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Diminution index: A novel 3D feature for pulmonary nodule detection
International Congress Series 1281 (2005) 1093 – 1098
www.ics-elsevier.com
Diminution index: A novel 3D feature for pulmonary nodule detection Sumiaki Matsumotoa,T, Yoshiharu Ohnoa, Hitoshi Yamagatab, Hiroshi Asahinab, Ken-ichi Komatsub, Kazuro Sugimuraa a
Department of Radiology, Kobe University Graduate School of Medicine, Japan b Toshiba Medical Systems Corporation, Japan
Abstract. The core issue in computer-aided detection (CAD) of lung nodules in CT (computed tomography) images is the problem of detecting nodules attached to vessels as well as isolated nodules while keeping the number of false positives due to pulmonary blood vessels at a low level. As a solution to this problem, we propose a novel 3D feature termed gdiminution indexh that has a capability to differentiate between pulmonary blood vessels and nodules attached to vessels. The diminution index deals with a 3D region obtained by exploring the nodule candidate at hand and its surrounding in a centrifugal direction with respect to the nodule candidate, and gives a measure of diminution of the 3D region in the centrifugal direction. In this study, a straightforward rule-based nodule detection scheme that employs the diminution index and 5 auxiliary features was evaluated using a data set prepared by placing simulated nodules contiguous to pulmonary blood vessels in clinical CT images. The scheme could detect the majority (78%) of simulated nodules with a moderate rate of false positives (5.3 per scan), indicating that the diminution index has a promising capability in computer-aided detection of lung nodules in CT images. D 2005 CARS & Elsevier B.V. All rights reserved. Keywords: Computer-aided detection; Lung nodule; Pulmonary blood vessel; Computed tomography
1. Introduction In computer-aided detection (CAD) of lung nodules in CT (computed tomography) images, pulmonary blood vessels constitute the main cause of false positives. Detection of pulmonary nodules would involve no difficulty if isolation of nodules from pulmonary blood vessels could be assumed. In practice, we often encounter nodules grossly attached T Corresponding author. E-mail address: [email protected] (S. Matsumoto). 0531-5131/ D 2005 CARS & Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2005.03.153
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to pulmonary blood vessels. Therefore, the core issue is the problem of detecting nodules attached to vessels as well as isolated nodules while keeping the number of false positives due to pulmonary blood vessels at a low level. As a solution to this problem, we propose a novel 3D feature that has a capability to differentiate between pulmonary blood vessels and nodules attached to vessels. Computation of this feature involves exploration of the nodule candidate at hand and its surrounding in a centrifugal direction with respect to the nodule candidate. This exploration yields a 3D region that captures a structure, if any, adjoining the nodule candidate in addition to the nodule candidate itself. If the nodule candidate is part of a blood vessel, the 3D region thus obtained just represents a short segment of the same blood vessel. Therefore, the diminution of the 3D region in the centrifugal direction is expected to be absent or at most mild for a nodule candidate representing part of a blood vessel; however, it is expected to be substantial for a nodule candidate that actually represents a nodule. The proposed 3D feature, termed gdiminution index,h gives a quantitative measure of the above diminution. In this study, we evaluated the effectiveness of the diminution index using a data set prepared by placing simulated nodules contiguous to pulmonary blood vessels in clinical CT images. 2. Materials and methods 2.1. Extraction of nodule candidates Nodule candidates are extracted using deformable ellipsoid models through the following steps. 1. After segmentation of the lung region in CT image data, the foreground of the lung region is obtained using adaptive thresholding [1]. 2. Referring to the extremal points of the distance transform as the initial points, an ellipsoid model is created and initialized with the sphere which is centered at the initial point at hand and has the radius given by the corresponding extremal value of the distance transform. 3. The ellipsoid model is deformed using a technique for deformable Fourier surfaces [2]. 4. Referring to the ellipsoid after deformation as the bounding ellipsoid, a tentative nodule candidate is defined as the part of the foreground enclosed by the bounding ellipsoid. 5. A local volume of interest containing the tentative nodule candidate is binarized by assigning 1 only to the voxels with gray levels greater than the mean gray level along the boundary of the tentative nodule candidate. 6. In the resultant binary volume data, the precursor region is defined as the connected components that overlap the tentative nodule candidate. Finally, the nodule candidate is obtained as the part of the precursor region enclosed by the bounding ellipsoid. 2.2. Computation of diminution index Now a 3D region is derived by means of directed region growing within the precursor region in a centrifugal direction with respect to the center of the bounding ellipsoid over a distance proportional to the size of the bounding ellipsoid. The directed region growing is carried out in multiple centrifugal directions according to a predetermined rule, yielding
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multiple instances of the 3D region. For each instance, a numeric is computed that quantifies the extent to which the current 3D region diminishes in the corresponding centrifugal direction; multiple instances of this numeric are thus computed. The computation involves division of the 3D region into its proximal and distal parts with the former being the part inside the bounding ellipsoid and the latter being the remaining part. The numeric is then given by (1 R), where R is the ratio of the volume of the distal part to that of the proximal part. The diminution index is defined as the minimum among the multiple instances of the numeric. Owing to this definition, the centrifugal direction corresponding to the instance of the 3D region that eventually determines the diminution index tends to be aligned with the axis of a vessel segment. Therefore, the diminution indices are generally low for nodule candidates caused by blood vessels. In particular, if the vessel segment shows no local tapering, the diminution index becomes 0. By contrast, the diminution index gets the maximum of 1 if nodule candidates represent ideally spherical or ellipsoidal isolated nodules. For nodule candidates representing nodules attached to vessels, the value of the diminution index is less than 1, but its expected range is higher than the range expected for nodule candidates caused by blood vessels. Examples of the instance of the 3D region that eventually determines the diminution index are shown in Fig. 1. 2.3. Nodule detection scheme To assess the proposed feature, we used a nodule detection scheme that employs the diminution index and 5 auxiliary features under a straightforward rule that any nodule candidate is rejected if one of its features is below a corresponding cut-off value. Given a nodule candidate, the 5 auxiliary features consist of (i) effective diameter of the nodule candidate, (ii) contrast, as defined by the difference between the mean gray level in the nodule candidate and that immediately outside the nodule candidate, (iii) sphericity, as defined through a principal component analysis of the nodule candidate [3], (iv) a measure of dispersion of the gray-level gradients on the bounding ellipsoid, and (v) a measure of displacement of the corresponding ellipsoid model with respect to the corresponding initial point. 2.4. Experiment The image data set used in this study was prepared by placing 130 simulated nodules ranging from 3 to 5 mm in diameter such that they were contiguous to pulmonary blood vessels in 16 almost normal clinical CT images of the chest. Each simulated nodule is created using a cross-section of a pulmonary blood vessel which can be indistinguishable from that of a nodule. Specifically, it is created by taking a small region of interest (ROI) containing such a cross-section of a vessel, subjecting the ROI to linear modification of gray levels, and rotating the ROI in a cartwheel fashion. Examples of the simulated nodules thus placed are shown in Fig. 2. The CT images were acquired using a multi-detector row CT scanner (Aquilion 16, Toshiba) with the following parameters: 120 kVp, 300 mAs, 16 0.5 mm collimation, 0.5 s per rotation, and table feed of 7.5 mm per rotation. All scanned images were reconstructed with the section width and interval of 0.5 mm and the pixel size of 0.53–0.64 mm.
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Fig. 1. Left lane—shown in the middle is a surface-rendered view of the precursor region for a nodule attached to vessels. The corresponding nodule candidate is the part of the precursor region enclosed by the overlaid ellipsoid (bounding ellipsoid). In another view of the precursor region at the bottom, the 3D region that eventually determines the diminution index is marked by shading its proximal part lightly and shading its distal part darkly. At the top, volume rendering of a neighbourhood of the nodule candidate is shown for reference. Right lane— similar illustrations with respect to a nodule candidate at a vessel branching.
Fig. 2. Examples of simulated nodules placed contiguous to pulmonary blood vessels.
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For the purpose of separate development and evaluation of the scheme, the image data set was split into two subsets. One subset reserved for development was prepared from 4 scans and contained 30 simulated nodules while the other subset reserved for evaluation was prepared from 12 scans and contained 100 simulated nodules. The cut-off values of the effective diameter and the contrast were preset to 3 mm and 140 Hounsfield units, respectively. The cut-off values of the remaining auxiliary features were adjusted using the subset reserved for development and fixed thereafter. To examine the performance of the nodule detection scheme with respect to the subset reserved for evaluation, a free-response receiver operating characteristic (FROC) curve was produced by varying the cut-off value of the diminution index. Pre-existing nodules in the data set were excluded from this analysis. 3. Results Fig. 3 shows the resultant FROC curve. At its rightmost point, the sensitivity of detecting simulated nodules was 100% and the number of false positives was 60 per scan. As the cut-off value of the diminution index increased, the number of false positives was markedly reduced, leading to 5.3 (64/12) false positives per scan with the sensitivity of 78% at the cut-off value of the diminution index of 0.71. Of the 64 false positives generated at this cut-off value, 50 were due to pulmonary blood vessels, occurring for the most part at or near the pulmonary hila. 4. Discussion Detection of nodules attached to vessels necessitates incorporation of some knowledge about the pulmonary vasculature into a CAD algorithm. Although it would be challenging to get computers to understand the entire pulmonary vasculature, it is less difficult to partially harness domain knowledge for the purpose of CAD. The pulmonary vasculature is made up of branching vessels, and as it goes from the pulmonary hila to the periphery of the lungs, the size of vessels gradually tapers down in general. The diminution index just
Fig. 3. Performance of nodule detection scheme. Plus sign corresponds to the cut-off value of the diminution index of 0.71.
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exploits this gradual tapering principle. The principle, however, breaks down near the pulmonary hila because pulmonary blood vessels decrease rapidly in size as they branch out of the mediastinum. Therefore, the frequent occurrence of false positives due to hilar pulmonary blood vessels as described above was a very logical result. Maybe our future CAD scheme has to take account of the positions of nodule candidates with respect to the pulmonary hila. Nevertheless, the present CAD scheme could detect the majority of simulated nodules with a moderate rate of false positives in spite of its straightforward rule, demonstrating the overall effectiveness of the diminution index. In conclusion, we have introduced a novel 3D feature that reflects a basic difference between nodules and pulmonary blood vessels. The result of this study indicates that the diminution index has a promising capability in computer-aided detection of lung nodules in CT images. References [1] S. Manay, A. Yezzi, Antigeometric diffusion for adaptive thresholding and fast segmentation, IEEE Trans. Image Process. 12 (2003) 1310 – 1323. [2] L.H. Staib, J.S. Duncan, Model-based deformable surface finding for medical images, IEEE Trans. Med. Imag. 15 (1996) 720 – 731. [3] G.D. Rubin, et al., Online-only appendix (http://radiology.rsnajnls.org/cgi/content/full/2341040589/DC1) to (Pulmonary nodules on multi-detector row CT scans: performance comparison of radiologists and computeraided detection, Radiology 234 (2005) 274–283.
www.ics-elsevier.com
Diminution index: A novel 3D feature for pulmonary nodule detection Sumiaki Matsumotoa,T, Yoshiharu Ohnoa, Hitoshi Yamagatab, Hiroshi Asahinab, Ken-ichi Komatsub, Kazuro Sugimuraa a
Department of Radiology, Kobe University Graduate School of Medicine, Japan b Toshiba Medical Systems Corporation, Japan
Abstract. The core issue in computer-aided detection (CAD) of lung nodules in CT (computed tomography) images is the problem of detecting nodules attached to vessels as well as isolated nodules while keeping the number of false positives due to pulmonary blood vessels at a low level. As a solution to this problem, we propose a novel 3D feature termed gdiminution indexh that has a capability to differentiate between pulmonary blood vessels and nodules attached to vessels. The diminution index deals with a 3D region obtained by exploring the nodule candidate at hand and its surrounding in a centrifugal direction with respect to the nodule candidate, and gives a measure of diminution of the 3D region in the centrifugal direction. In this study, a straightforward rule-based nodule detection scheme that employs the diminution index and 5 auxiliary features was evaluated using a data set prepared by placing simulated nodules contiguous to pulmonary blood vessels in clinical CT images. The scheme could detect the majority (78%) of simulated nodules with a moderate rate of false positives (5.3 per scan), indicating that the diminution index has a promising capability in computer-aided detection of lung nodules in CT images. D 2005 CARS & Elsevier B.V. All rights reserved. Keywords: Computer-aided detection; Lung nodule; Pulmonary blood vessel; Computed tomography
1. Introduction In computer-aided detection (CAD) of lung nodules in CT (computed tomography) images, pulmonary blood vessels constitute the main cause of false positives. Detection of pulmonary nodules would involve no difficulty if isolation of nodules from pulmonary blood vessels could be assumed. In practice, we often encounter nodules grossly attached T Corresponding author. E-mail address: [email protected] (S. Matsumoto). 0531-5131/ D 2005 CARS & Elsevier B.V. All rights reserved. doi:10.1016/j.ics.2005.03.153
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to pulmonary blood vessels. Therefore, the core issue is the problem of detecting nodules attached to vessels as well as isolated nodules while keeping the number of false positives due to pulmonary blood vessels at a low level. As a solution to this problem, we propose a novel 3D feature that has a capability to differentiate between pulmonary blood vessels and nodules attached to vessels. Computation of this feature involves exploration of the nodule candidate at hand and its surrounding in a centrifugal direction with respect to the nodule candidate. This exploration yields a 3D region that captures a structure, if any, adjoining the nodule candidate in addition to the nodule candidate itself. If the nodule candidate is part of a blood vessel, the 3D region thus obtained just represents a short segment of the same blood vessel. Therefore, the diminution of the 3D region in the centrifugal direction is expected to be absent or at most mild for a nodule candidate representing part of a blood vessel; however, it is expected to be substantial for a nodule candidate that actually represents a nodule. The proposed 3D feature, termed gdiminution index,h gives a quantitative measure of the above diminution. In this study, we evaluated the effectiveness of the diminution index using a data set prepared by placing simulated nodules contiguous to pulmonary blood vessels in clinical CT images. 2. Materials and methods 2.1. Extraction of nodule candidates Nodule candidates are extracted using deformable ellipsoid models through the following steps. 1. After segmentation of the lung region in CT image data, the foreground of the lung region is obtained using adaptive thresholding [1]. 2. Referring to the extremal points of the distance transform as the initial points, an ellipsoid model is created and initialized with the sphere which is centered at the initial point at hand and has the radius given by the corresponding extremal value of the distance transform. 3. The ellipsoid model is deformed using a technique for deformable Fourier surfaces [2]. 4. Referring to the ellipsoid after deformation as the bounding ellipsoid, a tentative nodule candidate is defined as the part of the foreground enclosed by the bounding ellipsoid. 5. A local volume of interest containing the tentative nodule candidate is binarized by assigning 1 only to the voxels with gray levels greater than the mean gray level along the boundary of the tentative nodule candidate. 6. In the resultant binary volume data, the precursor region is defined as the connected components that overlap the tentative nodule candidate. Finally, the nodule candidate is obtained as the part of the precursor region enclosed by the bounding ellipsoid. 2.2. Computation of diminution index Now a 3D region is derived by means of directed region growing within the precursor region in a centrifugal direction with respect to the center of the bounding ellipsoid over a distance proportional to the size of the bounding ellipsoid. The directed region growing is carried out in multiple centrifugal directions according to a predetermined rule, yielding
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multiple instances of the 3D region. For each instance, a numeric is computed that quantifies the extent to which the current 3D region diminishes in the corresponding centrifugal direction; multiple instances of this numeric are thus computed. The computation involves division of the 3D region into its proximal and distal parts with the former being the part inside the bounding ellipsoid and the latter being the remaining part. The numeric is then given by (1 R), where R is the ratio of the volume of the distal part to that of the proximal part. The diminution index is defined as the minimum among the multiple instances of the numeric. Owing to this definition, the centrifugal direction corresponding to the instance of the 3D region that eventually determines the diminution index tends to be aligned with the axis of a vessel segment. Therefore, the diminution indices are generally low for nodule candidates caused by blood vessels. In particular, if the vessel segment shows no local tapering, the diminution index becomes 0. By contrast, the diminution index gets the maximum of 1 if nodule candidates represent ideally spherical or ellipsoidal isolated nodules. For nodule candidates representing nodules attached to vessels, the value of the diminution index is less than 1, but its expected range is higher than the range expected for nodule candidates caused by blood vessels. Examples of the instance of the 3D region that eventually determines the diminution index are shown in Fig. 1. 2.3. Nodule detection scheme To assess the proposed feature, we used a nodule detection scheme that employs the diminution index and 5 auxiliary features under a straightforward rule that any nodule candidate is rejected if one of its features is below a corresponding cut-off value. Given a nodule candidate, the 5 auxiliary features consist of (i) effective diameter of the nodule candidate, (ii) contrast, as defined by the difference between the mean gray level in the nodule candidate and that immediately outside the nodule candidate, (iii) sphericity, as defined through a principal component analysis of the nodule candidate [3], (iv) a measure of dispersion of the gray-level gradients on the bounding ellipsoid, and (v) a measure of displacement of the corresponding ellipsoid model with respect to the corresponding initial point. 2.4. Experiment The image data set used in this study was prepared by placing 130 simulated nodules ranging from 3 to 5 mm in diameter such that they were contiguous to pulmonary blood vessels in 16 almost normal clinical CT images of the chest. Each simulated nodule is created using a cross-section of a pulmonary blood vessel which can be indistinguishable from that of a nodule. Specifically, it is created by taking a small region of interest (ROI) containing such a cross-section of a vessel, subjecting the ROI to linear modification of gray levels, and rotating the ROI in a cartwheel fashion. Examples of the simulated nodules thus placed are shown in Fig. 2. The CT images were acquired using a multi-detector row CT scanner (Aquilion 16, Toshiba) with the following parameters: 120 kVp, 300 mAs, 16 0.5 mm collimation, 0.5 s per rotation, and table feed of 7.5 mm per rotation. All scanned images were reconstructed with the section width and interval of 0.5 mm and the pixel size of 0.53–0.64 mm.
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Fig. 1. Left lane—shown in the middle is a surface-rendered view of the precursor region for a nodule attached to vessels. The corresponding nodule candidate is the part of the precursor region enclosed by the overlaid ellipsoid (bounding ellipsoid). In another view of the precursor region at the bottom, the 3D region that eventually determines the diminution index is marked by shading its proximal part lightly and shading its distal part darkly. At the top, volume rendering of a neighbourhood of the nodule candidate is shown for reference. Right lane— similar illustrations with respect to a nodule candidate at a vessel branching.
Fig. 2. Examples of simulated nodules placed contiguous to pulmonary blood vessels.
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For the purpose of separate development and evaluation of the scheme, the image data set was split into two subsets. One subset reserved for development was prepared from 4 scans and contained 30 simulated nodules while the other subset reserved for evaluation was prepared from 12 scans and contained 100 simulated nodules. The cut-off values of the effective diameter and the contrast were preset to 3 mm and 140 Hounsfield units, respectively. The cut-off values of the remaining auxiliary features were adjusted using the subset reserved for development and fixed thereafter. To examine the performance of the nodule detection scheme with respect to the subset reserved for evaluation, a free-response receiver operating characteristic (FROC) curve was produced by varying the cut-off value of the diminution index. Pre-existing nodules in the data set were excluded from this analysis. 3. Results Fig. 3 shows the resultant FROC curve. At its rightmost point, the sensitivity of detecting simulated nodules was 100% and the number of false positives was 60 per scan. As the cut-off value of the diminution index increased, the number of false positives was markedly reduced, leading to 5.3 (64/12) false positives per scan with the sensitivity of 78% at the cut-off value of the diminution index of 0.71. Of the 64 false positives generated at this cut-off value, 50 were due to pulmonary blood vessels, occurring for the most part at or near the pulmonary hila. 4. Discussion Detection of nodules attached to vessels necessitates incorporation of some knowledge about the pulmonary vasculature into a CAD algorithm. Although it would be challenging to get computers to understand the entire pulmonary vasculature, it is less difficult to partially harness domain knowledge for the purpose of CAD. The pulmonary vasculature is made up of branching vessels, and as it goes from the pulmonary hila to the periphery of the lungs, the size of vessels gradually tapers down in general. The diminution index just
Fig. 3. Performance of nodule detection scheme. Plus sign corresponds to the cut-off value of the diminution index of 0.71.
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exploits this gradual tapering principle. The principle, however, breaks down near the pulmonary hila because pulmonary blood vessels decrease rapidly in size as they branch out of the mediastinum. Therefore, the frequent occurrence of false positives due to hilar pulmonary blood vessels as described above was a very logical result. Maybe our future CAD scheme has to take account of the positions of nodule candidates with respect to the pulmonary hila. Nevertheless, the present CAD scheme could detect the majority of simulated nodules with a moderate rate of false positives in spite of its straightforward rule, demonstrating the overall effectiveness of the diminution index. In conclusion, we have introduced a novel 3D feature that reflects a basic difference between nodules and pulmonary blood vessels. The result of this study indicates that the diminution index has a promising capability in computer-aided detection of lung nodules in CT images. References [1] S. Manay, A. Yezzi, Antigeometric diffusion for adaptive thresholding and fast segmentation, IEEE Trans. Image Process. 12 (2003) 1310 – 1323. [2] L.H. Staib, J.S. Duncan, Model-based deformable surface finding for medical images, IEEE Trans. Med. Imag. 15 (1996) 720 – 731. [3] G.D. Rubin, et al., Online-only appendix (http://radiology.rsnajnls.org/cgi/content/full/2341040589/DC1) to (Pulmonary nodules on multi-detector row CT scans: performance comparison of radiologists and computeraided detection, Radiology 234 (2005) 274–283.