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LSTR: End-to-end Lane Shape Prediction with Transformers

November 2020

tl;dr: Use transformer to directly predict polynomial coefficients of lanes.

Overall impression

The paper uses transformers for lane line detections. It is inspired by DETR, which introduced the transformers to object detection.

The paper has a great session talking about the polynomial lane shape model with very detailed derivation.

The formulation of lane lines as parallel polynomials is a bit limiting as it cannot handle more complex topologies such as splits, merges and lanes perpendicular to the ego lane. However the idea is still applicable if we allow a more flexible representations of lane lines, as long as there is still the concept of individual countable lane line instances (number of query sequence).

The paper recycles a lot of the details from DETR but describes them differently. It is recommended that these two papers should be read together.

Key ideas

  • Polynomial lane shape model
    • Cubid curve for a single lane on flat ground (X, Z) $$X = kZ^3 + mZ^2 + nZ + b$$
    • Projected to (u, v). The primed parameters are composites of parameters and camera intrinsics and extrinsics. $$u = k' / v^2 + m' / v + n' + b' \times v$$
    • For tilted road (with pitch) $$u = k'' / (v - f'')^2 + m'' / (v - f'') + n' + b'' \times v - b'''$$
    • Vertical starting and ending offsets $\alpha, \beta$ in images.
    • If we assume a global consistent shape for all lanes, then $k'', f'', m'', n'$ will be shared for all lanes, and $b'', b'''$ will not be shared.
    • Therefore, the output of t-th lane is $$g_t = ((k'', f'', m'', n'), (b_t'', b_t''', \alpha_t, \beta_t))$$.
    • Each lane line is only different in bias terms and starting and ending positions.
  • Loss
    • Hungarian bipartite matching
      • Largely follow DETR.
      • N=7 lane lines at most. In case there are fewer than N lane lines in GT, pad with non-lanes with cls score c=0.
    • Location loss
      • L1, sample lanes at fixed intervals. Starting and ending positions are also predicted.
  • Architecture
    • ResNet-18 backbone
    • Input: HxWxC feature map is reshaped into HW sequence of length C. Concatenated with positional embedding (not necessarily the same size as input as the paper claims).
    • Encoder: two layers. QKV are all front the input sequence with length HW (each has a learnable matrix)
    • Decoder: two layers. Initial input to decoder $S_q$ are all zeros. Positional embeddings $E_{LL}$ are learned specialized workers attending to different types of lane lines. --> This is not described clearly in the original DETR paper.
  • FNN for predicting curve parameters
    • Nx2 for predicting each lane is lane or background
    • Nx4 to predict 4 specific parameters
    • Nx4 followed by average to regress shared 4 parameters

Technical details

  • Too many layers of encoder and decoder are causing overfitting and degraded generalization ability.

Notes