Paper: Robust Stereo Matching by Risk Minimization (ICLR-2024)

Reviewer comment (Experiments):
The current iterative optimization based methods such as RAFT-Stereo directly predict continuous prediction and show strong robustness. It seems the method in this paper is not suitable for these iterative optimization methods, which I consider a major weakness restricting its application.

Author response:
Thank you for highlighting this. This comment of yours aligns well with the advice provided by R2. Following this,  we performed experiments IGEV, an iterative optimization method. We have added Table 13 in the revised draft showing the benefit of our iterative optimization approach with a well-known existing  architecture in stereo matching.

Reviewer comment (Experiments):
How important is the Laplacian kernel for interpolation in Eq.(1)? I wonder if using the simple bilinear interpolation is enough for capturing continuous cost values.

Author response:
The importance of the Laplacian kernel can be observed from the Table 14 added in the revised draft. Using other popular kernel such as Gaussian kernel degrades the performance and over-smooths the solution, whereas, the Laplacian kernel preserves high-frequency details providing better results. We have added this ablation study on the choice of kernel in the appendix—refer Table 14.

Reviewer comment (Experiments):
Considering the paper builds its own network architecture, I wonder how the method can improve existing cost aggregation based networks such as PCWNet or GWCNet.

Author response:
In the revised draft, we have a table — Table 8, showing the benefit of our proposed optimization when applied to existing cost aggregation based networks such as PCWNet.

Reviewer comment (Experiments):
The L1 risk minimization a general concept that can be applied into various stereo matching methods. Note that the L1 risk minimization is the biggest contribution in the paper. However, the paper introduces a new network architecture. Thus, it is unclear whether the performance in the experimental results is because of the proposed new architecture or the L1 risk minimization. More detailed analysis and ablation study are required.

Author response:
In this paper, we primarily  aim to propose a method to capture the continuous disparity via stereo matching networks. Furthermore, we put forward the benefit of L1 formulation to risk minimization loss function and how it can be incorporated in a differentiable way for neural network optimization via the use of implicit function theorem. Following your comments, we have more experimental results and ablation study on different architectural backbone showing the benefit of our proposed L1 risk optimization. Kindly refer Table 8, Table 13 and Table 15 for statistical results in our revised draft.

Reviewer comment (Evaluation):
Does the proposed risk minimization really improve the cross-domain generalization?

Author response:
Yes, the experimental results show that the proposed risk minimization improved the cross-domain generalization. We have addressed this concern following your comments in Table 15 in our revised draft.

Reviewer comment (Experiments):
Is there any reason to choose ACVNet and PCWNet for comparison in Table 8? Is it possible to perform experiment where the L1-risk is also used in the training stage. More comparisons with other networks are needed.

Author response:
The reason we choose ACVNet and PCWNet is because those are recent feature aggregation networks that seems to work really well for stereo matching problems. Yes, it is possible to do risk optimization at train time. Yet for simplicity we used pretrained feature networks. That said this is an encouraging direction for future extension. 

We have added comparison with other network architecture such as IGEV. Kindly refer to table 13  in the revised draft.

Reviewer comment (Theory):
Is there any limitation of the proposed L1 risk minimization method?

Author response:
Despite its benefit, L1 risk minimization is slightly more time consuming than the popular loss function such as L2 loss. To make such a continuous optimization time efficient is an attractive avenue for research in deep learning. Kindly refer to Table 8  in our revised draft for inference time analysis.

Reviewer comment (Writing):
There are parts of the paper whose wording can be improved. Proofreading by a native speaker will further strengthen the paper. Examples:  
a) impressive deep-learning architecture -> advancements in deep-learning. Something being impressive doesn't necessarily mean that it works.  
b) Typical stereo matching algorithm will sample ... and compute a discrete distribution p: Typical stereo matching algorithms will compute a cost that merely can be described as a PMF.  
c) To take a value from -> To choose a value as the final prediction?  
d) where the Sign() is the sign function -> where the sign is the signum function?  
e) In implementation, we clip -> we clip...

Author response:
We appreciate you pointing out the paper's minor typos and writing mistakes. Thank you so much for this. We have improved the highlighted typos and minor mistakes in the revised draft.

Reviewer comment (Writing):
The symbols in the math equation can easily cause confusion:  
a) The symbol p is used to denote the probability mass function and the probability density function. It is common to use P for mass and F for density. Another option would be to use subscripts if the authors want to keep using the notation p(x;p) for the probability density function.  
b) In equation (2) y is on both the left and right hand sides of the equation. If y is the result of the argmin, shouldn't the right-hand y be defined as a variable in a range of values? Similarly for equation (4).

Author response:
Thank you for the great advice on the notation and its possible confusion. (a) We added superscript $m$ to $\mathbf{p}$, i.e. $\mathbf{p}^m$ to the notation of probability mass function to avoid the confusion. (b) We have refined the draft accordingly.

Reviewer comment (Presentation):
The binary search algorithm can be moved to the appendix.

Author response:
We have moved the binary search algorithm in the appendix–refer page 16 Algorithm 1.

Reviewer comment (Presentation):
The related work section is very dense. Moving the binary search algorithm to the appendix will free some space to expand this section.

Author response:
We agree that related work is dense. But this is mainly because stereo matching is a very classical problem with more than 25 years of literature.  In our paper’s related work, we have tried to keep the essence of classical as well as modern approaches. We have slightly detailed on the related work in our revised draft and added a few comparison with our approach.

Reviewer comment (Presentation):
Figure 3: The captions are not aligned with the different stages of the architecture. The schematics could be condensed to allow more space for risk minimization, since the other parts of the proposed architecture are described in prior art.

Author response:
Excellent advice for improving our draft. For now, we are keeping the Figure 3 illustration the same but we are open to changing it after the decision. We have changed the Figure 3 caption following your advice.

Reviewer comment (Experiments):
Table 4: Are these results after training and testing all these methods on Middlebury? Please specify in the captions of all tables if the reported results are after self-evaluation or the official results on the dataset evaluation page. Also, submit results on the test set of Middlebury.

Author response:
For Table 4, the methods are trained on SceneFlow and evaluated on the training set of Middlebury. For Table 2 and Table 3, the results are obtained from the KITTI official website. Following your comments, we revised the captions.

Reviewer comment (Experiments):
Since the main proposal of this paper is risk minimization, it would strengthen the paper if the authors apply their proposed module to more architectures, like IGEV or Raft-stereo, which have shown strong cross-domain generalization.

Author response:
Indeed that is good advice to strengthen the current paper. We have added Table 13 in the revised draft that shows the results of our formulation on IGEV network architecture. Furthermore,  we have shown results on two other networks namely, ACVNet and PCWNet —refer Table 8 in the revised draft.