A semiautomatic segmentation method for prostate in CT images using local texture classification and statistical shape modeling

Abstract

Purpose

Prostate segmentation in computed tomography (CT) images is useful for treatment planning and procedure guidance such as external beam radiotherapy and brachytherapy. However, because of the low, soft tissue contrast of CT images, manual segmentation of the prostate is a time‐consuming task with high interobserver variation. In this study, we proposed a semiautomated, three‐dimensional (3D) segmentation for prostate CT images using shape and texture analysis and we evaluated the method against manual reference segmentations.

Methods

The prostate gland usually has a globular shape with a smoothly curved surface, and its shape could be accurately modeled or reconstructed having a limited number of well‐distributed surface points. In a training dataset, using the prostate gland centroid point as the origin of a coordination system, we defined an intersubject correspondence between the prostate surface points based on the spherical coordinates. We applied this correspondence to generate a point distribution model for prostate shape using principal component analysis and to study the local texture difference between prostate and nonprostate tissue close to the different prostate surface subregions. We used the learned shape and texture characteristics of the prostate in CT images and then combined them with user inputs to segment a new image. We trained our segmentation algorithm using 23 CT images and tested the algorithm on two sets of 10 nonbrachytherapy and 37 postlow dose rate brachytherapy CT images. We used a set of error metrics to evaluate the segmentation results using two experts' manual reference segmentations.

Results

For both nonbrachytherapy and post‐brachytherapy image sets, the average measured Dice similarity coefficient (DSC) was 88% and the average mean absolute distance (MAD) was 1.9 mm. The average measured differences between the two experts on both datasets were 92% (DSC) and 1.1 mm (MAD).

Conclusions

The proposed, semiautomatic segmentation algorithm showed a fast, robust, and accurate performance for 3D prostate segmentation of CT images, specifically when no previous, intrapatient information, that is, previously segmented images, was available. The accuracy of the algorithm is comparable to the best performance results reported in the literature and approaches the interexpert variability observed in manual segmentation.

1. Introduction

Prostate cancer (PCa) is the leading cancer diagnosed among males in the United States.¹ It accounted for more than 26,000 cancer deaths in 2016.¹ Currently, image‐guided radiation therapy is one of the primary treatment methods for patients with localized PCa.^{2, 3} PCa radiation therapy planning is performed with the prostate border delineated on computed tomography (CT) images.⁴ However, due to the low soft tissue contrast between the prostate and surrounding tissues, manual contouring of the prostate in CT images is time consuming⁵ and is subject to high intraobserver and interobserver variability.^{6, 7, 8, 9} Therefore, computer‐assisted segmentation algorithms are being investigated and developed to perform prostate contouring more quickly and more reproducibly compared to manual segmentation.

Information regarding several automatic and semiautomatic, computer‐assisted methods have been published in the literature regarding three‐dimensional (3D) segmentation of the prostate on CT images. The majority of these studies were regarding learning‐based segmentation techniques. Feng et al.¹⁰ proposed an automatic algorithm for CT prostate segmentation, based on shape and appearance modeling using population‐ and patient‐specific statistics. Their method is more useful for radiotherapy treatment CT images when a series of previously segmented treatment images from the same patient is available. Liao et al.¹¹ presented a multiatlas sparse label propagation framework to estimate the prostate likelihood of image voxels using patch‐based representation in a discriminative feature space for semiautomatic prostate segmentation in treatment CT images. In their method, manual segmentation labels of the planning and the first two treatment CT images were needed. After each treatment image segmentation, they used an online update mechanism with potential offline manual adjustment of the segmentation label to add the newly segmented image to the training set. Shi et al.^{12, 13} presented a semiautomatic prostate segmentation method that first estimated the prostate‐likelihood map slice‐by‐slice, and then merged the 2D maps to generate a 3D prostate‐likelihood map. Finally, the segmentation labels of the planning and the previous treatment images of the same test patient were rigidly aligned to the prostate‐likelihood map and a majority vote was used to prepare the final segmentation label. Shi et al.¹⁴ also presented another segmentation algorithm in which they improved the segmentation performance by incorporating manually assigned prostate and nonprostate labels for a subset of test image voxels for training. Shao et al.¹⁵ presented a boundary voting technique for automatic prostate segmentation in CT images using a global regression forest for prostate boundary detection followed by a deformable prostate segmentation. They also presented a similar automatic boundary detection algorithm for segmentation of the prostate and rectum in radiotherapy planning CT images.¹⁶ They estimated the prostate and rectum borders by automatic landmark detection using regression forest followed by shape modeling. Ma et al.¹⁷ presented a semiautomatic, learning‐based segmentation method that was trained based on a combination of population and patient‐specific data. They used manual segmentation of three, 2D slices of the target image as the patient‐specific data. Ma et al. also presented an automatic, deep learning‐based prostate CT segmentation algorithm.¹⁸ They used the convolutional neural networks to determine the deep features of the discriminate prostate and nonprostate voxels. They refined the neural network output by applying a multiatlas label fusion. Table V compares the segmentation accuracy of the previously presented algorithms mentioned above.

In the previously presented learning‐based methods, a training dataset consisting of manually segmented images was used to study a set of different characteristics of the prostate in the image. Then, during segmentation, the learned information was used to delineate the prostate border on an unseen test image set. In some of these methods the training sets consisted of CT images from other patients only, and in some others the previously segmented treatment CT images from the same target patient were also included in the training set and that helps to have a more accurate computer‐assisted segmentation. However, it challenges the segmentation performance where no previously acquired CT images are available, for example, for radiotherapy planning CT image segmentation. Moreover, manual segmentation of one or more CT images from the same patient should be available as a prerequisite for segmentation of the next treatment image. The performance of the algorithm for each of the mentioned groups was evaluated using a reference segmentation which consisted of a segmentation from a single expert. However, due to high interobserver variability in manual segmentation of the prostate in CT images, the measured error metric values are dependent on the selected manual reference segmentation label and changing the reference could change the evaluation results. Therefore, it is useful for deeper understanding of the algorithm performance to take interobserver variability into account for evaluation.

In this manuscript, we present a semiautomatic algorithm for 3D prostate segmentation on CT images, based on learned prostate shape variability and local image texture near the prostate border. The proposed learning‐based method does not need to be trained on previously acquired and/or manually segmented images from the target patient. We use the prostate gland centroid point as the origin of the coordination system and define an interpatient correspondence between prostate surface points based on the spherical coordinates of the points. During training, we apply this correspondence to generate two point distribution models (PDM) for prostate shape using principal component analysis, that is, a low‐density (LD) model with 86 surface points and a high‐density (HD) model with 2056 surface points. To study the local image texture close to the prostate border, we train our algorithm on a number of rays emanating from the centroid, separately. For all the image voxels on a ray, inside and outside the prostate gland, we measure a set of local texture features using a cubic image patch centered at the voxel. For all the rays across the training set in the corresponding direction, we train a classifier using the local texture features to identify prostate vs nonprostate voxels. The segmentation algorithm is initiated with a bounding box for the gland and a number of manually selected landmark points on the prostate surface. The algorithm searches for a set of prostate border points in the 3D space by classifying the points close to the prostate border on a number of rays casted from the centroid of the gland. Then 3D point distribution models are used to regularize the segmentation and to reconstruct the 3D surface from the border points. We evaluate the segmentation algorithm against two expert reference segmentations, and to capture different types of error, we use a set of error metrics to measure surface distances, regional overlap errors, and volume differences. We also evaluate the algorithm performance on postlow dose rate (LDR) brachytherapy CT images. The main contributions of this work include: (a) A new semiautomatic prostate segmentation algorithm was proposed and implemented for CT images, which does not use the previous images of the same patient, that is, it is independent to the planning and/or previous treatment images of the same patient. (b) A local texture classification approach was developed to estimate the prostate border and to avoid negative effects of image texture distortion caused by necrotic tissue, tumors, or LDR brachytherapy seeds. (c) A new shape modeling was developed for the prostate, which is based on a smooth globular shape of the gland. (d) A comprehensive validation approach was used to evaluate the performance of the segmentation technique by capturing different performance aspects of importance to the potentially intended application of the algorithm.

2. Materials and methods

2.A. Materials

Our CT image dataset contained 70, 3D abdominal CT scans from 70 patients. Thirty‐seven of the images were acquired from post‐LDR brachytherapy patients. The size of each image was 512 × 512 × 27 voxels with the voxel sizes of 0.977 × 0.977 × 4.25 mm. For each image two segmentation labels manually drawn by two experienced radiologists were available.

2.B. Semiautomatic segmentation

The proposed semiautomatic segmentation algorithm consists of two main parts, that is, training and segmentation. Figure 1 shows the schematic block diagram of the algorithm. The training and segmentation components are described in detail in Sections 2.B.1 and 2.B.2, respectively.

Figure 1.

The general framework of the proposed segmentation method. [Color figure can be viewed at wileyonlinelibrary.com]

2.B.1. Training

During training, we use the training image set to extract a set of local texture features within each sector of the spherical space. The most discriminative features are then selected to train a classifier. We also use the manual segmentation labels of the training images to build an LD and an HD PDM for prostate shape. These shape models are used for shape regularization and reconstruction during segmentation. Each of the training blocks illustrated in Fig. 1 is described in detail below.

2.B.1.a. Preprocessing

Anteroposterior symmetry axis alignment. We rotated all of the training images and their manual reference segmentation labels about their inferior–superior axis in order to align the anteroposterior symmetry axes of the patients parallel to the anteroposterior axes of the images. To automatically measure a patient's anteroposterior symmetry axis angle in an image, we first roughly segmented the bones in the 3D image using a thresholding segmentation method (threshold level = 155) and kept the two largest segmented objects associated with the left and right hip bones and removed all of the other smaller objects [Figs. 2(a) and 2(b)]. We then measured the centroid of the bones to roughly estimate the prostate location [Fig. 2(b)] and cropped the images along the x‐ and y‐axes about the centroid so as to limit the image field of view. We selected the field of view large enough (121 pixels × 201 pixels) to ensure accommodating the prostate and its surrounding tissue [Fig. 2(c)]. For each two‐dimensional (2D) axial image slice, we flipped the slice about its anteroposterior axis [Fig. 2(e)] and aligned the original slice to the flipped one using a 2D rigid image registration [Fig. 2(f)]. We used gradient descent optimizer and mean square error (MSE) metric to run the image registration. After registration, we measured the rotation angles of all the image slices and used their median after removing outliers divided by two as the patient's anteroposterior symmetry axis angle. Figure 2 shows the different steps of the alignment process.

Figure 2.

Anteroposterior symmetry axis angle measurement. (a) Original 3D CT image. (b) Rough hip bone segmentation label after thresholding. The yellow cross shows the centroid of the bones. (c) The cropped region (dashed box) about the centroid. (d) ith 2D slice of the image and (e) its flipped version. (f) Rigid registration between (d) and (e). α _i,T is the rotation angle after rigid registration and α _i is the measured angle between the patient anteroposterior symmetry axis on ith slice and the anteroposterior axis of the image. [Color figure can be viewed at wileyonlinelibrary.com]

Hounsfield unit range adjustment. The Hounsfield unit (HU) of prostate and its adjacent soft tissues are above −100 and below 155. Therefore, in order to reduce the inconsistency in air cavities and bones, we truncated the HU dynamic range of the images and HU values of −100 and 155 were respectively assigned to the voxels with HU values below −100 and above 155. To choose these HU threshold levels, we observed the HU range for prostate voxels across the training images. The HU values after removing the 0.1% outliers varied from −85 to 151. We chose −100 to 155 to limit the dynamic range to 256 (eight bit) levels.

Median filtering. To reduce the image noise, we applied a 2D median filter as an edge‐preserving, low‐pass filter to each 2D axial slice. However, image filtering could disrupt the image pattern. Therefore, to preserve the image texture while reducing the image noise, we applied the filter with a 3 × 3 pixel window size which is the smallest size for median filtering.

Image resize. The images and their manual segmentation labels were up‐sampled along inferior–superior axes using nearest neighbor interpolation to make the voxels isotropic. This image resampling made it easier to search in 3D space and select cubic image patches.

2.B.1.b. Shape modeling

Low‐density point distribution model. To select a set of landmarks on the prostate surface and define a correspondence between the landmarks across the training set, we cast N ₁ = 86 equally spaced rays in 3D space, emanating from the centroid of the prostate gland and found the contact points between the rays and the prostate surface yielding a set of 86 landmarks. Using the centroid point as the origin of a sphere coordinate system, we defined all the landmarks with the same elevation and azimuth angles across the training set corresponding to each other. For modeling the prostate shape, we defined each shape with this cloud of 86 surface points and the centroid point, yielding 87 points in total. The shapes were then aligned (translating, rotating, and scaling transforms) using generalized 3D Procrustes analysis¹⁹ and the mean square distance between the points as the error metric.

High‐density point distribution model. We applied the similar process used for LD PDM to build an HD PDM with N ₂ = 2056 equally spaced casted rays. For HD PDM each shape was defined by 2057 points (2056 surface and 1 centroid points). To build the model the shapes were aligned (translating, rotating, and scaling transforms) using generalized 3D Procrustes analysis and the mean square distance between the points as the error metric.

2.B.1.c. Feature selection

Local feature extraction. For each of the 86 rays ($R_n,n=1,2,3,\dots ,86$) emanating from the prostate centroid $(x_C,y_C,z_C)$ we selected a set of points (${\mathit{p}}_{\mathit{n}}$) on the ray within a specific range around the prostate border point:

$${\mathit{p}}_{\mathit{n}}=\left\{(x,y,z)|r_{\mathit{min}}<r<r_{\mathit{max}},\theta ={\theta }_n,\phi ={\phi }_n\right\},$$ (1)

where $r$, $\theta$, and $\phi$ are, respectively, radial, elevation and azimuth coordinates of point $(x,y,z)$ in a spherical coordinate system [Eqs. (2), (3), (4)]. $r_{\mathit{min}}=r_b-d$ and $r_{\mathit{max}}=r_b+d$ are the radial coordinates of the first and the last points on the ray, respectively, where $r_b$ is the prostate border point on the ray and $d$ is the distance of the first and the last points from the border point. To focus on the local image textures near the prostate border, $d$ should be small relative to the gland dimensions (in this paper $d=5\text{mm}$). ${\theta }_n$ and ${\phi }_n$ are elevation and azimuth angles of points on the nth ray ($R_n$), respectively, and have constant values for all the points on the ray. Figure 3(a) illustrates the details.

Figure 3.

A schematic illustration of the prostate surface, (a) the selected points on a sample ray ($R_n$) used for feature extraction, and (b) a selected 3D cubic image patch centered at a sample point, $(x_p,y_p,z_p)$, on ray $R_n$.

$$r=\sqrt{{\left(x-x_C\right)}^2+{\left(y-y_C\right)}^2+{\left(z-z_C\right)}^2}$$ (2)

$$\theta ={cos}^{-1}\frac{z}{r}$$ (3)

$$\phi ={tan}^{-1}\frac{y}{x}$$ (4)

We extracted all of the texture features within a 3D cubic image patch. For the point $(x_p,y_p,z_p)$ on a 3D image, we defined the image patch $\mathcal{P}$ of size $W\times W\times W=(2D+1)\times (2D+1)\times (2D+1)$ centered at the point [Fig. 3(b)] as:

$$\begin{array}{cc}\hfill \mathit{P}=& \mathcal{P}(x_p,y_p,z_p)=\left\{(x,y,z)|x_p-D<x<x_p\right.\hfill \\ & \left.+D,y_p-D<y<y_p+D,z_p-D<z<z_p+D\right\}.\hfill \end{array}$$ (5)

In this paper, we chose fixed value of 5 mm for parameter $D$ to have patches that are small relative to the whole prostate gland but large enough to contain a 3D image pattern for texture analysis.

For each of the cubic patches, we calculated a feature vector of size 1 × 67 consisting of a set of first‐ and second‐order texture features that are listed in Table 1. The patches that are centered at a point inside the prostate were labeled “prostate” or “one” and those centered at a point outside the prostate were labeled “non‐prostate” or “zero”. We also measured the percentage of the patch volume within the prostate ($L_p$) for each patch. $L_p$ is the number of prostate voxels in a patch divided by the total number of the patch voxels multiplied by 100. For a patch that is completely inside the prostate region $L_p=100\%$ , for a patch that is completely outside the prostate $L_p=0$, and for patches that are as close to the prostate border to have an overlap with both prostate and nonprostate tissues, in which $L_p$ is greater than zero and less than 100%.

Table 1.

List of features and their descriptions

Feature	# of features	Description
First‐order features	10	Intensity of the patch center voxel, mean (${\mathit{\mu }}_{\mathit{P}}$), standard deviation (${\mathit{\sigma }}_{\mathit{P}}$), median (${\mathit{m}}_{\mathit{P}}$), minimum intensity, maximum intensity, skewness,20 kurtosis,20 entropy,20 and energy20 of a 3D patch intensity histogram. Since the first‐order texture features are measured based on the image histogram, they could be easily implemented for 3D patches
Histogram of oriented gradients (HOG)21	8	HOG describes the distribution of intensity gradients in an image. Eight, 2D orientation bins are defined as forming the HOG. In this study, we calculated one histogram per 2D axial patch slice and obtained the average of all the corresponding bins of the HOGs to form one, eight‐bin HOG for a 3D image patch
Histogram of Local binary patterns (LBP)22	8	LBP is calculated in 3D within a 3 × 3 × 3 mask. One, eight‐bin histogram is formed per 3D image patch
Grey‐level co‐occurrence, matrices‐based23 (GLCM)‐based features	32	For each pixel spatial relationship (pixel neighboring) in 2D (2D offset), GLCM for a 3D patch is defined as the average of the GLCMs of all the 2D axial patch slices related to the same pixel neighboring. GLCM‐based features were measured based on four, different 2D offsets, that is, (−1,0), (0,−1), (1,−1), (−1,−1), and consist of energy, entropy, contrast,20 homogeneity,24 inverse different moment,20 correlation,20 cluster shade,24 and cluster prominence24 of the four GLCMs
Mean gradient angle	1	Mean gradient angle of a 3D patch is the average of mean gradient angles of all the 2D axial slices
Edge‐based features	8	The eight‐bin histogram of edge directions in a 3D patch. The edges are detected using Sobel operator25 for edge detection for all the 2D slices
Total	67

Ray and feature selection. We collected the feature vectors from all the rays across the training images. Then for the values of each feature collected from all the corresponding rays, we applied the two‐tailed, heteroscedastic t‐test²⁶ to compare the values of the feature from prostate patches to the values of the same feature from nonprostate patches. In each case we tested the null hypothesis that the mean of the features measured from prostate patches is the same as the mean of the features measured from nonprostate patches. Rejection of the null hypothesis indicates a statistically significant difference between prostate and nonprostate means. For each of those features in which the null hypothesis was rejected (α = 0.01) we extracted two threshold values ($T_0$ and $T_1$); $T_0$ indicating that all of the feature values below/above it belong to nonprostate patches and $T_1$ indicates that all the feature values above/below it belong to prostate patches (see Fig. 4).

Figure 4.

Histograms of feature values measured from prostate and nonprostate image patches. $T_0$ is the threshold level in which all of the feature values above that level belong to nonprostate image patches, and $T_1$ is the threshold level in which the feature values below that level belong to prostate image patches. The feature values between $T_0$ and $T_1$ belong to either prostate or nonprostate image patches. [Color figure can be viewed at wileyonlinelibrary.com]

We also used Spearman's rank‐order correlation (ρ) to measure the monotonic relationship between each of the features and $L_p$. For each ray, those features with high (ρ > 0.6) and statistically significant (P < 0.001) correlation coefficients were selected for training a support vector machine²⁷ (SVM) classifier to classify between the prostate and nonprostate patches. Rays with no selected feature were excluded for SVM training; $M\le N_1$ is the number of selected rays.

2.B.2. Segmentation

2.B.2.a. Preprocessing

We applied a similar preprocessing to that used for the training image to the test image and which consisted of anteroposterior symmetry axis alignment, HU range adjustment, median filtering, and image resizing (see Section Preprocessing).

2.B.2.b. Initialization

Operator inputs. To initialize the segmentation algorithm, a set of inputs from the operator are required, including the prostate gland bounds along the right–left (x), anteroposterior (y), and inferior–superior (z) axes, as well as a number of points on the prostate surface (anchor points) at different subregions, that is, the apex, midgland, and base. For this purpose the operator approximated a minimum bounding box for the prostate gland that is limited inferiorly to the apex‐most slice and superiorly to the base‐most slice. The box included the entire prostate gland. Then for three, equally spaced slices between the defined apex and the base slices, the operator selected four anchor points on the prostate border on each slice and approximately at four, different sides, that is, the right, left, anterior, and posterior sides, yielded total of 12 anchor points on the whole surface.

Ray casting. We used the centroid of the bounding box as an approximation for the prostate gland center and similar to the training part and casted 86, equally spaced rays emanating from the center point [Fig. 5(a)].

Figure 5.

Segmentation procedure steps. (a) 86 rays cast from a center point of the gland. (b) Yellow dots show the candidate surface points. (c)–(e) Purple surface shows the algorithm results after shape regularization and reconstruction. (f) Comparison between the algorithm segmentation in purple and the reference in green. (g) and (h) show algorithm results in purple, reference in green, and surface candidate points (yellow dots). Note that yellow and green appear bright and purple appears dark in grayscale print. [Color figure can be viewed at wileyonlinelibrary.com]

Initially estimated prostate surface. We used the LD shape model generated during training to find a shape that fit within the bounding box and best matched the manually selected anchor points. For this purpose, we used the casted rays to determine the 12 corresponding points in the PDM to the anchor points. Then we used 3D thin‐plate spline (TPS) analysis²⁸ to nonrigidly warp the mean shape of the model to the 12 anchor points. This helped to estimate the missing points between the anchor points. We then aligned the estimated shape to the mean shape of the model using 3D Procrustes analysis and extracted representative shape parameters from the PDM. We then restricted each parameter to the range of $[-\sqrt{3}{\lambda }_k,\sqrt{3}{\lambda }_k]$ in which ${\lambda }_k$ is the kth eigenvalue of the shape model (corresponded to kth parameter), in order to determine the nearest shape of the model to the points.

2.B.2.c. Local classification

Classifier training. For each of the M selected rays during training, explained in Section Feature selection, we trained a linear kernel SVM algorithm for binary classification between prostate and nonprostate image patches, using the selected features for the ray.

Classification. We defined a search range ($[r_o-d_S,r_o+d_S]$) on each ray around the corresponding surface point from the initially estimated shape. $r_o$ is the radius of the surface point and $d_S$ is the distance of the first and the last search point on the ray from the surface point. We selected a set of image patches centered at the ray points within the defined range and measured the feature vectors for each patch. We applied the threshold levels ($T_0$ and $T_1$) obtained from training to the corresponding feature values in order to classify the corresponding image patches to prostate and nonprostate. We shifted start and stop points of the range on the ray if the adjacent points to them were classified by thresholds. This could make the range narrower. Then, we apply our SVM classifier to the features of the remaining unclassified patches to classify them into prostate and nonprostate. We shifted the initial surface point to the boundary of prostate and nonprostate points after removing potentially singular labels within the range. This process yielded a set of 86 candidate surface points [Fig. 5(b)].

2.B.2.c. Shape regularization and surface reconstruction

We replaced the corresponding surface points with manually selected anchor points, in case they have shifted along the rays. Then, we applied the HD PDM to the points to regularize the shape and in order to have a plausible smooth shape for the prostate and to reconstruct the surface with a larger set of points. For that purpose, we first used TPS warping to nonrigidly register the 2056‐point mean shape of the HD model to 86 obtained surface points, using the 86 corresponding points in the mean shapes as the reference points and yielding a 2056‐point candidate surface shape. We used 3D Procrustes analysis to register the shape to HD PDM and we measured the representing model parameters for the shape. We restricted each of the parameters, for example, kth parameter, to the range of $[-\sqrt{3}{\lambda }_k,\sqrt{3}{\lambda }_k]$, in which ${\lambda }_k$ is the corresponding (kth) eigenvalue. We then replaced the corresponding 12 points with the anchor points and also restricted the points to be within the bounding box. Finally, we used a scattered data interpolation²⁹ to generate a continuous surface out of the surface point set [Figs. 5(c)–5(e)], and resized the obtained label to the original image size so as to have the final segmentation results.

2.C. Evaluation

To evaluate our segmentation algorithm we compared the results against an expert observer's manual segmentations as the reference segmentations using a set of different types of error metrics explained in this section. We applied our error metrics to the entire prostate gland, as well as the inferior‐most third (apex region), the superior‐most third (base region), and the middle third (midgland) of the prostate.

2.C.1. Surface disagreement measurements

Mean absolute distance (MAD) measures the average disagreement between two surfaces where each surface is defined as a set of points. We defined MAD in unilateral and bilateral modes. See Ref. 30 for more details.

Hausdorff distance (HD) measures the maximum of the shortest distance between segmentation surface and reference surface. HD is sensitive to the noisy segmentation surface.

2.C.2. Regional overlap measurements

There are several, region‐based error metrics that measure the overlap between two volumes. Dice similarity coefficient³¹ (DSC) is the most commonly used and sometimes the only region‐based error metric reported in the literature. However, there are other region‐based methods, for example, recall or sensitivity rate (SR), precision rate (PR), and overlap error (OE) that have also been used to evaluate the segmentation algorithms and they could explain the error type, for example, partial overlap, oversegmentation and undersegmentation, better than DSC by itself. Reporting all the listed region‐based error metric values for an algorithm might seem redundant, but for comparison purposes we applied all of them to our algorithm's segmentation results. In this manuscript, we reported all of the region‐based error metrics in percentages (See Refs. ^{17, 30} for more details).

We also reported the signed volume difference ($\mathrm{\Delta }V$) between the algorithm segmentation and the reference, defined as:

$$\mathrm{\Delta }V\left(V_s,V_{\mathit{ref}}\right)=V_s-V_{\mathit{ref}},$$ (6)

where, $V_s$ and $V_{\mathit{ref}}$ are algorithm segmentation and reference segmentation volumes, respectively. $\mathrm{\Delta }V$ is reported in cm³ and as a percent in this manuscript. To measure the percentage of the $\mathrm{\Delta }V$, it is divided by the reference volume:

$$\mathrm{\Delta }V\left(V_s,V_{\mathit{ref}}\right)=\frac{V_s-V_{\mathit{ref}}}{V_{\mathit{ref}}}\times 100.$$ (7)

For comparison of two manual references, we reported the absolute value of the volume difference and considered the average of the volumes as the reference volume:

$$\mathrm{\Delta }V\left(V_{ref1},V_{ref2}\right)=\left|V_{ref1}-V_{ref2}\right|,\text{and}$$ (8)

$$\mathrm{\Delta }V(V_{ref1},V_{ref2})=\frac{\left|V_{ref1}-V_{ref2}\right|}{\frac{1}{2}(V_{ref1}+V_{ref2})}\times 100,$$ (9)

where, $V_{ref1}$ and $V_{ref2}$ are manual reference segmentations obtained from two experts.

3. Results

3.A. Implementation details

We implemented the proposed segmentation algorithm using MATLAB R2017a (version 9.2.0) on a 64‐bit Windows 7 desktop with a 3.0 GHz Intel Xeon processor and with 64 GB memory. To speed up the algorithm execution, we developed a parallel implementation of the algorithm using the MATLAB parallel computing toolbox and ran the code on 12 CPU cores.

To avoid interference of the brachytherapy seeds pattern on algorithm training, we trained our algorithm using non‐brachytherapy images only. We used one set of the manual segmentation (reference #1) for training. We randomly selected 70% of our nonbrachytherapy images, that is, 23 images, for training the algorithm. The remaining 10 images were used for testing the algorithm. We used all of the 37 post‐LDR brachytherapy images only for testing the algorithm.

For anteroposterior symmetry axis alignment during training, we selected HU of 155 as the threshold level for rough segmentation of bones. We cropped the images about the centroid to make a 121 pixels (along the x‐axis) × 201 pixels (along the y‐axis) 2D slices. We used the same image cropping for anteroposterior symmetry axis alignment during segmentation. We considered all of the rotation angles (${\alpha }_{i,T},i=1,2,3,\dots ,numberofaxialslices$) greater than 18 degrees as outliers. We set $d$ to 5 mm and $D$ to 5 mm ($W=2D+1=11\text{mm}$).

During segmentation we used the same patch size used during training (11 × 11 × 11 mm) and $d_S$ was initially set to 7 mm.

3.B. Interobserver variability in manual segmentation

We compared our two sets of manual segmentation labels using our segmentation error metrics to measure the interobserver variation in expert prostate border delineation. Table 2 shows the result. The mean ± standard deviation of the prostate gland volume based on the first and the second manual segmentations were 30.1 ± 12.6 cm³ and 28.0 ± 10.0 cm³, respectively.

Table 2.

The average and range of interobserver variability in manual prostate segmentation across the dataset. Mean ± standard deviation of observed difference between two experts based on our error metrics. As both segmentation labels in each pairwise comparison were from experts, the bilateral MAD (MAD_b) and |ΔV| are reported in this Table. N_pat and N_Img are the number of patients and the number of images, respectively

Region of interest	NPat	NImg	MADb (mm)	HD (mm)	DSC (%)	SR (%)	PR (%)	OE (%)	|ΔV| (cm3)
Whole gland	70	70	1.1 ± 0.5	6.2 ± 2.4	92 ± 4	89 ± 5	95 ± 5	15 ± 7	2.4 ± 3.3
Apex			1.1 ± 0.7	4.7 ± 2.3	91 ± 9	88 ± 8	94 ± 11	17 ± 12	0.9 ± 1.3
Midgland			1.1 ± 0.5	4.3 ± 1.6	93 ± 3	89 ± 5	98 ± 2	12 ± 5	1.2 ± 1.4
Base			1.2 ± 0.7	4.8 ± 2.0	91 ± 7	91 ± 6	92 ± 12	17 ± 11	1.2 ± 1.1

3.C. Segmentation algorithm accuracy and computation time

3.C.1. Single operator, single reference test on the nonbrachytherapy test dataset

We applied the proposed segmentation algorithm to 10 nonbrachytherapy test images using reference segmentation #1 for initializing the algorithm and evaluating the results. We defined the bounding box based on the reference label and selected 12 anchor points on the label surface, as described in Section Initialization. Table 3 shows the quantitative accuracy of the algorithm based on the error metrics. We conducted a one‐tailed t‐test between values of Table 3 and the corresponding metric values in Table 2. The null hypotheses were defined regarding the relative metric values, and the values in bold show where the null hypotheses were rejected with α = 0.05. Figures 6 and 7 illustrate the nonbrachytherapy image segmentation results qualitatively in 2D and 3D, respectively. The average measured segmentation computation time was 22 ± 2 s. per 3D image.

Table 3.

Quantitative accuracy of the segmentation methods on nonbrachytherapy images. Mean ± standard deviation of the error metrics for different regions of interest. N_pat and N_Img are the number of patients and the number of images, respectively. Twenty‐three nonbrachytherapy images were used for training the algorithm. There are statistically significant differences detected between those metric values in bold and the corresponding metric values in Table 6, where applicable (P < 0.05)

Region of interest	NPat	NImg	MAD (mm)	MADb (mm)	HD (mm)	DSC (%)	SR (%)	PR (%)	OE (%)	ΔV (cm3)
Whole gland	10	10	1.9 ± 0.5	2.0 ± 0.5	6.2 ± 1.6	88 ± 2	94 ± 3	82 ± 4	22 ± 3	5.3 ± 5.0
Apex			1.9 ± 0.6	1.9 ± 0.6	5.6 ± 1.5	85 ± 5	90 ± 5	82 ± 7	25 ± 7	1.0 ± 1.4
Midgland			1.8 ± 0.4	1.8 ± 0.4	5.1 ± 0.8	90 ± 2	97 ± 2	84 ± 4	18 ± 4	2.2 ± 1.1
Base			2.2 ± 0.8	2.3 ± 0.8	5.9 ± 1.8	85 ± 5	93 ± 4	80 ± 8	25 ± 7	2.1 ± 2.8

Figure 6.

Qualitative segmentation results on five, 2D axial slices for three sample prostates. Each row shows the results for one patient. The left column shows the apex slices, and the right column shows the base slices. The algorithm segmentation is shown with yellow (or bright in grayscale print) contours, the first reference is shown with black contours, and the second reference is shown with white dotted contours. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7.

Qualitative and quantitative segmentation results in 3D for the three, sample prostates shown in Fig. 2. [Color figure can be viewed at wileyonlinelibrary.com]

To show the effect of 12 anchor points on the performance of the algorithm, we also run the algorithm without the anchor points. Table 4 shows the results. We conducted a one‐tailed t‐test between the metric values in the table to the corresponding metric values in Table 3. The null hypotheses were defined regarding the relative metric values and the values in bold in Table 4 show where the null hypotheses were rejected with α = 0.05.

Table 4.

Quantitative accuracy of the segmentation methods on nonbrachytherapy images using no manually selected anchor points. Mean ± standard deviation of the error metrics for different regions of interest. N_pat and N_Img are the number of patients and the number of images, respectively. Twenty‐three nonbrachytherapy images were used for training the algorithm. There are statistically significant differences detected between those metric values in bold and the corresponding metric values in Table III, where applicable (P < 0.05)

Region of interest	NPat	NImg	MAD (mm)	MADb (mm)	HD (mm)	DSC (%)	SR (%)	PR (%)	OE (%)	ΔV (cm3)
Whole Gland	10	10	2.1 ± 0.3	2.2 ± 0.3	7.4 ± 1.7	85 ± 1	82 ± 3	89 ± 3	26 ± 2	−2.4 ± 2.0
Apex			2.5 ± 0.6	2.7 ± 0.5	6.8 ± 1.9	78 ± 5	71 ± 7	88 ± 11	36 ± 7	−1.6 ± 2.0
Midgland			1.8 ± 0.4	1.8 ± 0.4	5.1 ± 1.1	89 ± 2	89 ± 5	90 ± 5	19 ± 4	−0.4 ± 1.3
Base			2.3 ± 0.7	2.5 ± 0.7	6.4 ± 1.6	83 ± 5	80 ± 5	87 ± 8	29 ± 7	−0.4 ± 1.3

We compared the algorithm performance to some of the most recent segmentation algorithms presented in the literature in Table 5 using our error metric values where applicable. In those studies in which MAD was used as an error metric, but the mode of MAD calculation was not mentioned, we indicate the MAD values with an asterisk sign. We conducted one‐tailed t‐tests to compare our results with those of previous work where applicable. In these tests the null hypotheses were defined regarding the relative performance of the methods. The values in bold in Table 5 show where the null hypotheses were rejected with α = 0.05.

Table 5.

Comparison of the proposed method to previous work where applicable. Mean ± standard deviation of the error metrics for the whole prostate gland. The MAD mode (unilateral or bilateral) is not defined for those methods in which their MAD values are indicated with asterisks. There are significant differences detected between those metric values in bold and the corresponding metric values of our methods (P < 0.05)

Method, year	NPat	NImg	MAD (mm)	MADb (mm)	DSC (%)	SR (%)	PR (%)	OE (%)	Execution time (s)
Proposed algorithm	10	10	1.9 ± 0.5	2.0 ± 0.5	88 ± 2	94 ± 3	82 ± 4	22 ± 3	22 ± 2
Ma et al.18, 2017	92	92	–	–	84	–	–	–	–
Ma et al.17, 2016	15	15	–	–	85 ± 3	83 ± 1	–	26 ± 1	–
Shi et al.14, 2016	24	330	1.3 ± 0.8 *		92 ± 4	90 ± 5	–	–	–
Shi et al.13, 2015	24	330	1.1 ± 0.6 *		95 ± 3	93 ± 4	–	–	–
Shao et al.16, 2015	70	70	–	1.9 ± 0.2	88 ± 2	84	86	–	–
Shao et al.15, 2014	70	70	2.0 ± 0.8*		85 ± 6	84	86	–	–
Shi et al.12, 2013	24	330	1.1*		94 ± 3	92 ± 4	–	–	–
Liao et al.11, 2013	24	330	1.0	–	91	–a	–	–	156
Feng et al.10, 2010	24	306	2.1 ± 0.8*		89 ± 5	–	–	–	95.5

^aThe overall average was not reported.

3.C.2. Two operators, two references test on the nonbrachytherapy test dataset

To investigate the effect of using different operator on the algorithm performance, we applied the algorithm with the same configuration applied in Section 3.C.1 and used reference segmentation #2 for algorithm initialization. We evaluated the segmentation results by comparing the segmentation labels against reference segmentation #2 as the expected results. Figure 8 compares these results and the segmentation results obtained in Section 3.C.1 to the observed difference between two references for the 10 nonbrachytherapy images. Box plots of Fig. 8 summarize the comparison between the three groups in terms of any of the three metrics. We conducted the one‐way ANOVA test followed by pairwise t‐tests with the null hypothesis that the average of each metric for the three groups is the same. The results of the post ANOVA test are indicated in Fig. 8 where ANOVA detected a statistically significant difference (α = 0.05).

Figure 8.

Performance of the proposed segmentation algorithm based on two operators and two references vs interobserver variability in manual segmentation for 10 nonbrachytherapy test images in terms of (a)–(b) DSC, (c)–(d) MAD (for reference 1 to reference 2 comparison MAD _b was measured) and (e)–(f) HD error metrics. Box plots (b), (d), and (f) show the minimum (lower bar), 25 percentile to 75 percentile (blue box), maximum (upper bar), mean (blue cross symbol), median (red line segment) values of the metrics, and the outliers (blue “o” symbols) where they exist. Asterisk symbols indicate statistically significant differences between the averages of the metrics (P < 0.05). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 9.

Qualitative segmentation results on five, 2D axial slices for three sample post‐LDR brachytherapy prostate images. Each row shows the results for one patient. The left column shows the apex slices, and the right column shows the base slices. The algorithm segmentation is shown with yellow (or bright in grayscale print) contours, the first reference is shown with black contours, and the second reference is shown with white dotted contours. [Color figure can be viewed at wileyonlinelibrary.com]

3.C.3. Single operator, single reference test on the post‐LDR brachytherapy test dataset

Table 6 shows the measured segmentation error of the proposed algorithm for 37 post‐LDR brachytherapy images. The algorithm was trained using the same 23 nonbrachytherapy training images in Section 3.C.1. The average measured computation time was 21 ± 1 s. per 3D image. We conducted one‐tailed t‐tests between each of the metric values in this experiment and the metric values obtained on nonbrachytherapy (Table 3). In these tests, the null hypotheses were defined regarding the relative performance of the algorithm with different test datasets. The values in bold show where the null hypotheses were rejected with α = 0.05. Figures 9 illustrates the post‐LDR brachytherapy image segmentation results qualitatively.

Table 6.

Quantitative accuracy of the segmentation methods on post‐LDR brachytherapy images. Mean ± standard deviation of the error metrics for different regions of interest. N_pat and N_Img are the number of patients and the number of images, respectively. Twenty‐three nonbrachytherapy images were used for training the algorithm. The error values in bold show a statistically significant difference with the corresponding error value in Table III (P < 0.05)

Region of interest	NPat	NImg	MAD (mm)	MADb (mm)	HD (mm)	DSC (%)	SR (%)	PR (%)	OE (%)	ΔV (cm3)
Whole gland	37	37	1.9 ± 0.3	1.9 ± 0.3	6.3 ± 1.7	88 ± 2	92 ± 3	83 ± 4	22 ± 4	3.0 ± 2.2
Apex			1.7 ± 0.5	1.7 ± 0.5	4.9 ± 1.0	88 ± 4	91 ± 4	85 ± 6	22 ± 6	0.5 ± 0.7
Midgland			1.8 ± 0.5	1.8 ± 0.5	5.2 ± 1.0	89 ± 3	94 ± 3	85 ± 6	19 ± 5	1.2 ± 1.0
Base			2.3 ± 0.6	2.3 ± 0.6	6.2 ± 1.8	85 ± 4	91 ± 6	80 ± 7	26 ± 6	1.3 ± 1.3

3.C.4. Operator interaction time

To record the required operator interaction time for algorithm initialization, we asked two operators (a research scholar and an MD‐PhD graduate student both with experience in reading prostate CT images) to select the bounding box and the anchor points on all the nonbrachytherapy and post‐LDR brachytherapy test images. The average recorded time for selecting bounding box were 41 ± 9 s. (34 ± 9 s. for nonbrachytherapy test images and 42 ± 8 s. for post‐LDR brachytherapy test images) and 40 ± 14 s. (53 ± 15 s. for nonbrachytherapy test images and 37 ± 12 s. for post‐LDR brachytherapy test images) for the first and the second operators, respectively. The average recorded time for selecting 12 anchor points were 18 ± 3 s. (18 ± 1 s. for nonbrachytherapy test images and 18 ± 3 s. for post‐LDR brachytherapy test images) and 16 ± 2 s. (14 ± 2 s. for nonbrachytherapy test images and 16 ± 2 s. for post‐LDR brachytherapy test images) for the first and the second operators, respectively. The average total operator interaction time (selecting bounding box and 12 anchor points) were 59 ± 10 s. (53 ± 9 s. for nonbrachytherapy test images and 61 ± 9 s. for post‐LDR brachytherapy test images) and 56 ± 14 s. (67 ± 14 s. for nonbrachytherapy test images and 53 ± 12 s. for post‐LDR brachytherapy test images) for the first and the second operators, respectively.

4. Discussion

4.A. Interobserver variability in manual segmentation

Pairwise comparison of our two, manual reference segmentations (Table 2) shows high interobserver variation in manual segmentation of the prostate in CT images. For example, we observed that the measured disagreement between the experts for the whole prostate gland was ranging from 72% to 97% in terms of DSC, and from 0.4 to 3.3 mm in terms of MAD. This disagreement is slightly lower in the midgland region and higher in the base and apex regions, and we did not observe a meaningful difference between the base and the apex in terms of manual segmentation difficulty. This variation in manual segmentation between expert observers makes it challenging to evaluate the segmentation algorithm using a single‐observer reference segmentation. Furthermore, it challenges the comparison between two, proposed algorithms based on the reported error metrics when they have been tested on different image datasets with different reference segmentations. It could be helpful for reducing the interobserver variability effects on evaluation if we evaluate our algorithm's segmentations against multiple, manual reference segmentations on the same image dataset.

4.B. Segmentation algorithm accuracy and computation time

With respect to the interobserver variability observed in manual segmentation, there is no gold standard defined for validation of the prostate segmentation in CT images. Therefore, the best reasonable and measurable performance compared to a manual reference segmentation which could be reached for a computer‐assisted segmentation method should not be less than the highest observed variation range between each two experts in manual segmentation. For the proposed algorithm, a comparison between corresponding mean values of Tables 2 and 3 shows that there is still a gap between the performance of our algorithm and the measured difference between the two observers. The results suggest that there is still room for improvement of the algorithm in terms of the measured error metrics. However, comparing the standard deviation of the metrics and the ranges of the metric values in Tables 2 and 3 shows that the magnitude of this variation in terms of most of the error metrics is higher when two human experts are being compared together. It means that there are some cases for which the measured difference between the algorithm segmentation and a human expert manual segmentation is lower than the measured difference between that expert and another human expert's manual segmentation. In Fig. 8, the bar graphs of DSC and MAD [Figs. 8(a) and 8(c)] for P2 and P8 and the bar graphs of HD [Fig. 8(e)] for P2, P6, P7, and P8 also support this finding.

For comparison with previous work published in the literature, Table 5 shows that the performance of the proposed method was within the reported metric values in terms of MAD and DSC and it outperformed the other methods listed in the table in terms of SR. The better performance of those methods (Refs. ^{10, 11, 12, 13, 14}) in Table 5 that have used the previously acquired treatment images of the same target patient for training the algorithm seems reasonable. In general, the reported errors in terms of MAD and DSC for those segmentation methods that use prostate border information of previous planning and/or treatment images of the target patient are lower than the MAD and DSC errors we measured for our method. Our method has similar performance or outperformed the other methods in terms of MAD and DSC. We measured SR of 94% for the proposed segmentation method, and which is higher than the reported SR values of the previous method. This suggests that on average, our algorithm's segmentation label covers the reference better than the other algorithms and that is an important feature for an algorithm that may be utilized for radiation therapy. The measured PR of our algorithm, that is, the proportion of the segmentation that covers the reference, is lower than the SR (82%). This means that 18% of the voxels are incorrectly classified as prostate. Therefore, this could cause irradiation of the healthy tissues during radiotherapy and needs to be improved.

Comparing the measured error metrics for the proposed segmentation method tested on post‐LDR brachytherapy images (Table 6) to our results on nonbrachytherapy images (Table 3) showed no meaningful or significant difference between the corresponding metric values. This suggests that our method may be used for both nonbrachytherapy and post‐LDR brachytherapy images. One explanation for this finding may be that in our algorithm prostate the surface is searched locally and close to the boundary region where fewer brachytherapy seeds are located and interfere with the algorithm performance. The potential interference of few brachytherapy seeds in the prostate surface point search may be compensated by using shape model and shape regularization.

The main part of the segmentation procedure of the proposed algorithm is run on a set of rays, and the execution on each ray is completely independent of the others. Therefore, the segmentation part is computationally parallelizable and it makes the algorithm highly capable for computation speed up. A parallel implementation on an unoptimized MATLAB research platform, using 12 CPU cores yields to about 20 s. of the computation time per 3D image, and which is lower than the other reported execution time in Table 5. The total segmentation time including the manual operator interaction time was less than 1.5 min per 3D image which is substantially less than fully manual delineation time of 4.46 min reported in Ref. 5.

4.C. Limitations

The performance of our segmentation algorithm should be considered in the context of the strengths and limitations of the proposed method. To apply the fully 3D image search we resampled the images to deal with relatively large through‐plane to in‐plane voxel dimension ratio of 4.25:0.977 and make the voxel size isotropic. However, image resampling could affect the texture extraction part. We used nearest neighbor interpolation to reduce this effect as much as possible. Moreover, optimization on the size of the median filter for image denoising might be helpful to improve the texture‐preserving noise reduction process. We also used a fixed patch size of 11 × 11 × 11 voxels for this study. An optimization on patch size might help to improve the performance of the segmentation algorithm. The small size of the nonbrachytherapy testing dataset (10 images) is another limitation of this study.

5. Conclusions

In this manuscript, we have presented a semiautomatic, learning‐based technique for full 3D segmentation of the prostate on CT images. Our method is trained based on local texture and shape characteristics of the prostate in CT images. The algorithm is initialized with a set of operator inputs to start the search for prostate surface around an estimated prostate surface generated using a shape modeling method. A radial search is then performed to extract a set of local texture features of 3D cubic image patches centered at a set of points along a number of rays and close to the initial estimated surface. A ray‐specific trained SVM classifier is then used for each ray to predict the prostate surface point on the ray. The extracted surface points are regularized and interpolated to form a smooth, plausible 3D surface for the prostate. The proposed method is not related to patient‐specific data, that is, previously acquired and segmented CT images from the same patient, for segmenting a patient's image and could, therefore, also be used for radiotherapy planning CT image segmentation. To have a better interpretation of the algorithm performance, we evaluated our segmentation method against manual reference segmentation using a set of surface‐, region overlap‐, and volume‐based error metrics. We measured the error metrics for the whole prostate gland as well as for the apex, midgland, and base regions. We also used two, different sets of manual reference segmentations to evaluate our method robustness to changing the reference. The measured error for the proposed algorithm against manual segmentation shows that our segmentation method achieved a segmentation accuracy close to the variation range observed in manual segmentation and comparable to the previously presented work with a statistically significant higher sensitivity compared to the previous work.

Conflict of interest

The authors have no conflicts to disclose.