Symmetry-guided Mask Module for Vehicle Models

• SMM is a masking strategy that exploits the bilateral symmetry of vehicles to reduce redundancy and improve feature learning.
• It enforces that only one patch per symmetric pair remains visible, thereby increasing the challenge of the reconstruction task and enhancing discriminative representation.
• Empirical results demonstrate that SMM yields notable performance gains on vehicle-centric tasks, especially at high mask ratios, with minimal added computation.

The Symmetry-guided Mask Module (SMM) is a masking strategy designed for self-supervised pre-training of vehicle-centric perception models, specifically introduced in VehicleMAE-V2. SMM leverages the intrinsic bilateral symmetry of road vehicles to improve the efficiency and effectiveness of masked image modeling. By ensuring that at most one patch in each symmetric pair is visible during training, SMM reduces redundancy, enhances difficulty in the reconstruction task, and optimizes the representational learning process for vehicle-centric visual tasks (Wu et al., 22 Dec 2025).

1. Motivation and Rationale

Road vehicles exhibit strong bilateral symmetry, a property that conventional masked autoencoder (MAE) approaches ignore by randomly sampling masked and visible image patches. In symmetric objects, this practice leads to the simultaneous visibility of both patches in a symmetric pair (e.g., both headlights), wasting modeling capacity on redundant content. SMM addresses this by enforcing that only one patch per symmetric pair remains visible. The main effects are: (a) forcing the encoder to focus on complementary and non-redundant regions, (b) increasing the challenge of the reconstruction task, prompting the decoder to learn more discriminative and global representations, and (c) reducing the encoder's input with redundant information, thus lessening computational load (Wu et al., 22 Dec 2025).

2. Theoretical Formulation

Given an input image $I \in \mathbb{R}^{224 \times 224 \times 3}$, the image is divided into $N=14 \times 14 = 196$ non-overlapping patches of $16 \times 16$. A lightweight detector estimates:

• The bounding-box center $O=(c_x, c_y)$
• The yaw-angle $\theta$ of the vehicle's symmetry axis

The symmetry axis is modeled as an infinite line $\ell$ through $O$ at angle $\theta$. For a patch $i$ with center $p_i = (x_i, y_i)$, its symmetric counterpart is determined by reflecting $p_i$ across $\ell$:

$$R_\ell(p_i) = O + R_\theta^\top \begin{pmatrix} -1 & 0 \ 0 & 1 \end{pmatrix} R_\theta (p_i - O)$$

where

$$R_\theta = \begin{pmatrix} \cos\theta & -\sin\theta \ \sin\theta & \cos\theta \end{pmatrix}$$

The symmetric pair index $j$ is selected as the closest patch center to $R_\ell(p_i)$: $j = \arg\min_{k} \|R_\ell(p_i)-p_k\|_2$. Optionally, the symmetry distance metric $d_{sym}(i)=\|p_j-R_\ell(p_i)\|_2$ can quantify the match tightness, but due to uniform patch grids, nearest neighbor assignment is used in practice.

3. Algorithmic Implementation

SMM combines hierarchical masking with symmetry constraints via the following workflow:

1. Depending on availability, either a pure random mask ($M_{rnd}$), box-guided mask ($M_{box}$), or symmetry-guided mask ($M_{sym}$) is selected.
2. Given bounding box $B$ and orientation $\theta$, $M_{box}$ is first applied.
3. Symmetric patch pairs $S$ are identified as described above.
4. For each pair $(i,j)$, if both are unmasked (i.e., both would be visible), one is randomly masked to enforce the symmetry constraint.
5. The overall masking ratio is adjusted to maintain the desired global mask ratio $r$.

Pseudocode summary as presented in (Wu et al., 22 Dec 2025):

Input: patches P[1..N], mask-ratio r, detector output (B,θ) Output: binary mask array mask[1..N] (1=masked, 0=visible) // 1) Choose initial mask if no box B: mask ← M_rnd(P, r) elif B exists but no θ: mask ← M_box(P, B, r_in, r_out) else: // both B and θ mask ← M_box(P, B, r_in, r_out) S ← build_symmetric_pairs(P, B, θ) for each (i,j) in S: if mask[i]==0 and mask[j]==0: if rand()<0.5: mask[i]=1 else: mask[j]=1 // Adjust to maintain overall ratio r total_masked ← sum(mask) desired ← round(r * N) if total_masked > desired: extra ← total_masked - desired unmask_candidates ← indices k with mask[k]==1 randomly pick extra of them and set mask[k]=0 elif total_masked < desired: deficit ← desired - total_masked unmask_candidates ← indices k with mask[k]==0 randomly pick deficit and set mask[k]=1 return mask

After masking, visible patches and a [CLS] token are embedded and processed by a ViT-Base encoder, followed by standard MAE reconstruction (decoder reconstructs masked patches, $L_2$ pixel MSE loss).

4. Loss Strategy and Optimization

SMM introduces no new loss term. The standard masked autoencoder loss is retained:

$$L_{r} = \frac{1}{|\mathcal M|} \sum_{t\in \mathcal M} \|V_t - \hat V_t\|_2^2$$

where $\mathcal M$ indexes masked patches, $V_t$ is the original pixel, and $\hat V_t$ is the reconstruction. Additional structured priors such as contour-guided and semantic-guided modules operate independently of SMM (Wu et al., 22 Dec 2025).

5. Practical Considerations

• Patch size and grid: 16×16 patches, forming a 14×14 grid.
• Axis estimation: Relies on a monocular yaw-angle detector (YAEN); falls back to alternative masking if axis estimation fails.
• Computation: Reflection per patch is $O(1)$, yielding $O(N)=O(200)$ overall. Post-reflection, nearest grid cell assignment is a minimal overhead (< 1 ms per batch on GPU).
• Robustness: If orientation estimation is unreliable, the module degrades gracefully, reverting to box- or random-guided masking (Wu et al., 22 Dec 2025).

6. Empirical Impact and Downstream Performance

Evaluation on five representative vehicle-centric tasks demonstrates that SMM consistently yields improved performance at fixed masking ratios, with the most significant relative gains at high mask-ratios (e.g., 85%). Improvements (Δ) reported at 75% mask-ratio include:

Component	V-ReID mAP (%)	V-ReID R1 (%)
all losses (no SMM)	86.1	97.9
all losses + SMM	86.6 (+0.5)	98.0 (+0.1)

Related improvements are observed in attribute recognition (mA), detection (AP₀.₅), fine-grained recognition, and part segmentation (mIoU). The symmetry-guided approach's benefit increases as fewer patches are visible, indicating effective prioritization of unique, information-rich input regions (Wu et al., 22 Dec 2025).

7. Scope and Significance

SMM is a lightweight, modular strategy targeted at vehicle-centric vision systems. By explicitly incorporating vehicle symmetry priors into the masking process, it refines the information available for encoding, enhances challenging region reconstruction, and results in more robust learned representations. The method is computationally inexpensive, introduces no additional loss terms, and is orthogonally compatible with other structured prior modules. Application results on the Autobot4M dataset affirm its practical value for a range of downstream perception tasks (Wu et al., 22 Dec 2025).