginal empirical distributions of gray levels
F.sub.v,vasc: gray level co-occurrences and describe now all the cerebral vasculature from the training set.

[0089] In an embodiment, the method of processing a cerebrovascular medical image, wherein said prior appearance model excludes alignment of the training data. This being said, the model does not require an alignment stage.

[0090] In an embodiment, the method of processing a cerebrovascular medical image, wherein said current appearance model comprises a Linear combination of Discrete Gaussians (LCDG) model and an EM-based model for linear combination of Gaussian approximation.

[0091] In another embodiment, the method of processing a cerebrovascular medical image, wherein said generating current appearance features comprises estimating first Gibbs probability densities of voxels to be blood vessels (P (q Vessels)) and estimating second Gibbs probability densities of voxels to be brain tissues other than blood vessels (P (q Brain)) according to the following equations respectively and making probabilistic decisions based on said first and second calculated Gibbs probability densities:

[00017]$P\left(q|\mathrm{Brain}\right)=\frac{1}{}.Math.\underset{r=1}{\overset{2}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right)$$P\left(\mathrm{qVessels}\right)=\frac{1}{1-}.Math.\underset{r=3}{\overset{C_p}{.Math.}}.Math.\mathrm{wp},r.Math..Math.\left(q|.Math..Math.p,r\right)-\underset{l=1}{\overset{C_n}{.Math.}}.Math.w_{n,l}.Math.\left(q|{}_{n,l}\right)$$\mathrm{Where}.Math..Math.=\frac{\mathrm{wp},1+\mathrm{wp},2}{\underset{r}{\overset{}{.Math.}}.Math.w_{p,r}}$

wherein C.sub.p, C.sub.n, w.sub.p, w.sub.n, .sub.p, .sub.n denotes the parameters of the LCDG.

[0092] In an embodiment, the method of processing a cerebrovascular medical image, further comprising applying bias correction and skull stripping to the MRA image prior to the segmentations.

[0093] In an embodiment, the method of processing a cerebrovascular medical image, wherein the adjusting of the MRA image comprises analysing the MRA image using a 3D connectivity analysis based on the first and second prior appearance features and the current appearance futures.

[0094] In an embodiment, the method of processing a cerebrovascular medical, wherein the adjusting the MRA image is conducted using a Random Forest model.

[0095] In an embodiment, the method of processing a cerebrovascular medical image, wherein the blood vessels comprise small and large blood vessels.

[0096] In an embodiment, the method of processing a cerebrovascular medical, wherein said MRA image of a cerebrovascular tissue is related to a mammalian.

[0097] In an embodiment, the method of processing a cerebrovascular medical image, wherein said mammalian is a human.

[0098] It is also an object of the present invention to provide a system for processing a cerebrovascular medical image, the system comprising a data input interface for receiving a magnetic resonance angiography (MRA) image associated with a cerebrovascular tissue comprising blood vessels and brain tissues other than blood vessels, at least one processor for processing the received MRA image, the MRA image processing comprising segmenting the MRA image using a prior appearance model for generating first prior appearance features representing a first-order prior appearance model and second appearance features representing a second-order prior appearance model of the cerebrovascular tissue, wherein the current appearance model comprises a 3D Markov-Gibbs Random Field (MGRF) having a 2D rotational and translational symmetry such that the MGRF model is 2D rotation and translation invariant; segmenting the MRA image using a current appearance model for generating current appearance features distinguishing the blood vessels from the other brain tissues; adjusting the MRA image using the first and second prior appearance features and the current appearance futures; and generating an enhanced MRA image based on said adjustment.

[0099] In an embodiment, the system for processing a cerebrovascular medical image, wherein the adjusting the MRA image is conducted using a Random Forest model.

[0100] In an embodiment, the system for processing a cerebrovascular medical image, further comprising a display for displaying the enhanced MRA image to a user.

[0101] In another embodiment, the system comprises a scanner to capture an MRA image and send it to the data input interface.

[0102] Many changes, modifications, variations and other uses and applications of the subject invention will become apparent to those skilled in the art after considering this specification and the accompanying drawings, which disclose the preferred embodiments thereof. All such changes, modifications, variations and other uses and applications, which do not depart from the spirit and scope of the invention, are deemed to be covered by the invention, which is to be limited only by the claims which follow.