Dataset
To train the quality prediction models, we used a set of 60 prostate MRI images along with automatically generated contours that had previously been produced by a bespoke deep segmentation network [38, 39] with a modified 3Dadopted EfficientDetB0 [36] architecture (see Sect. 2.4 for additional details on this architecture). Each image contour pair had an accompanying ground truth segmentation mask against which the quality of the automatically generated contours could be calculated. The ground truth segmentations were generated manually by consensus from two expert radiologists (> 5 years’ experience). In addition, 20 images had an additional set of automatically generated contours produced by a slightly different network, such that the model could learn to distinguish the difference between different contours on the same image. In total, there were 60 prostate images and 80 automatically generated contours. The Dice values of the contours were all in the [0.847, 0.943] range.
The images used for segmentation were axial T2weighted MRI scans of the prostate acquired using a 1.5 T scanner (slice thickness 3.0–3.6 mm, slice gap 0.3 mm, pixel spacing 0.59 × 0.59 mm, echo time 118 ms, and repetition time 3780 ms) [31, 32]. All images underwent N4 bias field correction (SimpleITK 2.0.2 with default parameters) before segmentation and model training, and all images had equal voxel sizes.
The following clinical characteristics were available for each patient for use in the baseline model: age, prostate volume, ISUP grade, PIRADS score, iPSA, and risk class.
The study was performed within the notification presented to the Ethics Committee of IRCCS Istituto Europeo di Oncologia and Centro Cardiologico Monzino (via Ripamonti 435, 20,141 Milano, Italy) (CE notification n. UID 2438). All patients had given their consent for use of their data for research and educational purposes.
Predicting contour quality
We framed the problem of quality assurance as a regression problem, where the input to the model is an image contour pair and the output is a measure of quality (see Fig. 1 for an illustrative overview). The specific quality metric we chose was the Dice coefficient because it is mathematically well defined, easily interpreted, bounded, and widely used within the medical imaging community.
For two binary pixel arrays (e.g., segmentation maps) A and B, the Dice coefficient is defined as
$${textit{Dice}}left( {A,B} right) = frac{{2left {A cap B} right}}{left A right + left B right}$$
(1)
Its value ranges from 0 to 1 where 1 corresponds to perfectly overlapping segmentations and 0 corresponds to having no intersection.
To measure the performance of the quality prediction models, we used mean absolute error (MAE) between the predicted Dice and the target Dice values, as well as the Spearman rank correlation between them. The Spearman correlation measures how correct the order of an ordered set is, and ranges from 1 (all samples are placed in correct order) to − 1 (all samples are placed in the opposite order). Random placement has an expected rank correlation of zero. As such, it gives an intuitive understanding of how well the algorithm can tell good contours from bad ones. In this work, the use of rank correlation will be implied whenever correlations are mentioned.
Baseline quality prediction model
The baseline model tries to predict how well an arbitrary segmentation algorithm would perform on a patient given only the clinical variables for that patient. The rationale for this is to examine whether any clinical variables are predictive of how hard it is to segment a given prostate. Because this model makes no use of images, it cannot distinguish between different segmentations of the same patient, but it can still be useful as an analytical tool and a benchmark. As the baseline model architecture, we chose a gradient boosted decision tree model implemented in CatBoost version 1.0.3 [33] with Python 3.7. For the 20 images with two different segmentations, we used the mean value of the Dice coefficients as the target value.
To train this model, we first perform a 64step parameter search with the Optuna Python package [34] with default settings to find suitable parameters. The search space is displayed in Table 1. Each parameter set was evaluated by its mean absolute error after eight repeated random fivefold crossvalidations. The best model was then further evaluated with 64 repeated random fivefold crossvalidations.
In order to gauge the usefulness of the baseline model, we compared its performance against a naïve baseline that predicts the mean Dice value for all samples.
Quality prediction network
The deep learning model we trained to predict segmentation quality was a modified EfficientDet [35] architecture (see Fig. 2). This architecture is an extension of the EfficientNet model [36] that is tailored toward object detection—it includes an EfficientNet backbone with seven levels (P1 to P7) connected to repeated “BiFPN” blocks (Bidirectional Feature Pyramid blocks). Our modifications included adaptation to 3D convolutions as well as an expansion factor reduction (from 6 to 2) and a custom regression head. The regression head consisted of serially connected fast normalized fusion nodes (see [35] for details) followed by batch normalization, PReLU, a singlechannel convolution, and a final sigmoid activation function. The EfficientNet [36] backbone was a B0 type with the default filter parameters of 32, 16, 24, 40, 80, 112, and 192 channels for the P1 to P7 levels, respectively. Our BiFPN blocks were repeated three times and used 64 filters each (Fig. 3).
To reduce the memory consumption of the model, the images were centercropped from 320 × 320 × 28 to 160 × 160 × 28 voxels. The images were also normalized by linearly mapping the 0th and 99th percentiles to the [0, 255] range, after which the 100th percentile values were appended. The MRI images and segmentation maps were concatenated on the channel dimension to form 4D tensors of shape 160 × 160 × 28 × 2 for each sample. These 4D tensors were used as the input to the model.
The network was trained for 200 epochs with MSE loss and batch size 2. We used the Adam optimizer with a learning rate of 0.002, which was reduced to 0.0002 after 120 epochs. Validation of the model was done with a random fivefold crossvalidation.
To give the network the ability to interpolate outside the narrow range of target Dice values typical of prostate segmentation, we used an elaborate data augmentation scheme to generate novel contours. At each epoch, one of the two samples had its corresponding contour switched with another contour randomly chosen from the training set such that each batch consisted of one real and one “fake” image contour pair. The fake contour was then scaled by a random factor in [0.55, 1.8]. After this procedure, we also applied standard data augmentation two both samples (in order): horizontal flips, uniform inplane rotation (in the (pm frac{pi }{12}) range), uniform 2D x and y translation (in ± 10%), uniform zoom (in ± 10%), and elastic deformation. This procedure also eliminates bias that could be introduced by only using contours from a single segmentation model.
Failure case studies
We evaluated how well the model predicts the quality of different variations of failed contours, for which the predicted Dice score ought to be low. The following failure modes were investigated (see Fig. 7 for illustrations):

1
empty contours (every pixel in the array is zero—no prostate tissue has been identified),

2
uniform binary noise (each pixel in the array is randomly assigned a value of zero or one),

3
filled matrix of ones (every pixel in the array is one—the whole image has been identified as prostate tissue)

4
shifted ground truth masks (the ground truth segmentation is randomly shifted uniformly by ± 50% in the x and ydirection).
These cases were constructed from the 16 patients in the test set at each validation fold, such that each failure case generated 80 independent samples in the course of the crossvalidation procedure.
In addition, we evaluated the predictions on the 16 unseen ground truth segmentations at each validation fold (for a total of 80 ground truth images). This allowed us to test the model performance on the opposite end of the domain, where all target values are 1.
We also defined a global accuracy score to indicate how well the model performed across all test samples (80 from the standard test set, 320 failure case samples, and 80 ground truth samples). This is useful because the MAE is not always indicative of how helpful the model’s predictions are. For example, if there is a segmentation with a true Dice value of 0.0, and the model predicts a Dice value of 0.5, the contour would still be flagged as “poor quality,” because both 0.0 and 0.5 Dice are considered bad. This means that the prediction is qualitatively correct, even though the MAE of 0.5 is very large. For a predicted Dice value ŷ and target Dice value y, we defined a failed prediction as either:

1.
(ŷ < 0.75)∧(y > 0.8), i.e., a predicted Dice value of less than 0.75 when the target Dice value is larger than 0.8, or

2.
(ŷ > 0.8)∧(y < 0.75), i.e., a predicted Dice value larger than 0.8 when the target Dice value is less than 0.75.
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