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BA-Net: Dense Bundle Adjustment Networks

July 2020

tl;dr: Feature-metric differentiable bundle adjustment.

Overall impression

BA-Net proposed to do BA on feature maps to avoid sensitivity to photometric changes in the input, while still leverages denser information than keypoints. It also uses a new formulation of depth prediction from a series of prototype depth maps (cf YOLACT). --> The compact depth representation by coefficient is very similar to CodeSLAM where an AutoEncoder is used to compress depth maps. This compact depth representation decreases the search space of LM algorithm.

Note that there is no PoseNet to predict ego motion. The output of the BA layer is the camera pose sequence and point cloud depths.

The idea of feature metric loss is further extended in Feature metric monodepth ECCV 2020.

DeepV2D is similar to BA-Net.

  • BA-Net tries to optimize one joint nonlinear optimization over all variables, and thus needs to decompose depth prediction with depth basis to reduce search space.
  • DeepV2D decomposes joint optimization into more tractable subproblems of optimization of depth and motion, and do block coordinate descent. It allows the depth estimation module to be more expressive and thus directly estimate per-pixel depth.
  • Performance of DeepV2D is better than BA-Net across the board.
Background of BA
  • Keypoint BA
    • Only information from corners and blobs
    • Feature matching with RANSAC still gives outliers
  • Photometric BA: Direct method uses dense pixel values and leverages more information
    • Sensitive to initialization
    • Sensitive to photometric calibration (camera exposure, white balance)
    • Sensitive to outliers such as moving objects
  • Feature-metric BA:
    • Higher level feature, insensitive to photometric calibration and MOD outliers
    • Less sensitive to initialization as it has more clear global minimum
    • It is like doing DSO with learned and more robust feature map (rather than original image).

Key ideas

  • Bundle Adjustment is hard to integrate into neural network due to two reasons.
    • Iterative: this can be
    • If/Else switch on predicting the damping factor.
  • BA-Net fixed the iteration to 5, and uses an MLP to predict the damping factor. This makes BA end-to-end differentiable.
  • Architecture
    • Input: from previous $X$ (state: camera pose and point depth) and Feature maps, error is computed. Error is fed into an MLP to get damping factor.
    • Damping factor and Diagonal matrix from Jacobian yields $\Delta X$
    • $X$ gets updated and feed into next iteration.
  • Basis depth map
    • instead of dense prediction, BA-Net predicts 128 basis depth channels and predict 128-dim weighting factor w.

Technical details

  • Uses 5 consecutive frames for optimization on KITTI and achieves very good performance than most one frame based depth estimation.
  • The performance on KITTI looks too good to be true. Almost on par with supervised method DORN. The sqr rel has some issues per author's answer here in 知乎.
  • Note that the Sq Rel value in BA-Net is not reliable, as pointed out by DeepV2D.

Notes

  • Questions and notes on how to improve/revise the current work