__ Summary and Contributions__: The authors develop a model for learning reliability of individuals from noisy data, and to show the true segmentation label distributions. They propose two CNNs; one as an 'annotator' that must be as bad as possible while remaining as close as possible to training data. The second to provide an automatic segmentation which is combined with a matrix of each annotator.
The output should be a segmentation that is as close as possible to the 'true segmentation' rather than just being an average of multiple segmentations for a given image.

__ Strengths__: The motivation that we lack a good ground truth for segmentation is strong. This is indeed a challenge and the discussion of prior work here is basically good.
The use of three different metrics to evaluate is helpful.

__ Weaknesses__: If I understand correctly, STAPLE (reference 9) just aggregates the ground truths of multiple different annotators. This is different from automatic segmentation, which is what the authors are looking at with the other baselines (their model, naive CNNs and probabilistic U-net). So it’s somewhat confusing to include this in the table as if it was an automatic segmentation benchmark.
In general the comparison the benchmarks on segmentation accuracy is confusing, as it is difficult on a first read to understand if the goal is overall accuracy - i.e., the proposed model is a way of improving accuracy for automatic segmentation on previously unseen images - or if the goal is modelling the reliability of individual labellers, and that this information could be used in education, or as a filter to identify just the GT annotations to use for model training. The authors should make sure this is more clear.
The work assumes all individuals err in the a similar way, but when discussing future work the authors do mention they want to include metadata that might help learn deviations in how humans make mistakes. An important piece of metadata is whether the individuals have experiencing segmenting professionally (e.g., radiotherapy) or if they have just done it for a study. I.e., errors from the action of segmenting itself will be different from errors in the interpretation of medical imaging boundaries.
UPDATE: the authors rebuttal addressed my concerns sufficiently to warrant an upgraded assessment.

__ Correctness__: The claims are correct.
The claim that there is only one true segmentation map of the underlying anatomy is not always correct in medical imaging. While I agree with the authors that multiple hypotheses can arise from ambiguities in human interpretations, ambiguities in the imaging process itself may mean that multiple variations of a ground truth are plausible.

__ Clarity__: While other figures were displayed in colour, Figure 2 was black and while. This is a shame as the legend even stated that colours were needed!

__ Relation to Prior Work__: Prior work is clearly discussed.

__ Reproducibility__: Yes

__ Additional Feedback__:

__ Summary and Contributions__: The segmentation labels provided by multiple human annotators for a given
training dataset are potentially noisy versions of the real, unknown
ground-truth. Authors explore this idea to propose a method that simultaneously
learns to estimate the pixel-wise confusion matrices (CMs) for each annotator
and the real ground-truth. Training minimizes the cross-entropy between the
noisy labels of each annotator and the estimated labels for that annotator
obtained by multiplying the estimated CMs and estimated labels. An additional
regularization term minimizes the reliability of each annotator. Authors prove
that, under some mild conditions, this regularization produces CMs whose column
k-th will match the column k-th of the true CMs, being k the correct class.
Experiments apply this idea to train segmentation networks by aggregating
information from five different noisy annotators. The attained results
outperforms other baselines methods, sometimes by a large margin.

__ Strengths__: To the extent of my knowledge, this is the first work that learns how to
aggregate the information from multiple annotators by modeling the nature of
their mistakes while training a segmentation network.
Unlike previous works, authors model annotation errors conditioned not only to
the correct class, but also to the contents of the input image in a pixel-wise
manner. These is a sensible idea, as annotators are prone to making mistakes in
an image-dependent manner, and they are unlikely to consistently make the same
type of mistakes throughout the entire image.
The proposed regularization term is critical for the proper operation of the
training. Authors show its importance both theoretically in Theorem 1 and
empirically in the experimental section.
Finally, I found the conducted experiments extensive and convincing. Authors
compare their method against a large collection of baselines in four different
dataset with both synthetic and real annotators. The experiments are limited to
medical datasets, but I do not find this to be a limitation, as medical datasets
are challenging enough to be representative of the performance in other
real-world scenarios.

__ Weaknesses__: The method and theoretical contributions are very close to those from [28].
[28] proposes to learn a global CM for each annotator in classification tasks.
The present work extends this idea for segmentation tasks by conditioning the
CMs to the input image via a fully convolutional network. While this is not a
trivial improvement, I find the way it is done to be a straightforward extension
from [28].
[28] also introduces the trace of the CMs as a regularization term, and proves
that it leads to the true CMs under some mild conditions. Theorem 1 and its
proof are minor modifications of these theoretical contributions from[28] to
the case of pixel-wise CMs.
Given the similarity to [28], I am surprised that authors did not include a
"global CMs" method (in the spirit of [28] but in a segmentation task) as a
baseline in the experimental section. I think it is critical that authors show
that global CMs underperform when compared to the pixel-wise image-conditioned
CMs of the proposed method. This is not a trivial point to me: while global CMs
might ignore important image information, they are also much less prone to
overfitting than local CMs.

__ Correctness__: Both the claims and the method seem correct to me. I did not find issues
regarding this point.

__ Clarity__: Sections 3 and 4 have multiple issues. In some cases I had to guess what the
authors did. In some other cases I had to resort to [28] to solve my doubts.
Section 3 has some notation typos and issues that hinder the readability:
- There are a considerable and sometimes confusing abuse of notation regarding
per-pixel operations. This is specially problematic in Equations (3) and (4).
For example, the dot product A(x)·p(x) is in practice multiplying two
multichannel images (one containing a probability distribution per pixel and one
containing a CM per pixel). The CE operator also acts over entire images, but
the reader needs to guess how it aggregates the per-pixel cross-entropy into a
single value. It is not clear to me how to interpret 1(y_n^{(r)} \in
\mathcal{S}(x)), given that y_n^{(r)} is a vector of labels (one label per
pixel) and \mathcal{S}(x) seems to be a set of annotators.
- Is there a different between S(x_n) introduced in line 128 and the
\mathcal{S}(x_n) described in line 181? I guess they are the same function.
But in that case, the term 1(y_n^{(r)} \in \mathcal{S}(x)) in equations (3) and
(4) should be 1(r in \mathcal{S}(x)), as happens in line 168.
- In Equation (4) x_i should be x_n.
- In line 195, the mean CM A^* and its estimate \hat{A}^* have the very same
definition.
- Is the definition of \hat{A}^{(r)} in line 194 correct?
Section 4 also has multiple issues:
- Tables 1 and 2 show results for "dense labels" and "one label per image",
respectively. However, I had to read [28] to understand what "one label per
image" means and how that label is chosen. I could not find this explanation in
the paper.
- Tables 1, 2, and 3 show results with standard deviations, but it is not
specified over how many runs.
- It is not clear to me how the "Oracle (Ours but with known CMs)" of Table 1
was performed.
- The caption of Figure 2 ("CMs of 5 simulated annotators on MNIST dataset (Best
viewed in colour [...])") is unrelated to its contents. I do not see CMs in
Figure 2. There are no colors. It shows results for MNIST and MS Lesion.

__ Relation to Prior Work__: The review seems correct to me. I do not have objections regarding this point.

__ Reproducibility__: Yes

__ Additional Feedback__:

__ Summary and Contributions__: The main goal of this paper is to estimate the unknown true segmentation map. To solve the high inter-observer variability problem in the medical images segmentation task, the author proposed a supervised disentangling model trained by multiple noisy annotations.
The author used the probabilistic model to describe the principle of noisy medical annotations. The theory is clear and logical. One component of the model was trained to learn the real segmentation map, and the other models the annotators' behavior to reconstruct noisy annotations based on it. The first component was trained to generate a realistic map by minimizing the cross-entropy of noisy annotators.
This paper demonstrated the method on four datasets, including two medical datasets with synthetic annotations and real annotations by multiple experts. Compared to five label fusion baselines, this method gets better performance on each criterion and gets better results visually.

__ Strengths__: This paper describes a common problem in medical image segmentation, and it's meaningful to solve it. In summary, the proposed framework is innovative. The strengths are given as follows:
1. The task is beneficial for the application of machine learning in medical images. Since the high inter-observer variability is ubiquitous in this field, noisy labeling problems might restrict many methods' performance.
2. Compared to other methods, using probabilistic models to combine the ground truth map and annotators' characteristics is closer to reality. It's brilliant to use two parts to simulate the generation process of several noisy annotations, which guides the model to learn the real segmentation map.
3. The related work is elaborate. The author introduced various fusing label methods and analyzed the features and deficiency of previous researches.
4. The segmentation results are better than other related methods on both digit images and medical images, and the generated segmentation map is visually accurate merely by several noisy annotations.
5. The author uses public datasets to evaluate and give enough details of this work to be reproducible.

__ Weaknesses__: 1. The probability model is impressive, but the second assumption might limit the model performance. In practice, annotations of different pixels aren't independent. The pixels around a region are more likely to be labeled the same category than pixels far away. It's more reasonable to integrate each point's surrounding pixels in GT map to get macroscopic information.
2. The method was validated on four datasets, but only one dataset has real-world annotations. The morphological operations to generate noisy labels seem to be simplex, and the annotations in the LIDC-IDRI dataset have little variability. The author mentioned the Gleason'19 dataset, which has high inter-observer variability. It would be more credible to evaluate on datasets like that.

__ Correctness__: Yes

__ Clarity__: Yes. The paper is written clearly.

__ Relation to Prior Work__: Yes. This author pointed out the features of former researches on fusing labels. This work solves the common drawback by integrating information across multiple annotations. So the differences between this work and previous work are clearly indicated.

__ Reproducibility__: Yes

__ Additional Feedback__: 1. Since the annotations of the BraTS and the LIDC-IDRI dataset have few differences, it’s better to adjust the figures to be more intuitive. Besides, the annotations of the first and third examples in the LIDC-IDRI dataset are too similar, which can’t embody the performance.
2. The title is Disentangling Human Error from Ground Truth in Segmentation. But in the experiments part, it’s more like correcting boundary deviation than disentangling error. The inverse segmentation as an error in the BraTS dataset is not convincing enough.
3. As mentioned earlier, I think integrating surrounding information in the probability model will help learn the realistic pattern. Take brain segmentation, for example. Some experts may draw a large circle to point out the problem region, even though there are some small parts of the normal area. And some experts may be precise and point out every single region in the slide. And this phenomenon can be modeled by a probability framework with macroscopic information.
----------------------------------------------------
After reading the rebuttal, the work can be summarized as follows:
-- The authors propose a novel segmentation approach to estimate the latent ground truth from several noisy annotations.
-- The main idea is using predicted confusing matrixes to model the annotators, which assist the network in reconstructing the ground truth.
--The whole framework is like an extension of reference [28] from classification to segmentation, but the image-conditioned CMs proposed in this paper are more reasonable than global CMs, especially in medical images tasks. （weakness）
--Besides, the authors did extensive experiments in four datasets to prove the performance of the model. And the supplementary experiment result also shows the superiority of image-dependent CMs. However, maybe there are few satisfactory datasets, but it will be more convincing to validate real-world datasets with high variation. （weakness）
I will hold my original score.

__ Summary and Contributions__: The authors of this paper propose a method that jointly learns the ground-truth segmentation labels and the residual errors incurred by human annotators. There are two major contributions. First, the proposed model is able to learn both tasks without access to the groud-truth labels. Second, the model is able to learn the noise pattern associated with each annotator on a population rather than on a single image.

__ Strengths__: First of all, noise among labels is a very common problem in the medical imaging domain. The problem that this paper is trying to solve is very clinically relevant. Moreover, the authors propose a rigorous framework to formulate the task. The design of the trace-based regularization is particularly novel. In addition, extensive experiments are performed to demonstrate the superior performance of the model.

__ Weaknesses__: The major weakness of this paper is the lack of experiments with non-synthetic labeler noise. While the proposed method is benchmarked on the real-world dataset, all the noisy labels are created by artificially distorting the segmentation labels. However, the synthetic noise generation process does not necessarily reflect the noise generated by human annotators. For instance, annotator 2,3,5 impose very severe distortion that a professional annotator, especially in medical imaging, wouldn't do. To truly prove the clinical usage of this paper, the author needs to perform experiments on the settings where noise is generated by human labelers. An ideal dataset would contain GT labels created by experienced annotators (radiologists for instance) and noise labels created by inexperienced annotators (medical students).
Update: this concern is mostly addressed in the author feedback.

__ Correctness__: The experiment set up is sensible. The authors provide sufficient support for the claims made in this paper.

__ Clarity__: The overall quality of writting in this paper is satisfactory. The authors could improve the quality of writting by avoid complicated long sentences. There are a few minor grammar error / typo such as line 24, 226.

__ Relation to Prior Work__: Yes, there is suffcient discussion on the prior works as well as how the proposed method is different from them.

__ Reproducibility__: Yes

__ Additional Feedback__: