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Title: BA-Net: Dense Bundle Adjustment Networks

Paper content:
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.
The Structure-from-Motion (SfM) problem has been extensively studied in the past a few decades.
Almost all conventional SfM algorithms BID46 BID39 BID16 BID13 jointly optimize scene structures and camera motion via the Bundle-Adjustment (BA) algorithm BID43 BID1 , which minimizes the geometric BID46 BID39 or photometric BID17 BID13 error through the Levenberg-Marquardt (LM) algorithm BID35 .
Some recent works BID44 attempt to solve SfM using deep learning techniques, but most of them do not enforce the geometric constraints between 3D structures and camera motion in their networks.
For example, in the recent work DeMoN BID44 , the scene depths and the camera motion are estimated by two individual sub-network branches.
This paper formulates BA as a differentiable layer, the BA-Layer, to bridge the gap between classic methods and recent deep learning based approaches.
To this end, we learn a feed-forward multilayer perceptron (MLP) to predict the damping factor in the LM algorithm, which makes all involved computation differentiable.
Furthermore, unlike conventional BA that minimizes geometric or photometric error, our BA-layer minimizes the distance between aligned CNN feature maps.
Our novel feature-metric BA takes CNN features of multiple images as inputs and optimizes for the scene structures and camera motion.
This feature-metric BA is desirable, because it has been observed by BID17 that the geometric BA does not exploit all image information, while the photometric BA is sensitive to moving objects, exposure or white balance changes, etc.
Most importantly, our BA-Layer can back-propagate loss from scene structures and camera motion to learn appropriate features that are most suitable for structure-from-motion and bundle adjustment.
In this way, our network hard-codes the multi-view geometry constraints in the BA-Layer and learns suitable feature representations from training data.We strive to estimate a dense per-pixel depth, because dense depth is critical for many tasks such as object detection and robot navigation.
A major challenge in solving dense per-pixel depth is to find a compact parameterization.
Direct per-pixel depth is computational expensive, which makes the network training intractable.
So we train a network to generate a set of basis depth maps for an arbitrary input image and represent the result depth map as a linear combination of these basis 2 RELATED WORK Monocular Depth Estimation Networks Estimating depth from a monocular image is an ill-posed problem because an infinite number of possible scenes may have produced the same image.
Before the raise of deep learning based methods, some works predict depth from a single image based on MRF BID37 BID36 , semantic segmentation BID29 , or manually designed features BID27 .
BID15 propose a multi-scale approach for depth prediction with two CNNs, where a coarse-scale network first predicts the scene depth at the global level and then a fine-scale network will refine the local regions.
This approach was extended in BID14 to handle semantic segmentation and surface normal estimation as well.
Recently, BID30 propose to use ResNet BID24 based structure to predict depth, and BID47 construct multi-scale CRFs for depth prediction.
In comparison, we exploit monocular image depth estimation network for depth parameterization, which only produces a set of basis depth maps and the final result will be further improved through optimization.Structure-from-Motion Networks Recently, some works exploit CNNs to resolve the SfM problem.
BID22 solve the camera motion by a network from a pair of images with known depth.
employ two CNNs for depth and camera motion estimation respectively, where both CNNs are trained jointly by minimizing the photometric loss in an unsupervised manner.
implement the direct method BID40 as a differentiable component to compute camera motion after scene depth is estimated by the method in .
In BID44 , the scene depth and the camera motion are predicted from optical flow features, which help to make it generalizing better to unseen data.
However, the scene depth and the camera motion are solved by two separate network branches, multi-view geometry constraints between depth and motion are not enforced.
Recently, propose to solve nonlinear least squares in two-view SfM using a LSTM-RNN BID26 as the optimizer.Our method belongs to this category.
Unlike all previous works, we propose the BA-Layer to simultaneously predict the scene depth and the camera motion from CNN features, which explicitly enforces multi-view geometry constraints.
The hard-coded multi-view geometry constraints enable our method to reconstruct more than two images, while most deep learning methods can only handle two images.
Furthermore, we propose to minimize a feature-metric error instead of the photometric error in to enhance robustness.
This paper presents the BA-Net, a network that explicitly enforces multi-view geometry constraints in terms of feature-metric error.
It optimizes scene depths and camera motion jointly via feature-metric bundle adjustment.
The whole pipeline is differentiable and thus end-to-end trainable, such that the features are learned from data to facilitate structure-from-motion.
The dense depth is parameterized as a linear combination of several basis depth maps generated from the network.
Our BA-Net nicely combines domain knowledge (hard-coded multi-view geometry constraint) with deep learning (learned feature representation and basis depth maps generator).
It outperforms conventional BA and recent deep learning based methods.
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assistant: text: This paper introduces a network architecture to solve the structure-from-motion (SfM) problem via feature bundle adjustment (BA)