BA-Net: Dense Bundle Adjustment Networks
This paper introduces a network architecture to solve the structure-from-motion (SfM) problem via feature-metric bundle adjustment (BA), which explicitly enforces multi-view geometry constraints in the form of feature-metric error. The whole pipeline is differentiable, so that the network can learn suitable features that make the BA problem more tractable. Furthermore, this work introduces a novel depth parameterization to recover dense per-pixel depth. The network first generates several basis depth maps according to the input image, and optimizes the final depth as a linear combination of these basis depth maps via feature-metric BA. The basis depth maps generator is also learned via end-to-end training. The whole system nicely combines domain knowledge (i.e. hard-coded multi-view geometry constraints) and deep learning (i.e. feature learning and basis depth maps learning) to address the challenging dense SfM problem. Experiments on large scale real data prove the success of the proposed method.
 This paper presents a novel approach to bundle adjustment, where traditional geometric optimization is paired with deep learning. Specifically, a CNN computes both a multi-scale feature pyramid and a depth prediction, expressed as a linear combination of "depth bases". These values are used to define a dense re-projection error over the images, akin to that of dense or semi-dense methods. Then, this error is optimized with respect to the camera parameters and depth linear combination coefficients using Levenberg-Marquardt (LM). By unrolling 5 iterations of LM and expressing the dampening parameter lambda as the output of a MLP, the optimization process is made differentiable, allowing back-propagation and thus learning of the networks* parameters. The paper is clear, well organized, well written and easy to follow. Even if the idea of joining BA / SfM and deep learning is not new, the authors propose an interesting novel formulation. In particular, being able to train the CNN with a supervision signal coming directly from the same geometric optimization process that will be used at test time allows it to produce features that will make the optimization smoother and the convergence easier. The experiments are quite convincing and seem to clearly support the efficacy of the proposed method. I don*t really have any major criticism, but I would like to hear the authors* opinions on the following two points: 1) In page 5, the authors write "learns to predict a better damping factor lambda, which gaurantees that the optimziation will converged to a better solution within limited iterations". I don*t really understand how learning lambda would _guarantee_ that the optimization will converge to a better solution. The word "guarantee" usually implies that the effect can be somehow mathematically proved, which is not done in the paper. 2) As far as I can understand, once the networks are learned, possibly on pairs of images due to GPU memory limitations, the proposed approach can be easily applied to sets of images of any size, as the features and depth predictions can be pre-computed and stored in main system memory. Given this, I wonder why all experiments are conducted on sets of two to five images, even for Kitti where standard evaluation protocols would demand predicting entire sequences.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
BA-Net: Dense Bundle Adjustment Networks
This paper introduces a network architecture to solve the structure-from-motion (SfM) problem via feature-metric bundle adjustment (BA), which explicitly enforces multi-view geometry constraints in the form of feature-metric error. The whole pipeline is differentiable, so that the network can learn suitable features that make the BA problem more tractable. Furthermore, this work introduces a novel depth parameterization to recover dense per-pixel depth. The network first generates several basis depth maps according to the input image, and optimizes the final depth as a linear combination of these basis depth maps via feature-metric BA. The basis depth maps generator is also learned via end-to-end training. The whole system nicely combines domain knowledge (i.e. hard-coded multi-view geometry constraints) and deep learning (i.e. feature learning and basis depth maps learning) to address the challenging dense SfM problem. Experiments on large scale real data prove the success of the proposed method.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 This paper presents a novel approach to bundle adjustment, where traditional geometric optimization is paired with deep learning. Specifically, a CNN computes both a multi-scale feature pyramid and a depth prediction, expressed as a linear combination of "depth bases". These values are used to define a dense re-projection error over the images, akin to that of dense or semi-dense methods. Then, this error is optimized with respect to the camera parameters and depth linear combination coefficients using Levenberg-Marquardt (LM). By unrolling 5 iterations of LM and expressing the dampening parameter lambda as the output of a MLP, the optimization process is made differentiable, allowing back-propagation and thus learning of the networks* parameters. The paper is clear, well organized, well written and easy to follow. Even if the idea of joining BA / SfM and deep learning is not new, the authors propose an interesting novel formulation. In particular, being able to train the CNN with a supervision signal coming directly from the same geometric optimization process that will be used at test time allows it to produce features that will make the optimization smoother and the convergence easier. The experiments are quite convincing and seem to clearly support the efficacy of the proposed method. I don*t really have any major criticism, but I would like to hear the authors* opinions on the following two points: 1) In page 5, the authors write "learns to predict a better damping factor lambda, which gaurantees that the optimziation will converged to a better solution within limited iterations". I don*t really understand how learning lambda would _guarantee_ that the optimization will converge to a better solution. The word "guarantee" usually implies that the effect can be somehow mathematically proved, which is not done in the paper. 2) As far as I can understand, once the networks are learned, possibly on pairs of images due to GPU memory limitations, the proposed approach can be easily applied to sets of images of any size, as the features and depth predictions can be pre-computed and stored in main system memory. Given this, I wonder why all experiments are conducted on sets of two to five images, even for Kitti where standard evaluation protocols would demand predicting entire sequences.
assistant
 This paper presents a novel approach to bundle adjustment, where traditional geometric optimization is paired with deep learning. Specifically, a CNN computes both a multi-scale feature pyramid and a depth prediction, expressed as a linear combination of "depth bases". These values are used to define a dense re-projection error over the images, akin to that of dense or semi-dense methods. Then, this error is optimized with respect to the camera parameters and depth linear combination coefficients using Levenberg-Marquardt (LM). By unrolling 5 iterations of LM and expressing the dampening parameter lambda as the output of a MLP, the optimization process is made differentiable, allowing back-propagation and thus learning of the networks* parameters. The paper is clear, well organized, well written and easy to follow. Even if the idea of joining BA / SfM and deep learning is not new, the authors propose an interesting novel formulation. In particular, being able to train the CNN with a supervision signal coming directly from the same geometric optimization process that will be used at test time allows it to produce features that will make the optimization smoother and the convergence easier. The experiments are quite convincing and seem to clearly support the efficacy of the proposed method. I don*t really have any major criticism, but I would like to hear the authors* opinions on the following two points: 1) In page 5, the authors write "learns to predict a better damping factor lambda, which gaurantees that the optimziation will converged to a better solution within limited iterations". I don*t really understand how learning lambda would _guarantee_ that the optimization will converge to a better solution. The word "guarantee" usually implies that the effect can be somehow mathematically proved, which is not done in the paper. 2) As far as I can understand, once the networks are learned, possibly on pairs of images due to GPU memory limitations, the proposed approach can be easily applied to sets of images of any size, as the features and depth predictions can be pre-computed and stored in main system memory. Given this, I wonder why all experiments are conducted on sets of two to five images, even for Kitti where standard evaluation protocols would demand predicting entire sequences.