British Journal of Radiology (2007) 80, 996-1004
© 2007 British Institute of Radiology
doi: 10.1259/bjr/20861881
Combining 2D wavelet edge highlighting and 3D thresholding for lung segmentation in thin-slice CT
P Korfiatis, MSc
1
S Skiadopoulos, PhD
1
P Sakellaropoulos, PhD
1
C Kalogeropoulou, PhD, MD
2 and
L Costaridou, PhD
1
Departments of 1 Medical Physics and 2 Radiology, School of Medicine, University of Patras, 265 00 Patras, Greece
Correspondence: Lena Costaridou, Department of Medical Physics, School of Medicine, University of Patras, 265 00 Patras, Greece. E-mail: costarid{at}upatras.gr
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Abstract
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The first step in lung analysis by CT is the identification of the lung border. To deal with the increased number of sections per scan in thin-slice multidetector CT, it has been crucial to develop accurate and automated lung segmentation algorithms. In this study, an automated method for lung segmentation of thin-slice CT data is presented. The method exploits the advantages of a two-dimensional wavelet edge-highlighting step in lung border delineation. Lung volume segmentation is achieved with three-dimensional (3D) grey level thresholding, using a minimum error technique. 3D thresholding, combined with the wavelet pre-processing step, successfully deals with lung border segmentation challenges, such as anterior or posterior junction lines and juxtapleural nodules. Finally, to deal with mediastinum border under-segmentation, 3D morphological closing with a spherical structural element is applied. The performance of the proposed method is quantitatively assessed on a dataset originating from the Lung Imaging Database Consortium (LIDC) by comparing automatically derived borders with the manually traced ones. Segmentation performance, averaged over left and right lung volumes, for lung volume overlap is 0.983±0.008, whereas for shape differentiation in terms of mean distance it is 0.770±0.251 mm (root mean square distance is 0.520±0.008 mm; maximum distance is 3.327±1.637 mm). The effect of the wavelet pre-processing step was assessed by comparing the proposed method with the 3D thresholding technique (applied on original volume data). This yielded statistically significant differences for all segmentation metrics (p<0.01). Results demonstrate an accurate method that could be used as a first step in computer lung analysis by CT.
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Introduction
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CT has enabled the quantitative analysis of emphysema [1, 2], lung cancer [3–5], pulmonary embolism [6, 7] and diffuse lung disease [8]. Introduction of multidetector CT with near isotropic sub-millimetre resolution acquisition, resulting from the large amount of image-generated data, has driven the development of computer analysis systems that aim to assist radiologists in data interpretation. The first step of computer analysis systems based on lung CT data is the identification of lung borders. With the increased number of sections per scan produced with thin-slice multidetector CT, it is crucial to develop accurate and automated algorithms to deal with the difficult task of lung border delineation. Challenges for lung volume segmentation algorithms [9–11] include (i) left/right lung volume separation, (ii) susceptibility to partial volume effects that affect thin antero-posterior junction lines, and (iii) under-segmentation of mediastinum owing to anatomical structures such as vessels and high-density abnormalities connected to the borders (e.g. juxtapleural nodule exclusion at segmentation stage resulting in unrecoverable loss in subsequent computer analysis).
A number of algorithms have been developed to improve the accuracy of lung border delineation [10–14]. Brown et al [12] provided a knowledge-based method to segment the lung fields from CT thoracic images, in which anatomical knowledge stored in a semantic network was used to guide low-level image processing routines, such as thresholding, region growing and morphological operations. Hu et al [13] followed an iterative three-dimensional (3D) thresholding approach for initial lung field segmentation. Left and right lungs were segmented by identifying junction lines with dynamic programming. Finally, a sequence of morphological operations was used to smooth the resulting border irregularities along the mediastinum. Recently, Ukil et al [11] utilized the algorithm proposed by Hu et al [13] to propose smoothing for correcting left and right lung borders around the mediastinum, guided by anatomical information obtained from the segmented airway tree. Armato et al [10], who highlighted the need and provided specifications for general purpose lung segmentation algorithms, reported a scheme based on a two-dimensional (2D) approach using multiple grey level thresholding. A "rolling ball" was used to deal with juxtapleural nodules. A 3D approach was recently proposed by Sun et al [14], using an adaptive 3D region growing algorithm to segment lung volumes, to apply on CT sections preprocessed by a de-noising filter. The region-growing algorithm used seed points located with the use of the fuzzy C-means method. 3D morphological closing was used to deal with incomplete lung volume.
Here, a 3D automated method for lung segmentation of thin-slice CT data is proposed. The method exploits the advantages offered by a 2D wavelet pre-processing step for lung border delineation. The core of the method is automated 3D grey level thresholding (obtained with the minimum error technique) that was introduced by Kittler and Illingworth [15]. Thresholding combined with the wavelet pre-processing step successfully deals with antero-posterior junction lines, resulting in separation of left and right lung volumes and juxtapleural nodules. Finally, to deal with mediastinum border under-segmentation, 3D morphological closing with a spherical structural element is applied. The performance of the proposed method is assessed using quantitative metrics by comparing automatically derived lung borders with manually traced borders from an experienced radiologist. Datasets originating from the thin-slice thoracic CT data made available by the Lung Imaging Database Consortium (LIDC) [16, 17], intended for nodule segmentation, are chosen to facilitate the comparison of methods.
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Methods and materials
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Automated 3D grey level thresholding
In this study, a 3D approach [18] to lung field segmentation is proposed based on automated 3D grey level thresholding combined with 2D wavelet processing to highlight lung borders. A 3D morphological processing step is applied to deal with segmentation of the mediastinum following suggested approaches [11, 13].
In Figure 1
, the normalized grey level histogram (solid line) of a representative upper part of a thoracic volume is provided. Three peaks are shown corresponding to (a) lung parenchyma, (b) fat and (c) muscles. Two distributions are considered for thorax volume segmentation: one including lung parenchyma and background, and the other including fat and muscles. The separation of the two distributions is performed automatically by using minimum error thresholding, a method introduced by Kittler and Illingworth [15]. Specifically, the automated threshold selection (
) is formulated by minimizing the criterion function J(T):
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Figure 1. Original volume histogram of an upper partial lung volume(solid line), corresponding to lung parenchyma (a), fat (b) and muscle (c). The histogram is modelled by two Gaussian distributions, according to the minimum error thresholding method. Dashed lines: parenchyma (---), fat and muscle (...).
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Assuming modelling of the histogram by two Gaussian distributions (bimodal model), J(T) is given by:
where T expresses different grey level threshold values, h(g) is the frequency of occurrence of normalized grey level value (g), g
[0, 1], Pi are the priori probabilities, µi and 
i are the corresponding mean values and standard deviations, respectively, for the two distributions (i = 1,2).
The threshold value () yielding the lowest value for the criterion function corresponds to the minimum overlap area between the two Gaussian distributions, estimated by the minimum error thresholding technique. The two Gaussian distributions, as well as the threshold value (), are also provided in a representative example in Figure 1
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Wavelet lung border highlighting
Multiscale contrast enhancement accomplished in the context of a redundant wavelet representation is used for lung border highlighting. Wavelet transform provides information about local grey level variation (contrast) [18, 19]. The great advantage of wavelet analysis is that the image can be decomposed in different size scales, providing the capability to selectively enhance features of a certain size and to control noise amplification. At large scales (s), the wavelets have a large spatial extent to analyse coarse features such as pulmonary nodules whereas, at small scales, they have a small extent to analyse fine details such as thin junction lines. As a result, grey levels of lung border features are differentiated from the grey levels of their local background.
A fast, biorthogonal, redundant dyadic discrete wavelet transform, originally used to characterize signals from multiscale edges [20], is utilized in this work. The transform is implemented using a filter bank algorithm, called "algorithme à trous" (algorithm with holes) [21], which does not involve sub-sampling. The original image f(x,y) is decomposed into a multiresolution hierarchy of sub-band images, consisting of coarse approximation images Ssf and a set of wavelet images 
which provide the details that are available on the original image but which have disappeared in Ssf. All sub-band images have the same number of pixels as the original, and thus the representation is highly redundant. Coefficient sub-band images are proportional to the horizontal (h) and vertical (v) components of the multiscale gradient vector, as the wavelet basis functions used are approximate to the first derivative of a Gaussian distribution along the x and y axis. The magnitude representation of the gradient vector (M), exploited for isotropic processing is:
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In this study, two scales (s = 1,2) are considered suitable for capturing lung border anatomical features, as use of more than two scales results in over-segmentation errors owing to edge smoothing. Edge highlighting is accomplished by applying a gain factor (G) on wavelet magnitude sub-band image values.
where Ms(x,y) and 
are the initial and enhanced gradient magnitude values at position (x,y), respectively, and Gs>1 is the gain factor for each scale s. The edge-highlighted image is derived by reconstruction of the approximation images and the detail images based on the modified wavelet coefficients of the first two scales.
A combination of gain factors across the two scales 
was used to differentiate CT lung border features, such as junction lines and high-density pathologies attached to lung border. Initially, the useful range of gain factor values was determined to be 1–20, as gain factors >20 result in noise amplification artefacts in the reconstructed image. Selection of an optimal gain factor combination per scan 
was automatically guided by the value of the minimum error thresholding criterion function, based on wavelet-processed 3D bimodal Gaussian histogram modelling:
with k and l spanning 1–20.
In Figure 2, the volume histogram of the thorax (the same scan as in Figure 1) after the wavelet-highlighting step, the two Gaussian distributions that model the data, and the corresponding threshold value are provided.
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Figure 2. Volume histogram of the same upper partial volume asFigure 1 after application of wavelet pre-processing, as well as the two Gaussian distributions as modelled by the minimum error thresholding method. Dashed lines: parenchyma (---), fat and muscle (...). Vertical dashed line corresponds to the final threshold.
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Following the above methodology, optimal thresholds are automatically derived, based on wavelet-processed 3D stacks on a scan basis, and used to segment lung volumes. In addition to left and right lung volumes, segments such as trachea, left and right main bronchi, background pixels and cavities are also included. In order to exclude the above segments, size and connectivity criteria are used. Specifically, trachea and left and right main bronchi are eliminated using volume criteria, because left and right lung fields are the largest among the segmented structures. Background pixels outside the body, corresponding to grey level values lower than lung parenchyma, are eliminated by tracking objects connected to image borders. Finally, cavities contained in left and right lung volumes, corresponding to pixels with grey level values higher than those for lung parenchyma, are included by region filling [18, 22].
3D morphological processing
Application of the proposed automated 3D thresholding method tends to exclude anatomical structures belonging to lung parenchyma in the mediastinum, resulting in under-segmentation. To deal with under-segmentation of the mediastinum, 3D morphological processing is used. Specifically, 3D morphological closing operators were applied on left and right lung volume borders, treated as separate data, in order to avoid connection of the two lungs in the anterior and posterior junctions. To perform morphological closing, a spherical structural element with radius 9.380 mm was selected in order to capture the size of vessels, in agreement with other studies [11, 13, 18]. As a result of morphological closing, a smooth lung border is obtained, by joining breaks and filling holes, such as high-density pathologies attached to borders, smaller than the structuring element.
CT data sample
The thin-slice (thickness 0.625 mm) thoracic CT database available from LIDC, which contains lung nodules, consists of partial lung CT data (23 scans) and covers upper (8/23), lower (10/23) and middle (5/23) parts of lung volume, and is used for segmentation validation purposes. The database contains five scans with focal and/or diffuse high-density abnormalities attached to lung borders. This sample corresponds to a total of 883 2D slice images, with the number of slices per scan ranging from 28 to 62 (a mean of 38 slices per scan). Each CT slice has an image matrix of 512x512 pixels. Pixel size ranged between 0.625 mm and 0.742 mm, with mean value of 0.692 mm, depending on the physical size of the patient. From the 23 scans available in the database, one scan corresponding to thick-slice thickness (2.5 mm) was excluded.
Segmentation metrics
Accuracy of segmentation algorithms are usually evaluated by means of size (area or volume of the object) and shape metrics [23–25]. The main challenge in estimating lung field segmentation performance is "ground truth", i.e. defining lung field borders. In this study, an expert observer, a radiologist with 10 years of experience in interpretation of CT images, has defined the ground truth by generating manual outlines of the lung fields. For manual delineation of lung borders, a tablet (Wacom Intuos3, Tokyo, Japan) was used with an active area of 305x305 mm with 5080 dpi and an accuracy of±0.25 mm. For delineation of lung borders in the mediastinum, bifurcation of the main bronchi was considered to represent the lung border.
The degree of overlap between the two segmented volumes, as derived by observer (O), "ground truth" and computer (C), was used to assess size accuracy for left and right lungs separately. Overlap is defined as the ratio of intersection over the union of the two segmented volumes, the ground truth and the computer-generated "truth" [26]:
The value of OVERLAP is bound between zero (no overlap) and one (exact overlap).
To assess the difference in segmented border shape, mean, root mean square (rms) and maximum distance between the computer-defined and manually defined borders were calculated for each lung volume separately. Specifically, for each pixel on the computer-defined border (q), the minimum distance to the manually defined border (r) was calculated by:
where 
are the computer-defined border pixel locations and 
are the manually defined border pixel locations. The mean, rms and maximum distance were computed using Equations 11–13, respectively [13]:
where p is the number of pixels on the computer-defined border.
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Results
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Figure 3, which shows the effect of the 2D wavelet-highlighting step for four characteristic cases of the database analysed, demonstrates the thin anterior (a–c) and posterior (d–f) junction lines, a juxtapleural nodule (g–i) and a diffuse high-density abnormality (j–l). Low contrast edges between anterior or posterior junction lines (b, e) and abnormalities attached to lung borders (h, k) are also highlighted. For each case, the computer-defined border is provided as white colour overlay on the original images (c, f, i, l). An indicative 3D segmentation example of a lung middle part resulting from application of the proposed method with and without the 3D morphological processing step is provided in Figure 4a and Figure 4b, respectively. 3D morphological processing corrects the under-segmentation errors in the mediastinum.
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Figure 3. Parts of original, wavelet edge-highlighted and corresponding lung border obtained by the proposed method for four representative border features: (a–c) a thin anterior junction line, (d–f) a posterior junction line, (g–i) a juxtapleural nodule, and (j–l) a diffuse high-density abnormality. The selected gain factor combinations are (16, 16), (12, 16), (8, 9) and (8, 9), respectively.
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Figure 4. 3D partial lung volume(a) before and (b) after smoothing, with arrows indicating under-segmentation errors.
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In Figure 5, boxplots of the volume overlap accuracy of the proposed method are provided for left and right lungs separately. A segmentation overlap accuracy of 0.982±0.006 and 0.984±0.009 (mean±standard deviation) was obtained for left and right lung volumes, respectively. Border shape accuracy is provided in Figure 6 in terms of mean, rms and maximum border distance for left and right lung volumes of the data sample. Specifically, sample means obtained for left and right lung volumes, respectively, are 0.571±0.137 mm and 0.470±0.154 mm for dmean, 0.853±0.203 mm and 0.688±0.265 mm for drms, and 4.048±1.419 mm and 2.628±1.508 mm for dmax. The observed differences between left and right lung volumes, which are statistically significant (two-tailed Student's t-test for paired data, p<0.01), are attributed to the heart, which is more pronounced for the left lung and so results in shifting of the left lung contour from slice to slice [11]. The overall segmentation performance accuracy of the proposed method averaged over left and right lung volumes is 0.983±0.008 for lung volume overlap, whereas for shape differentiation it is 0.770±0.251 mm in terms of mean distance, 0.520±0.008 mm for rms distance and 3.327±1.637 mm for maximum distance.
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Figure 5. Overlap segmentation accuracy of the proposed segmentation method for left and right lung volumes of the 22 LIDC scans studied.
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Figure 6. Border shape differentiation metrics of the proposed segmentation method for left and right lung volumes of the 22 LIDC scans studied.
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To evaluate the effect of the wavelet edge-highlighting step of the proposed method in lung volume segmentation accuracy, the minimum error 3D thresholding method [15] was also applied to original 3D data. Application of the 3D minimum error thresholding technique without the wavelet pre-processing step results in failure to separate left and right lung volumes in half of the data sample (11 scans). Segmentation accuracy results are shown in Figures 7 and 8 for the rest of the cases (11 scans). Segmentation accuracy analysis is calculated for the entire lung volume by averaging left and right lung volumes. Specifically, segmentation volume overlap accuracy is 0.982±0.009 for the wavelet preprocessed data, compared with 0.968±0.005 for original data (Figure 7). This difference is statistically significant (p<0.0001) according to a paired two-tailed Student's t-test. Furthermore, the sample means for original and wavelet-processed CT scans, respectively, are 0.824±0.738 mm and 0.525±0.175 mm for dmean, 1.372±1.066 mm and 0.740±0.249 mm for drms, and 5.799±4.183 mm and 3.198±1.729 mm for dmax (Figure 8). These differences are also statistically significant (two-tailed Student's t-test for paired data, p<0.01).
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Figure 7. Overlap segmentation accuracy of the entire lung volume for 11 of the 22 original and wavelet-processed CT scans of the LIDC data sample.
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Figure 8. Border shape differentiation metrics of the entire lung volume for 11 of the 22 original and wavelet-processed CT scans of the LIDC data sample.
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Discussion
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In this work, an automated method for 3D lung field segmentation was developed and validated. Algorithm design has taken into account specifications for general purpose lung segmentation algorithms such as left and right lung separation, and dealing with juxtapleural nodules, mediastinum border, trachea and diaphragm. Specifically, a 3D minimum error thresholding technique is combined with a wavelet pre-processing step, with the aim of further highlighting the lung border. Lung border highlighting is targeted to lung border image features, such as junction lines and high-density focal and diffuse abnormalities, obtained by appropriate gain factor selection across two scales of wavelet analysis, automatically guided by the value of the minimum error thresholding criterion function. Finally, a morphological closing operation with a spherical structural element was applied to correct under-segmentation errors associated with the mediastinum. The processing time required to segment a scan consisting of 50 slices, using a 2.8 GHz core duo Intel processor with 2 GB RAM, is approximately 3 min.
The performance of the proposed method was assessed by comparing automatically derived lung borders with the manually derived ones traced by a radiologist, and by considering volume overlap and shape distance metrics. Specifically, segmentation performance in terms of overlap and drms averaged over left and right lung volumes was 0.983±0.008 and 0.770±0.251 mm, respectively. Furthermore, the performance was 0.520±0.008 mm and 3.327±1.637 mm in terms of dmean and dmax, respectively, averaged over left and right lung volumes. The results demonstrate that accurate segmentation is offered by the proposed segmentation method and justify the advantage of the wavelet pre-processing step, when compared with the 3D minimum error thresholding technique applied to original data. Of note, according to radiologists' comments, the five scans containing focal and/or diffuse high-density abnormalities attached to the lung borders were accurately segmented.
Comparison of method performance with other recently proposed lung field segmentation methods for CT data cannot be directly achieved owing to differences in slice thickness, data sets and segmentation accuracy metrics. Segmentation performance results based on quantitative metrics are also affected by manual border tracing (considered as the "ground truth") owing to the lack of established clinical criteria for defining lung borders and the amount of effort required to delineate lung volumes. Furthermore, volume overlap accuracy metrics proposed in the literature differ with respect to the union [23, 25] or the average [11, 14] between the computer-generated and manually defined borders, used as the denominator in Equation 9. Adopting the former definition, segmentation overlap accuracy tends to be decreased.
Besides the aforementioned differences, the performance of lung segmentation systems is provided. Specifically, Sun et al [14] reported a scheme, tested on a thick-slice database (10 mm thickness) containing 20 cases, which provided volume overlap as 0.885±0.043. Ukil et al [11] reported a segmentation scheme, tested on a thin-slice database (0.5 mm thickness) of eight normal cases, which gave a drms difference of 0.869 mm and overlap of 0.996. Hu et al [13], using thin-slice CT data (1–2 mm thickness), reported a drms value of 0.54 mm.
A limitation of the current study is the use of partial volume CT data, as they were the only reference data publicly available at the time of the study. However this is not expected to affect the algorithm's performance because the partial volumes span the entire length of the lungs. Use of LIDC reference thin-slice CT lung data is expected to facilitate the comparison of methods. Finally, improvement in the proposed method should include an automated 3D morphological smoothing step adapted to various sizes [11] of lung border irregularities.
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Conclusions
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An automated 3D lung segmentation algorithm was developed combining wavelet pre-processing for highlighting lung border edges and the minimum error thresholding technique to segment the lung volume. The proposed method was tested on a partial volume reference dataset, consisting of thin-slice CT data, provided by LIDC. The results demonstrate an accurate system in terms of both volume and shape. The effect of the wavelet pre-processing step was beneficial to the method, as assessed by comparing the proposed method with 3D minimum error thresholding. The method could be used as an initial step in applications aimed at computerized detection, classification and quantification of focal or diffuse lung abnormalities.
Received for publication December 22, 2006.
Revision received April 2, 2007.
Accepted for publication April 26, 2007.
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Abstract
Introduction
