An iterative Bayesian approach for liver analysis: tumors validation study

. We present a new method and validation study for the nearly automatic segmentation of liver tumors. The method is part of a nearly automatic system for simultaneous segmentation of liver contours, vessels, and tumors from abdominal CTA scans. It repeatedly applies multi-resolution, multi-class smoothed Bayesian classiﬁcation followed by morphological adjustment and active contours reﬁnement. The method uses multi-class and voxel neighborhood information to compute an accurate intensity distribution function for each class. Only one user-deﬁned voxel seed for the liver and a few extra seeds for the tumors are required for initialization, without any manual adjustment of internal parameters. A retrospective study on a validated clinical dataset totaling 20 tumors from 9 patients CTAs’ was performed as part of the MICCAI’08 liver tumors segmentation grand-challenge. An aggregated competition score of 61 was obtained on the test set of this database. In addition we measured the robustness of our algorithm to diﬀerent seeds initializations. These results suggest that our method is clinically applicable, accurate, eﬃcient, and robust to seed selection compared to manually generated ground truth segmentation and to other semi-automatic segmentation methods.


Introduction
Accurate detection and monitoring of liver tumors is a key task in many clinical applications such as hepatomegaly and liver cirrhosis assessment, hepatic volumetry, hepatic transplantation planning, liver regeneration after hepatectomy, evaluation and planning for resection liver surgery, and monitoring of liver metastases, among many others.
Currently, most radiologists use simple guidelines to estimate tumor volume and response from clinical images.For 2D X-ray images, the 1979 World Health Organization (WHO) guidelines define the tumor burden as the product of its maximum diameter -the largest distance between to in-tumor points -and the maximum perpendicular diameter [1].The drawback of this measure is that it is only a rough approximation based on a single 2D image.When 3D CT images are available, radiologists employ the three-parameter ellipsoid formula (length × depth × width × 0.5233) [2] to estimate the tumor volume.This yields reasonable volume estimates for tumors with nearly spherical or ellipsoid shapes, which may be found in specific types of both benign and malignant tumors.However, it is less accurate for most tumors, as they usually have irregular borders and may have necrotic centers.Additionally, this method quantifies the tumor shape with three dimensions, which restrict its use in further comparative studies.
Medical image processing techniques provide the means to obtain more accurate and informative measures.Tumor volume can be measured by performing manual and semi-automatic segmentation (e.g.livewire [3]) on multiple image slices.Volume calculation is then performed by incorporating the data obtained from each slice [4].Manual segmentation is time-consuming, user-dependent, error-prone, and requires expert knowledge to yield accurate and robust results.In contrast, automatic or nearly automatic methods have the potential to provide fast, robust, user-independent accurate segmentation.Nearly automatic CT-based liver tumors segmentation is known to be a very challenging task.The main difficulties include the ambiguity of the liver and tumors boundaries, the complexity of the tumors surfaces, the contrast variability between liver parenchyma, tumors and vessels, the different tumor sizes and shapes, and the possible presence of many small metastases.
Researchers have developed in the past decade, a variety of methods for semi-automatic and automatic segmentation and visualization of liver structures.Most of these methods segment one structure at a time, usually starting with the liver surface, followed by the vessels and the tumors.The individual structure segmentation uses various techniques, such as intensity thresholding, region growing, and level-sets based methods.For example, [5,6] use adaptive binary thresholding to separately segment the liver surface, vessels, and tumors, followed by a deformable model refinement for each.Since it does not use voxel neighborhood information, it may yield noisy or erroneous liver surface segmentations, especially when large tumors are present, as they bias the intensity distribution function.Metaxas et al [7] used Markov Random Field (MRF) estimation coupled with Deformable models for the segmentation of tumors.Peitgen et al. [8] describes an edge-based segmentation method for the liver contour and an interactive region-growing method for the vessels and tumors.Since it requires many seeds per CT slice, it is of limited clinical use.In [9] a machine learning based approach used to classify the 1D intensity profiles of tumors in liver.However, this method is biased to blob-like tumors and less accurate for the majority of tumors which are defined by irregular borders.Grady et al [10] proposed a random-walker based 3D segmentation of liver tumors, with only one seed.The additional seeds required for the random walker produced from a 2D fuzzy-connectedness segmentation of the slice with the seed.
A key observation is that by considering each liver structure individually, the intrinsic relations between the liver parenchyma, vessels, and tumors are lost.This makes the classification more sensitive and error-prone.As an alternative, we developed a new method for the simultaneous segmentation of liver contours, vessels, and tumors from abdominal CTA scans [11,12].The method repeatedly applies multi-resolution, multi-class smoothed Bayesian classification followed by morphological adjustment and active contours refinement.The method requires only one seed for the liver and additional according to the number of tumors inside the liver for initialization, with no manual adjustment of internal parameters.By using the multi-class and voxel neighborhood information, it significantly improves the discrimination quality of the intensity distribution function for each class.The multi-resolution iterative approach allows the segmentation of the entire liver surface without prior shape information and/or significant user interaction.Our method yields accurate and robust results on two clinically validated datasets totaling 56 CTA studies, and achieved a very high score compared to other semi-automatic methods presented in the MICCAI 2007 grand-challenge for liver segmentation [13].
In this paper, we briefly describe the method as it applies to tumor segmentation and present the results of the validation study that we conducted on the current MICCAI 2008 grand-challenge workshop [14] database.

Method
Our method consists of four steps: 1) multi-class intensity model generation; 2) voxel classification; 3) morphological adjustment, and; 4) geodesic active contours refinement.The steps are performed in sequence and repeatedly applied to the image until no further changes occur.After each iteration, the internal parameters of the multi-class intensity model are updated.This iterative updating is designed to overcome a biased classification due to ambiguous liver boundaries and biased seed selection.
Our algorithm is initialized with a multi-class intensity model.The model describes the Probability Distribution Function (PDF) of the Hounsfield units of each structure (e.g.liver parenchyma, and tumors) using Gaussian distributions.The model is initialized by using the mean and the variance of a rectangular neighborhood around one manually selected seed inside the healthy liver tissue and additionall seeds inside the tumors.One seed is required for each tumor.Fig. 1(a,d,g) illustrates the required initialization seeds.A separate model is computed for the liver and for each tumor to cope with intensity variations between different lesions and with both hypo and hyper-intensity lesions.In subsequent iterations, the segmented region from the previous iteration is used to compute the mean and the variance of the liver and tumor classes.The remaining four classes are modeling explicitly the background organs with intensities above/below the liver and tumor values.
The classification step uses the smoothed Bayesian classification of Teo et al [16].It is applied twice, once for the liver class, and once for the tumor class.During the tumors classification, the liver class is considered as part of the background classes.The results are combined by taking into account only the tumor voxels inside the liver.The classification updates the classes intensity models by first computing the mean and variance of the liver and tumor classes from the current liver and tumor regions, and then updates the background classes by computing their mean and variance parameters.The output of the classification process is a labels map, which classify each voxel as either background, liver, blood vessels, or tumors.The morphological adjustment and the active contours refinement are then applied on the resulting regions to find the refined liver and tumors regions.The iterations are necessary to fine-tune the intensity model to improve the classification, to minimize the dependence on the initial voxel seed selection.
To speed up the segmentation and make it more robust and accurate, we use a multi-resolution approach.The first few iterations are performed on a downsampled CTA dataset to obtain a rough contour segmentation.Subsequent iterations are performed on the original CTA dataset until no further improvements can be made.To cope with small tumors and to improve the accuracy of tumors segmentation, a refinement iteration is applied to each tumor Region Of Interest (ROI) separately on the original dataset resolution.A detailed description of our method can be found in [11,12].

Experimental results
We implemented our method using the ITK software library [17] and the smoothed Bayesian classification module [18].Computations were performed on an Intel Core2 Quad 2.4 GHz PC with 3GB of memory.
We performed a retrospective study on the database provided by the MIC-CAI 2008 3D Liver Tumors Segmentation workshop [14].The dataset consists of 20 tumors from clinical datasets of 9 patients.It is divided into two groups.The first group consists of 10 tumors from 4 patients and is used for training and fine-tuning of the algorithm; The second group consists of 10 tumors form 5 patients and is used to evaluate segmentation algorithms.The evaluation followed the method described in [13].We compared our segmentation results to the ground-truth using five metrics: 1) volumetric overlap; 2) relative absolute volume difference; 3) average symmetric absolute surface distance; 4) symmetric RMS surface distance, and; 5) maximum symmetric absolute surface distance.
Table 1 summarizes the results.Based on these metrics results an aggregate score was computed.Our average score was 61.The mean (std) computation time for each liver, including segmentation of the entire liver, blood vessels and tumors was 8.34 (std=2.47)minutes.The required user-time was only a few seconds for seeds selection.Fig. 1 illustrates our results on the test set for the best and worst cases.We also measured the robustness of our method to three different seeds initializations on the 10 training tumors.Table 2 summarizes the results.These results show that our method is very robust to different seeds initializations, whereas other semi-automatic methods, which require significantly more user interaction, are prone to be less robust.

Conclusion
We present a new method and validation study for the nearly automatic segmentation of liver tumors.The method is part of a nearly automatic system for simultaneous segmentation of liver contours, vessels, and tumors from abdominal CTA scans.The main advantage of our method is that it simultaneously segments the liver contour, the blood vessels, and tumors inside the liver with only several user-selected seeds.Experimental results on the current MICCAI 2008 grand-challenge workshop database [14], totaling 20 tumors from 9 patients, show that our method is clinically applicable, accurate, efficient, and robust to seed selection when compared to manually generated ground truth segmentation.In the future, we plan develop an integrated software package for the visualization and quantitative analysis of the liver to support diagnosis and surgical planning.

Table 1 .
Results of the comparison metrics and scores for all ten tumors.

Table 2 .
Results of the comparison between metrics and final scores for different initializations on the ten training cases.The values are the mean pairwise difference between the results of three initializations.