Vascular segmentation plays an important role in medical image analysis. A novel technique for the automatic extraction of vascular trees from 2D medical images is presented, which combines Hessian-based multiscale filtering and a modified level set method. In the proposed algorithm, the morphological top-hat transformation is firstly adopted to attenuate background. Then Hessian-based multiscale filtering is used to enhance vascular structures by combining Hessian matrix with Gaussian convolution to tune the filtering response to the specific scales. Because Gaussian convolution tends to blur vessel boundaries, which makes scale selection inaccurate, an improved level set method is finally proposed to extract vascular structures by introducing an external constrained term related to the standard deviation of Gaussian function into the traditional level set. Our approach was tested on synthetic images with vascular-like structures and 2D slices extracted from real 3D abdomen magnetic resonance angiography (MRA) images along the coronal plane. The segmentation rates for synthetic images are above 95%. The results for MRA images demonstrate that the proposed method can extract most of the vascular structures successfully and accurately in visualization. Therefore, the proposed method is effective for the vascular tree extraction in medical images.
Accurate segmentation and quantification of vascular structures in medical images is a critical task for clinical practices such as computer-aided diagnosis, treatment, surgical planning, and navigation. However, it is highly challenging to extract vascular structures in 2D and 3D medical images. The reasons lie in two aspects. On one hand, some vascular structures involve numerous vascular branches and complex patterns [
Various extraction techniques have been proposed for vascular tree segmentation, that is, pattern recognition techniques, model-based approaches, mathematical morphology, multiscale filtering approaches, vessel tracking, and matched filtering (see Kirbas and Quek [
The paper is structured in five sections; Section
The presence of numerous nonvascular structures in clinical medical images such as liver and kidney, will negatively affect the extraction of vascular structures. Considering that morphological top-hat transformation is a powerful technique for image enhancement, especially in extracting bright features from a dark background [
Following the morphological top-hat transformation, the Hessian-based multiscale filtering [
In practice, the second-order partial derivatives of input image
Possible structure orientations in 3D images depending on the eigenvalues of Hessian matrix.
Orientation pattern | 3D image | ||
---|---|---|---|
|
|
| |
Noisy, no preferred direction | L | L | L |
Plate-like structure (bright) | L | L | H− |
Plate-like structure (dark) | L | L | H+ |
Tubular structure (bright) | L | H− | H− |
Tubular structure (dark) | L | H+ | H+ |
Blob-like structure (bright) | H− | H− | H− |
Blob-like structure (dark) | H+ | H+ | H+ |
L: Low, H+: high positive, H−: high negative.
Based on the eigenvalues of
The first ratio
Assuming a bright blood image, the vesselness function can be defined as follows:
For 2D images, we use the following vesselness measure defined by Frangi et al. [
Active contour methods have been popular in a wide range of problems including visual tracking and image segmentation since they were first proposed in 1988 by Kass et al. [
In region-based active contour methods, a curve is iteratively evolved by optimizing an objective function to find the boundary
It is well known that level set methods are the most widely used way to represent a contour because of their simple implementation. In addition, it allows very complex curve behavior and automatic topology adaptation [
In this paper, we use Chan-Vese model [
Since Gaussian convolution tends to blur vessel boundaries and makes scale selection inaccurate, and the blur level of vessel boundaries is associated with standard deviation
By combining
If one regularizes the Heaviside function
In general,
We define regularizations of
In each step, the
The process of the vascular extraction terminates when the evolution does not change within bounds 0.4 mm2 on successive iterations or the maximum number of iterations is reached. The improved active contour method converges to the boundary of vascular structures exactly in a few iterations.
Vessel enhancement with morphological top-hat transformation and Hessian-based multiscale filtering; Get the initial contour Initialize Compute Solve ( Reinitialize Check whether the solution is stationary or the stopping criteria is met. If not, go back to Step 4; Otherwise stop evolution.
To evaluate the performance of the proposed method, we test it on synthetic images containing different vessel-like structures with different diameters and different directions. For quantification, we use the segmentation rate to measure the effectiveness of our method. The segmentation rate is used to estimate the completeness of a segmented vessel, and it is defined as the ratio of the number of segmented pixels to the number of gold standard pixels whose coordinates are known in synthetic images.
Figure
Synthetic images. (a) Image with different diameters. (b) Image with different directions. (c) Image with different intensities.
The vascular tree model with different complexities. (a) A branch. (b) Two branches. (c) Four branches. (d) Six branches. (e) Eight branches.
Figure
The segmentation rate with different (a) vessel diameters, and (b) vessel directions, (c) vessel intensities, (d) vessel complexities.
To investigate the sensitivity of the proposed method to noise, we used the synthetic image of size 256 × 256 with a vessel-like structure of varying width and orientation in Figure
Analysis of noise sensitivity. (a) Original image. (b) Influence of noise levels.
The segmentation results at different noise levels. (a) Original image. Standard deviation is 5, 10, 20, and 30 from (b) to (e).
In this section, we compared the segmentation results of the proposed method with those of other two vessel segmentation techniques, Hessian-based multiscale filtering [
The segmentation results of the above three methods. (a) Original image. (b) Hessian-based multiscale filtering. (c) Hessian-based multiscale filtering combined with Chan-Vese model. (d) The proposed method.
In this section, we applied the proposed method on 2D slices extracted from a 3D abdomen MRA image. The image size is 512 × 512 × 60 voxels with pixel spacing 0.51 mm × 0.51 mm × 1 mm which is acquired from syngo MR B15 by routine clinical scan. The 2D slices were generated by slicing through the 3D image in the direction of the coronal plane with 3D Quantify (a multiplanar visualization software) [
Figure
Segmentation results of the above three methods. (a) A 2D slice view. (b) Hessian-based multiscale filtering. (c) Hessian-based multiscale filtering combined with Chan-Vese model. (d) The proposed method.
Enlarged view of the marked green box in Figure
This paper presented an automatic technique for extracting vascular tree in medical images. Distinctively, the proposed method introduces an external constrained term
This work was partly supported by the National Natural Science Foundation of China (NSFC) (Grant no. 30911120497), the National 973 project (Grant no. 2011CB933103), the Project of the National 12th-Five Year Research Program of China (Grant no. 2012BAI13B02), and Graduates’ Innovation Fund of Huazhong University of Science and Technology (Grant no. HF-11-08-2013).