Pairwise Camera-Distance Normalization

• Pairwise Camera-Distance Normalization is a technique that aligns score distributions across different camera pairs to mitigate bias in multi-camera systems.
• It employs both explicit methods such as global min–max scaling and implicit approaches like camera-based batch normalization to standardize distances.
• Empirical evaluations demonstrate that such normalization improves key metrics, including increased rank-20 accuracy and more reliable re-identification performance.

Pairwise camera-distance normalization refers to strategies that mitigate inconsistencies or biases in distance or similarity scores across different camera pairs in multi-camera vision systems. This normalization is essential when features extracted from different cameras are compared, such as in person re-identification (ReID), where variations in illumination, viewpoint, and imaging conditions result in statistically mismatched distributions and consequently biased distance measures. Recent research has examined multiple normalization techniques—explicit and implicit—to ensure that cross-camera distances are commensurate, improving ranking consistency and retrieval accuracy.

1. Motivation for Pairwise Camera-Distance Normalization

Cross-camera normalization is motivated by the intrinsic heterogeneity of real-world camera networks. In person ReID and related tasks, different cameras generate distance matrices that vary widely in scale due to differing photometric and geometric characteristics. As a result, raw pairwise distances between feature embeddings computed for probe and gallery images can be poorly aligned: gallery images from some cameras may seem "closer" in a purely numeric sense than others, even when true visual similarity is not higher. Without normalization, these scale inconsistencies degrade retrieval fairness and lead to suboptimal cumulative matching characteristic (CMC) and mean average precision (mAP) scores across datasets.

The central aim is to rectify or neutralize these shifts, either by direct score normalization, by distributional alignment at the feature level, or by metric adaptation that explicitly incorporates camera labels.

2. Explicit Score Normalization Methods

A direct approach to pairwise camera-distance normalization is the post-hoc normalization of the computed distance matrix, ensuring that all pairwise distances are mapped onto a common range regardless of their original scale.

Min–Max Normalization of Matching Scores

In "Improving CNN-based Person Re-identification using score Normalization" (Chouchane et al., 2023), the authors introduce an explicit min–max normalization applied globally to all probe–gallery (pairwise) score entries. Let $x$ be the vectorized set of Mahalanobis distances between all probe and gallery features (obtained from a CNN + XQDA pipeline):

$d_M(x_i, x_j) = (x_i - x_j)^T M (x_i - x_j)$

where $M = \Sigma_{s'}^{-1} - \Sigma_{d'}^{-1}$ is the learned metric in a discriminative subspace.

Normalization proceeds as: $N = \frac{x - x_{\min}}{x_{\max} - x_{\min}}$ with $x_{\min} = \min_i x_i$, $x_{\max} = \max_i x_i$ computed over all probe–gallery pairs in the dataset.

Key properties:

• Normalization is global (not per-camera-pair), with a single set of bounds.
• There is no dataset-specific or camera-pair-specific parameter fitting.
• This process preserves all pairwise rankings but removes scale bias, providing a consistent $[0,1]$ dynamic range for distances.

The normalization is applied before constructing the CMC or evaluation rank lists, ensuring that cross-camera retrieval is not hindered by underlying score incommensurability.

3. Integration into Metric Learning Pipelines

Normalization fits into standard discriminative metric learning systems as a final post-processing stage. For the widely used "CNN + XQDA" pipeline:

• Feature Extraction: Images are embedded into high-dimensional descriptors using a CNN backbone (e.g., AlexNet FC7, producing 4,096-D features).
• Metric Learning: An XQDA module learns a Mahalanobis metric optimized to maximize discrimination between intra- and inter-class differences under a Fisher criterion, with explicit covariance estimation:

$M = \Sigma_{s'}^{-1} - \Sigma_{d'}^{-1}$

• Pairwise Distance Calculation: For each probe–gallery pair, compute $d_M(x_i, x_j)$.
• Score Normalization: Globally normalize all scores via min–max scaling.
• Evaluation: Construct ranking lists and compute performance metrics using the normalized distances.

The normalization step does not require retraining or adaption of previous stages, and the entire pipeline is compatible with any feature extractor or metric learner outputting real-valued distances.

4. Impact on Retrieval Metrics and Empirical Performance

The empirical effect of global score normalization on ReID accuracy is pronounced, particularly in datasets characterized by large inter-camera variation. The following table summarizes the effect on rank-20 accuracy as reported for four ReID datasets (Chouchane et al., 2023):

Dataset	Without Normalization (%)	With Min–Max Normalization (%)	Gain (pp)
CUHK01	83.90	89.30	+5.40
GRID	61.92	64.64	+2.72
PRID450S	96.22	98.76	+2.54
VIPeR	92.03	92.78	+0.75

For the GRID dataset, the application of normalization resulted in a +2.72 percentage point increase in rank-20 accuracy; for CUHK01, the improvement is +5.40 pp. The normalization consistently enhances early retrieval rates in both challenging and high-performance regimes.

The improvement is attributed to the removal of cross-camera scale bias, yielding rank orderings in the CMC that are more consistent with semantic similarity, and reducing the negative impact of the most distorted camera pairs.

5. Alternative and Implicit Normalization Approaches

Pairwise camera-distance normalization can also be achieved via methods that align feature distributions or adapt metric computation, without an explicit post-hoc normalization scalar.

Camera-based Batch Normalization

Camera-based Batch Normalization (CBN) (Zhuang et al., 2020) replaces batch-level statistics in normalization layers with camera-specific statistics:

$$\hat{x}_m = \gamma \frac{x_m^{(c)} - \mu_{(c)}}{\sqrt{\sigma^2_{(c)} + \varepsilon}} + \beta$$

This technique standardizes feature activations for each camera separately, forcing features from all cameras to share common first and second order statistics before classification. The result is that raw feature distances computed across cameras are more naturally commensurate, and the scale bias in distance matrices is minimized. CBN results in substantial direct-transfer gains (e.g., +13.6% Rank-1 across benchmarks), without additional inference cost or architecture alterations beyond BN to CBN replacement.

Camera-Aware Jaccard Distance

CA-Jaccard (Chen et al., 2023) implicitly implements pairwise distance normalization in the context of re-ranking and clustering by splitting k-reciprocal neighbor sets into intra- and inter-camera subsets, and rebalancing their influence. With CKRNNs and camera-aware local query expansion (CLQE), both the neighbor selection and expansion steps account for camera identity, up-weighting reliable inter-camera neighbors and down-weighting intra-camera negatives. The final CA-Jaccard distance,

$$D_{i,j}^{\mathrm{CAJ}} = 1 - \frac{\sum_l \min(V^e_{i,l},\,V^e_{j,l})}{\sum_l \max(V^e_{i,l},\,V^e_{j,l})}$$

computes soft-neighbor overlaps that are by construction normalized across camera pairs. There is no explicit scalar normalization, but the support set construction guarantees camera-balanced representation, enforcing implicit normalization of pairwise distances.

6. Limitations, Extensions, and Recommendations

Explicit min–max normalization assumes that raw distances are monotonic and that cross-camera inhomogeneity is primarily a scale effect rather than a deeper issue in statistical distribution. It does not require camera-pair specific modeling, and no explicit adaptation to dataset statistics is performed beyond computing the global bounds.

Implicit normalization strategies such as CBN or CA-Jaccard require architectural changes or auxiliary label annotation (camera IDs), but can address more complex biases than simple scale. These approaches may be further generalized across domains or extended to handle video, time-varying cameras, or cases where the assumption of within-camera homogeneity fails.

For practitioners:

• The explicit global min–max normalization method is easily applied to any distance matrix in retrieval or matching contexts, with measurable gains in datasets with strong cross-camera domain shifts (Chouchane et al., 2023).
• When access to camera labels and integration at the feature or neighborhood-expansion stage is possible, implicit normalization via CBN or CKRNN/CLQE may provide superior alignment and generalization.
• Care must be taken that the normalization process does not inadvertently collapse meaningful distances when the original dynamic range is required for downstream applications.

7. Related Concepts and Distinctions

Pairwise camera-distance normalization should be distinguished from camera calibration and geometric normalization (e.g. the “baseline-constraint” method for resolving 3D reconstruction scale (Vupparaboina et al., 2015)). Whereas camera calibration aims to infer physical camera parameters in a Euclidean embedding, distance normalization addresses bias in semantic or feature space matching scores. Both share a conceptual goal of removing nuisance factors specific to particular camera pairs—scale, offset, or distributional deviation—that hinder fair and accurate cross-camera comparison. The normalization of computed similarity or distance matrices is thus a complementary technique to feature alignment, metric learning, and cross-domain adaptation within multi-camera vision systems.