Can the spherical gold standards be used as an alternative to painted gold standards for the computerized detection of lesions using voxel-based classification?

Abstract

Purpose

For the development of computer-assisted detection (CAD) software using voxel-based classification, gold standards defined by pixel-by-pixel painting, called painted gold standards, are desirable. However, for radiologists who define gold standards, a simplified method of definition is desirable. One of the simplest methods of defining gold standards is a spherical region, called a spherical gold standard. In this study, we investigated whether spherical gold standards can be used as an alternative to painted gold standards for computerized detection using voxel-based classification.

Materials and methods

The spherical gold standards were determined by the center of gravity and the maximum diameter. We compared two types of gold standard, painted gold standards and spherical gold standards, by two types of CAD software using voxel-based classification.

Results

The time required to paint the area of one lesion was 4.7–6.5 times longer than the time required to define a spherical gold standard. For the same performance of the CAD software, the number of training cases required for the spherical gold standard was 1.6–7.6 times that for the painted gold standards.

Conclusion

Spherical gold standards can be used as an alternative to painted gold standards for the computerized detection of lesions with simple shapes.

Appendix: Algorithm of CAD software

Basic detection algorithm

In the preprocessing, input images are first resampled using trilinear interpolation to obtain the isotropic volume. The resampled voxel size is equal to the pixel size of the input image. After that, segmentation is carried out.

In the lesion candidate extraction, a classifier ensemble trained by AdaBoost [13] is employed to classify the voxels of the target region. All the weak classifiers within the classifier ensembles are decision stumps [14]. The 21 feature values used in the voxel-based classification are as follows:

• voxel value

• statistics of voxel value: four types (mean, standard deviation, skewness, and kurtosis) × three cubic region of interest (ROI) sizes (length = {3, 5, 9} [voxels])

• difference of Gaussian (DoG) (three pairs of σ, {1, 2}, {2, 4}, {4, 8} [voxels])

• shape index [15] (σ = {2, 4} [voxels])

• multiscale dot and line enhancement filter [16]

• multiscale vessel enhancement filter [17] (the parameters α, β, and c are set to 0.5, 0.5, and 500, respectively).

The number of weak classifiers is set to 200 in the experiments. In the training of the classifiers, random under sampling is carried out to reduce the number of normal samples relative to the number of lesion samples. The voxels for which the output of the classifier is greater than or equal to 0 are extracted, and component analysis is performed. After that, small-region removal is performed.

In the region-based classification, a classifier ensemble trained by AdaBoost is employed to calculate the likelihoods of the lesion candidates based on 70 feature values of the candidates. All the weak classifiers within the classifier ensembles are decision stumps. The number of weak classifiers is set to 200 in the experiments. The feature values are as follows:

• volume (V) (mm³) and surface area (mm²)

• two surface features (surface exposure ratio R_SE and surface area to volume ratio R_SV in [18])

• contrast measures (Contrast1 and Contrast2 in [19])

• sphericity, ratio of V to the volume in the bounding box, and similarity to sphere [3]

• statistics of the distance between the center of the candidate and its boundary (minimum, maximum, mean, second moment, standard deviation, skewness, kurtosis, and minimum/maximum)

• statistics of voxel value, DoG, shape index, multiscale dot enhancement filter, multiscale line enhancement filter, and multiscale vessel enhancement filter¹ (minimum, maximum, mean, standard deviation, skewness, and kurtosis).

Cerebral aneurysm detection

In the preprocessing, the artery region is extracted by the algorithm in [20]. In the lesion candidate extraction, the voxels with shape index (σ = 2.0 [voxel]) ≥ 0.75 in the artery region are input to the voxel-based classifier. The range of σ for calculating the multiscale dot, line, or vessel enhancement filter is set to {1, 2^1/2, 2, 2^3/2, 4} voxels. The threshold for the small-region removal is set to 1 (mm³) in the experiments. In the region-based classification, the surface region for calculating R_SE is extracted from the extracted artery region.

Lung nodule detection

In the preprocessing, the lung volume L is obtained by the algorithm written in the later subsection. Using the extracted lung volume L, the binarized lung volume L_bin is extracted as follows:

$${\mathbf{L}}_{\text{bin}} = \, \left\{ p|I({\mathbf{x}}) \ge - 7 50,p \in {\mathbf{L}}\right\} ,$$

(5)

where I(x) is the CT value (HU) of voxel p and x is the three-dimensional (3D) coordinates of voxel p. In the lesion candidate extraction, the voxels in L_bin are input to the voxel-based classifier. The range of σ for calculating the multiscale dot, line, or vessel enhancement filter is set to {1, 2, 4, 8} voxels. The threshold for the small-region removal is set to 8 (mm³) in the experiments. In the region-based classification, the surface region for calculating R_SE is extracted from L_bin.

Algorithm of lung volume segmentation

The processing procedure of lung segmentation is described as follows.

• (1) Extraction of the body trunk region R_body.

  • (1-1) The CT volume data are resampled to 2.0 mm isotropic voxels.

  • (1-2) In each axial slice, the largest binarized area with a CT value of − 150 HU or higher is selected. After that, two-dimensional (2D) cavity deletion [21] is carried out.

  • (1-3) Morphological closing with a spherical kernel of 10 mm radius is carried out.

  • (1-4) After resampling to the original size, the result is defined as R_body.

• (2) Extraction of the bone region R_bone.

  • (2-1) The CT volume data are resampled to 2.0 mm isotropic voxels.

  • (2-2) In R_body, the largest binarized area with a CT value of 200 HU or higher is extracted. After that, morphological closing with a spherical kernel of 5 mm radius is carried out.

  • (2-3) After resampling to the original size, morphological dilation with a spherical kernel of 1.5 voxel radius is carried out. The result is defined as R_bone.

• (3) Extraction of thoracic slice range.

  • (3-1) The CT volume data are resampled to 2.0 mm isotropic voxels.

  • (3-2) In each axial slice of R_body, the likelihood of thoracic slice L_th(z) is calculated as follows:

    $$L_{\text{th}} (z) = \frac{{M_{\text{B}} (z)}}{{\overline{{M_{\text{B}} }} }}R_{\text{air}} (z),$$

    (6)

  • (3-3) where M_B(z) is the second moment of R_bone in axial slice z, $\overline{{M_{\text{B}} }}$ is the mean of M_B(z), and R_air(z) is the ratio of the number of voxels with CT value ≤ − 500 HU to the total number of voxels of R_body in the axial slice.

  • (3-4) The slice range above the mean of L_th(z) including the maximum of L_th(z) is defined as the thoracic slice range Z_th = [z_{th_min}, z_{th_max}].

• (4) Estimation of border between left and right sides of body trunk.

  • (4-1) The CT volume data are resampled to 2.0 mm isotropic voxels.

  • (4-2) In each axial slice from the center quarter region of Z_th, partial maximum intensity projection images of R_body and R_bone, named M_body(z) and M_bone(z), respectively, are generated from five axial slices centered at z.

  • (4-3) The center of gravity of M_body(z) (g_x(z), g_y(z)) is calculated. After that, the number of voxels for which M_bone(z) = 1 is counted every three degrees around M_body(z), and the maximum direction is defined as deg(z).

  • (4-4) The medians of g_x(z) and g_y(z) converted to the coordinates of the original CT volume are defined as G_x and G_y, respectively. The median of deg(z) is defined as D. The border between the left and right sides of the body trunk is set using these values.

• (5) Extraction of pulmonary initial lung mask R_init.

  • (5-1) In R_body within the thoracic slice range Z_th, an initial threshold Th_init is calculated using Otsu’s method [22]. After that, the binarized area with a CT value of Th_init or lower is extracted. These processes are performed on the left and right sides of body trunk, which are divided at the border determined in (4-4).

  • (5-2) In each axial slice from the range of Z_th, connected component analysis is performed, and then up to two components with an area of 2500 mm² or more are extracted as seed areas.

  • (5-3) Region growing is carried out in R_body, where the growing threshold is set to Th_init.

  • (5-4) Morphological dilation with a spherical kernel of 1.9 voxel radius is carried out. The result is defined as R_init.

• (6) Extraction of the bronchi region R_bronchi.

  • (6-1) A gray-scale histogram of the voxels in R_init is generated, and the peak CT value of the histogram between the minimum CT value in R_body and − 650 HU, named T_peak, is obtained.

  • (6-2) In R_init within 10 cm of the upper end of the range of Z_th, the binarized area with a CT value of Th_peak or lower is extracted, and then morphological opening with a spherical kernel of 2.5 mm radius and connected component analysis are carried out. Among the obtained connected components, the component with the shortest distance between the center of gravity of the component and (G_x, G_y) within 10 cm is extracted

  • (6-3) Morphological opening with a spherical kernel of 2.5 mm radius and connected component analysis are carried out, and then the largest component is extracted.

  • (6-4) The region obtained in (6-3) is set as a seed region, and region growing is repeated at most eight times with the following extension condition:

    $$T_{\text{bronchi}} (n) = \left\{ {\begin{array}{*{20}l} {{ \hbox{max} }\left( {I_{ \hbox{min} } ,\mu_{\text{seed}} - \sigma_{\text{seed}} } \right)} \hfill & {{\text{if }}\,n = 1} \hfill \\ {T_{\text{bronchi}} (1) + \frac{64}{{2^{{\left( {n - 2} \right)}} }}} \hfill & {{\text{if }}\,2 \le n \le 8} \hfill \\ \end{array} } \right.,$$

    (7)

    where I_min is the minimum CT value in R_body. μ_seed and σ_seed are the mean and standard deviation of the CT values in the seed region, respectively. If the volume of the nth region growing is less than twice the volume of the initial region growing, the result of the nth region growing is utilized. However, if this condition is not satisfied after the eighth region growing, the result of the initial region growing is used.

  • (6-5) Morphological dilation with a spherical kernel of 2.5 mm radius is carried out. The result is defined as R_bronchi.

  • (6-6) The region obtained by removing R_bronchi from R_init is defined as R_coarse.

• (7) Lung separation.

  Connected component analysis is performed in R_coarse, and the two largest connected components are extracted. If the number of voxels of the largest component exceeds 90% of the number of voxels of R_coarse, it is considered that both lung regions are connected, and the following processing is performed.

  • (7-1) In each axial slice, the Canny filter [23] is applied to detect the edges. The parameters of hysteresis thresholding are set to Th_min = 250 and Th_max = 2500. After that, morphological closing with a spherical kernel of 2.5 mm radius is carried out. The result is defined as E(x, y, z).

  • (7-2) In each axial slice of R_coarse, the largest binarized area is extracted. If the number of voxels of the extracted area exceeds 90% of the number of voxels of R_coarse in the same axial slice, it is considered that both lung regions are connected, and separation voxels, named Sep(x, y, z), are set as follows:

    • (a) Both lungs are separated in the axial slice at z − 1:

      $${\text{Sep}}(x,y,z) = \left\{ {\begin{array}{*{20}l} { 1} \hfill & {{\text{if}}\,R_{\text{coarse}} (x,y,z) = 1\,{\text{and}}\,R_{\text{init}} (x,y,z - 1) = 0\,{\text{and}}\,E(x,y,z) = 1} \hfill \\ { 0} \hfill & {\text{otherwise}} \hfill \\ \end{array} } \right.,$$

      (8)

      where R_coarse(x, y, z) is the voxel of R_coarse at (x, y, z), and R_init(x, y, z) is the voxel of R_init at (x, y, z).

    • (b) Both lungs are connected in the axial slice at z − 1:

      $${\text{Sep}}(x,y,z) = \left\{ {\begin{array}{*{20}l} { 1} \hfill & {{\text{if}}\,R_{\text{coarse}} (x,y,z) = 1\,{\text{and}}\,{\text{Sep}}^{'(x,y,z - 1)} = 0\,{\text{and}}\,E(x,y,z) = 1} \hfill \\ { 0} \hfill & {\text{otherwise}} \hfill \\ \end{array} } \right.,$$

      (9)
      $${\text{Sep}}^{\prime } (x,y,z) = \left\{ {\begin{array}{*{20}l} { 1} \hfill & {{\text{if}} \sum\nolimits_{i = x - 1}^{x + 1} {\sum\nolimits_{j = y - 1}^{y + 1} {\text{Sep}} } (i,j,z) \ge 1} \hfill \\ { 0} \hfill & {\text{otherwise }} \hfill \\ \end{array} } \right..$$

      (10)

  • (7-4) The voxels with Sep(x, y, z) = 1 are removed from R_coarse.

  • (7-5) Connected component analysis is performed on the result of (7-3). If the regions of both lungs are not separated, morphological erosion with a spherical kernel of 1.9 voxel radius is repeated until both lungs are separated (up to five times). The result, called R_separated, is represented by ternarized volume data (0: background, 1: label of the right lung, 2: label of the left lung).

  • (7-6) Gray-scale morphological reconstruction by recursive dilation [24] with a spherical kernel of 1.9 voxel radius is applied to R_separated. R_coarse is utilized as the mask of the reconstruction. The result is used in the next step.

• (8) Resegmentation of left and right lungs.

  • (8-1) Closing with a spherical kernel of 10 mm radius is applied to the masks for the left and right lungs to include lung nodules and pulmonary vessels. After that, 3D cavity deletion [21] is carried out.

  • (8-2) After obtaining the union before and after the processing of (8-1), intersection voxels of R_bronchi and R_bone are removed. The result is defined as L.