# HPS-Net: Multi-Task Network for Medical Image Segmentation with Predictable Performance
## 4 Experiments and Results  
In the experiments, two aspects of HPS-Net were evaluated. The first aspect was to evaluate whether HPS-Net can perform as well as PHiSeg after introducing the measure network. The second aspect was to evaluate the performance of HSP-Net on predicting different measurement values. Experiments were conducted on the LIDC-IDRI dataset [11] and the ISIC2018 dataset [12]. The LIDC-IDRI dataset contains 1018 thoracic CT images from 1010 subjects with lesions annotated by four experienced thoracic radiologists. The original in-plane resolution of the CT images was between 0.461 mm and 0.977 mm. In the experiments, all CT images were normalized to 0.5 mm \(\times\) 0.5 mm resolution. Based on the lesion positions annotated by the radiologists, the lesion patches of size 128 \(\times\) 128 pixels were cropped out. The processed dataset was then partitioned into the ratio of 60:20:20 for training, testing, and validation, respectively. The ISIC2018 dataset consists of 3694 skin lesion images, including a training set, a validation set, and a test set. The training set consists of 2594 images and 2594 corresponding ground-truth response masks. The validation set and the test set consist of 100 images and 1000 images, respectively. The initial size of images in ISIC2018 varied from 1024 \(\times\) 768 to 512 \(\times\) 384. In our experiments, these images were normalized to 512 \(\times\) 512. To compare with PHiSeg [10], we followed the setting of [10] in all experiments, setting seven resolution levels for both PHiSeg and HPS-Net. In the first experiment, we firstly trained the models with the masks from all four radiologists and then trained the models with only one mask from a single radiologist. When training with all masks, one mask was randomly selected per image in each batch. When training with one mask, only the mask from the same radiologist was used for the corresponding image in each batch. We used a conventional Dice score to gauge the similarity between an output segmentation hypothesis and a mask. To compare a set of segmentation hypotheses and a set of masks, namely, to compare two sets of segmentation distributions, we used the generalized energy distance [9; 19]:  
\[D_{GED}^{2}(P_{gt},P_{out})=2\mathbb{E}[d(S,Y)]-\mathbb{E}[d(S,S^{\prime})]- \mathbb{E}[d(Y,Y^{\prime})] \tag{5}\]  
where \(Y\) and \(Y^{\prime}\) are independent masks from the ground-truth distribution \(P_{gt}\), \(S\) and \(S^{\prime}\) are independent segmentations from the predicted distribution \(P_{out}\), and \(d(\cdot,\cdot)=1-IoU(\cdot,\cdot)\). \(1-IoU(\cdot,\cdot)\) has been proved to be a metric [20; 21]. \(D_{GED}\) is also a metric in this case if \(d(\cdot,\cdot)\) is also a metric, which has been proved in [22]. Like [10], we also used the average normalized cross correlation (NCC) to evaluate the correlation between the predicted distribution and the ground-truth distribution from a visual perspective:  
\[S_{NCC}(P_{gt},P_{out})= \mathbb{E}_{Y\sim P_{gt}}[NCC(\mathbb{E}_{S\sim P_{out}} \tag{6}\] \[CE(\overline{S},S)],\mathbb{E}_{S\sim P_{out}}[CE(Y,S)])]\]  
where \(CE\) denotes cross entropy and \(\overline{S}\) is the mean segmentation prediction. Table 1 show the results of the first experiment, which compares the segmentation performance of different methods on the LIDC-IDRI dataset. From Table 1, we can observe that, using all annotations, HPS-Net (L = 5) and PHiSeg (L = 5) performed better than prob. U-Net in terms of \(D_{GED}\) and \(S_{NCC}\). With single annotation, HPS-Net (L = 5) and PHiSeg (L = 5) outperformed prob. U-Net and det. U-Net in terms of \(Dice\), \(D_{GED}\), and \(S_{NCC}\). Additionally, we can observe that HPS-Net showed slightly better performance than  
PHiSeg with the same number of resolution levels in the cases of both single annotation and all annotations, but the performance difference was small.