This paper presents an efficient liver-segmentation system developed by combining three ideas under the operations of a level-set method and consequent processes. First, an effective initial process creates mask and seed regions. The mask regions assist in prevention of leakage regions due to an overlap of gray-intensities between liver and another soft-tissue around ribs and verte-brae. The seed regions are allocated inside the liver to measure statistical values of its gray-intensities. Second, we introduce liver-corrective images to represent statistical regions of the liver and preserve edge information. These images help a geodesic active contour (GAC) to move without obstruction from high level of image noises. Lastly, the computation time in a level-set based on reaction-diffusion evolution and the GAC method is reduced by using a concept of multi-resolution. We applied the proposed system to 40 sets of 3D CT-liver data, which were acquired from four patients (10 different sets per patient) by a 4D-CT imaging system. The segmentation results showed 86.38% ± 4.26% (DSC: 91.38% ± 2.99%) of similarities to outlines of manual delineation provided by a radiologist. Meanwhile, the results of liver segmentation only using edge images presented 79.17% ± 5.15% or statistical regions showed 74.04% ± 9.77% of similarities.
Liver image segmentation is an important procedure in the computer-aided diagnosis (CAD) and surgery (CAS). For example, it is used to determine the liver’s volume [
Many algorithms have been proposed to give high efficiency and reduce user involvement as presented in [
Alternatively, improvement in a quality of anatomical representations in a given image can give good segmentation results. For instance, in [
Consequently, we are motivated to create an efficient liver-segmentation system from a combination of three main ideas. It is intended to perform under the conditions of a level-set method and consequent processes. These three ideas are presented to achieve several purposes as follows.
· The effective initial-process is proposed for excluding all information outside the ribcage and creating seed regions in axial images. The exclusion process assists in prevention of leakage regions when a given curve moves near ribs and vertebrae. The seed regions are completely allocated inside the liver for measuring statistical values of gray intensities. Further, it helps to obtain the start and stop indexes of axial images that contain liver regions.
· Liver-corrective images are created to represent statistical regions of the liver and preserve the edge information. These liver-corrective images help a level-set method based on reaction-diffusion (RD) evolution and a geodesic active contour (GAC) model to cope with high level of image noises. Further, an advanced image- filter is unnecessary.
· We use a concept of multi-resolution to combine with the RD-GAC based level-set method in order to reduce computation time.
We applied the proposed system to 40 sets of 3D CT-liver data, which were acquired from four patients by using a 4D-CT imaging system. The 10 different sets of 3D CT data were collected in a free-breathing cycle for each patient. In addition, we compared the proposed system with the liver-segmentation methods using only edge or statistical-region representation.
The rest of paper is organized as follows. Section 2 briefly describes related methods, and section 3 explains details of the proposed system. Next, the experimental results are illustrated and discussed. Finally, we conclude this study in the last section.
This approach transforms given images into edge images before performing liver segmentation. We refer to Lee, J. et al. [
(SI) is constructed from a gradient magnitude image
where
respectively. By choosing proper
ate an inverted binary image called seed region growing as
are constructed from all axial-images, a level-set method is applied to segment the liver’s region in each axial image.
However, this approach is inappropriate for the curve propagation in an inward direction. Thus, it is necessary to create an initial region for constructing a zero level-set function (LSF) inside the liver’s region. Further, for 3D CT data, liver regions in axial images expand from the top to around the middle; then, they shrink to small regions at the bottom of the volume. Consequently, each 3D CT data set needs to be divided at least two sections in z-axis (top-to-bottom) for placing initial curves inside the liver’s regions. Then, the first image in each section requires manual drawings of seed regions to initialize the zero LSF. In addition, complexity of edge information is reduced by using a segmentation result of previous image slice as an initial curve for a consecutive image. Further, the narrow bands are applied to limit areas of the curve propagation.
This approach statistically describes liver regions by measuring mean
Generally, a level-set method requires a re-initialization process to preserve an accurate numerical-solution, but this process consumes high computation cost as mentioned in [
to produce the reaction term. If a geodesic active contour (GAC) model [
where
The proposed system (see
To exclude all information outside the ribcage, we create a mask region for each axial image by performing the following procedures. First, a median filter is used to reduce noise. Then, a two-stage multi-thresholding Otsu’s (TSMO) method [
Indeed, the original TSMO method [
field unit (HU) computed from the linear attenuation coefficient of materials [
We perform the following steps to represent statistical regions of liver and preserve edge information in a given image. First, some samples of liver regions are measured their means
Moreover, we use the selected region to construct a zero LSF
tion, that is
As for the RD-GAC based level-set method in section 2.3, we combine it with a concept of multi-resolution as shown in
down to the lowest resolution. Next, the level-set method is operated. Afterwards, the result is used to construct the zero LSF in the higher resolution. Meanwhile, the edge detector function at the original resolution is scaled down to the desirable resolution. Then, the level-set method is repeatedly calculated to continue propagating the given curve from the lower resolution. Similarly, the process of segmentation is repeated until a final contour at the original resolution is released.
After we remove all regions outside the ribcage (section 3.1) in a given 3D CT volume, coronal images are reconstructed by cutting the 3D CT volume in x-z planes (see
This process contains three main operations. First, we use seed regions produced by the process in section 3.4 to create liver-corrective images (section 3.2) in axial-image planes. Afterwards, the multi-resolution level-set method (section 3.3) is utilized to segment a liver’s volume.
From the segmentation results in section 3.5, they are refined by applying a Gaussian smooth filter to coronal and sagittal image planes. In addition, we use a hole-filling method to get outside boundaries of the liver regions. However, we can preserve hole-regions by intersecting these hole-filling regions with regions of holes.
We applied the proposed system to 40 sets of 3D CT-liver data, which were acquired from four patients by a 4D-CT imaging system (a GE Discovery ST machine and a Varian RPM system) in a cine mode. In each patient, 10 different sets of 3D CT data corresponded to a breathing cycle, which were counted from 0% to 90% phases of a breathing cycle with an equal different time phase. These data sets are provided by the MIDAS community, http://midas.kitware.com/community/view/47. Each 3D-CT data set includes 136, 120, 150, and 120 slices of 16-bits axial-images for patient A, B, C and D. The size of each axial image is 512 × 512 pixels with resolution 0.98 square millimeters, and slice thickness is 2.5 millimeters.
When we used a GAC model to control the curve propagation and allocated the boundaries of the zero LSF inside the liver, the following three conditions were used to adjust parameters. First, the reaction factor of the RD method (section 2.3) should be large enough to move a given curve in the outward direction. However, if this reaction factor were over defined, the curve would easily move outwards from boundaries of liver. We set it to
be 0.005 and 0.03 for coronal and axial images, respectively. Next, the diffusion factor should be
as mentioned in [
In addition, we simply defined the maximum number of iterations to stop the curve propagation as 300 iterations. However, if we segment liver’s regions in axial images, it will be possible to reduce the number of iterations. We automatically adjusted the number of iteration by performing parallel projection of liver-segmentation results in coronal images onto the vertical axes of coronal images. Actually, a position on the vertical axis is equivalent to the index of axial image. If the projection data at the position
In this study, we validated similarities between the segmentation results of the proposed system and liver’s volumes delineated by a radiologist. Further, these segmentation results were compared with the liver-segmenta- tion methods based on the level-set speed image (LSSI) and statistical thresholding (ST) techniques, which were implemented in accordance with diagrams in section 2.1 and section 2.2, respectively.
In
Next,
This study validated the segmentation results by using relative absolute volume similarity (RAVS), volume overlapped coefficient (VOC) and dice similarity coefficient (DSC) [
under-segmentations are measured by false positive rate (FPR) and false negative rate (FNR) [
where
The proposed system was operated under MATLAB environment on 3.40 GHz Intel(R) Core(TM) i7 2006 CPU. It spent around seven minutes 35 seconds to compute in the effective initial process. Further, liver segmentation in axial images consumed about 16 minutes and six seconds. Thus, the proposed system required around 23 mi-
Measure Types | Proposed | LSSI | ST | |||
---|---|---|---|---|---|---|
Average | STDEV | Average | STDEV | Average | STDEV | |
RAVS | 83.51 | 4.90 | 73.95 | 7.07 | 63.84 | 16.14 |
VOC | 84.25 | 4.89 | 76.78 | 5.12 | 73.68 | 7.81 |
DSC | 91.38 | 2.99 | 86.77 | 3.24 | 84.61 | 5.37 |
FPR | 5.01 | 1.80 | 10.96 | 7.18 | 32.49 | 17.32 |
FNR | 11.47 | 6.08 | 15.09 | 3.33 | 3.67 | 2.17 |
Measure Types | Patient A | Patient B | Patient C | Patient D | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Proposed | LSSI | ST | Proposed | LSSI | ST | Proposed | LSSI | ST | Proposed | LSSI | ST | |
RAVS | 84.36 | 66.03 | 50.68 | 76.62 | 71.55 | 75.75 | 86.50 | 74.64 | 56.31 | 86.58 | 83.58 | 72.59 |
VOC | 85.24 | 71.80 | 67.48 | 77.24 | 74.00 | 79.99 | 87.11 | 77.32 | 69.27 | 87.43 | 84.01 | 77.99 |
DSC | 92.02 | 83.57 | 80.29 | 87.09 | 85.04 | 88.73 | 93.11 | 87.20 | 81.84 | 93.28 | 91.29 | 87.59 |
FPR | 5.93 | 20.08 | 46.53 | 2.76 | 9.38 | 17.66 | 4.76 | 11.72 | 42.03 | 6.60 | 2.66 | 23.76 |
FNR | 9.71 | 13.89 | 2.79 | 20.62 | 19.07 | 6.59 | 8.75 | 13.64 | 1.65 | 6.82 | 13.75 | 3.65 |
nutes and 41 seconds to segment a liver volume from 3DCT data that consists of 120 - 150 axial-image slices.
This study proposes an efficient liver-segmentation system based on a level-set method and consequent processes. The proposed system is composed of three main ideas. First, an effective initial process prevents the leakage of regions outside the ribcage when a given curve propagates near ribs and vertebrae. Further, it generates seed regions completely inside a liver’s volume for measuring statistical values of gray-intensities. Second, liver-corrective images are created to represent statistical regions of liver and preserve the edge information. The objective of these images is to improve accuracy of liver-segmentation. Lastly, computation time in the RD- GAC based level-set method is reduced by using a concept of multi-resolution.
We applied the proposed system to 40 sets of 3D CT-liver data, which were acquired by a 4D-CT imaging system from four patients. For each patient, 10 different sets of 3D CT were collected in different time phases of a breathing cycle. The segmentation results were compared with livers’ volumes, which were manually delineated by a radiologist. An average of similarity measures presented around 86.38 ± 4.26 percent. Further, the proposed system showed the highest accuracy compared with the liver-segmentation methods based on edge or statistical region information. However, the major problem found in the proposed method is a kind of under- segmentation. It appeared when liver’s regions were small and dirty edge information was produced by some artifacts. Thus, this problem will be addressed in the future work.