Person re-identification by Local Maximal Occurrence representation and metric learning

Shengcai LiaoYang HuXiangyu ZhuS. Li

article2014CVPR2,144 citations

Automated surveillance systems often struggle to track individuals across multiple camera views due to significant differences in lighting, pedestrian orientation, and low image resolution. Conventional techniques typically address this by separating visual feature extraction from statistical distance matching into disconnected steps, which frequently leads to degraded matching accuracy and high computational overhead.

The article evaluates a unified framework that combines a resilient visual representation, termed Local Maximal Occurrence (LOMO), with an integrated metric learning technique, Cross-view Quadratic Discriminant Analysis (XQDA). The objective is to demonstrate that simultaneously optimizing dimensionality reduction and cross-camera matching substantially improves identification accuracy and processing efficiency.

To evaluate this framework, the authors conducted empirical testing across four standard public benchmark datasets: VIPeR (632 image pairs), QMUL GRID (250 pedestrian pairs plus 775 distractor images), CUHK Campus (971 identities), and CUHK03 (13,164 images across 1,360 pedestrians). The LOMO approach extracts multi-scale color and texture features, using illumination correction and horizontal occurrence maximization to handle angle shifts. XQDA then projects these high-dimensional features into a compact subspace while directly learning a cross-view distance metric using closed-form statistical decomposition.

The findings show substantial improvements over existing state-of-the-art methods across all test environments. On the VIPeR benchmark, the proposed framework achieved a top-rank identification rate of 40.00%, surpassing the prior best benchmark of 37.80%. On the challenging underground GRID dataset, the approach reached 16.56% top-rank accuracy without camera-specific tuning, compared to 12.24% for competing models. Gains were especially pronounced on larger benchmarks: top-rank accuracy reached 63.21% on CUHK Campus (an absolute improvement of 28.91 percentage points over the prior 34.30% record) and 52.20% on CUHK03 (a 31.55 percentage point increase over deep-learning baselines).

Beyond accuracy, the framework demonstrates significant computational efficiency. LOMO processes an image in approximately 0.012 seconds, while XQDA model training completes in 1.86 seconds on a standard desktop computer—vastly faster than iterative metric learning methods that require tens to hundreds of seconds. These results indicate that high-performing person re-identification can be deployed in near real-time operational environments without requiring expensive specialized computing infrastructure or cumbersome camera-by-camera retraining.

Organizations implementing automated multi-camera tracking should adopt the joint subspace and metric learning architecture while utilizing generalized models rather than camera-pair-specific configurations, which are difficult to maintain in dynamic networks. Next steps include exploring additional local texture and color descriptors within the occurrence-maximization pipeline and extending the matching algorithm to related visual search tasks such as cross-domain face recognition. While confidence in the benchmark results is high, practitioners should note that operational accuracy will naturally be lower in real-world deployments involving severe occlusions, imperfect automated bounding boxes, or extremely crowded scenes.

Person Re-identi Cation Metric Metric Learning

Liao et al (2014).pdf

Paper: Learning a similarity metric discriminatively, with application to face verification, Sumit Chopra et al. (2005). Introduces discriminative metric learning using Siamese architectures, establishing the cross-view distance comparison principles that underpin metric learning formulations in person re-identification.
Paper: Eigenfaces vs. Fisherfaces: Recognition Using Class Specific Linear Projection, Peter N. Belhumeur et al. (1996). Presents foundational linear discriminant analysis techniques for appearance variation, providing the classical statistical subspace basis generalized by Cross-view Quadratic Discriminant Analysis (XQDA).
Paper: Evaluating Color Descriptors for Object and Scene Recognition, K. V. D. Sande et al. (2010). Provides a systematic framework for color descriptor invariance under severe illumination shifts, directly informing the illumination-corrected multi-scale color feature design used in LOMO.
Paper: Histograms of Oriented Gradients for Human Detection, Navneet Dalal et al. (2005). Establishes gradient orientation histograms for robust human representation, laying the groundwork for the local texture and horizontal stripe descriptor extraction used in person retrieval.

Paper: Scalable Person Re-identification: A Benchmark, Liang Zheng et al. (2015). Introduces the large-scale Market-1501 benchmark and evaluates scalable deep feature baselines, continuing the field's shift from handcrafted descriptors like LOMO to scalable deep learning frameworks.
Paper: Beyond Part Models: Person Retrieval with Refined Part Pooling, Yifan Sun et al. (2017). Builds on horizontal striping concepts seen in LOMO by introducing refined part pooling in deep convolutional architectures for body-part feature alignment.
Paper: In Defense of the Triplet Loss for Person Re-Identification, Alexander Hermans et al. (2017). Demonstrates how end-to-end deep metric learning with triplet loss formulations outperforms traditional statistical metric learners like XQDA on standard person re-identification benchmarks.
Paper: Performance Measures and a Data Set for Multi-target, Multi-camera Tracking, Ergys Ristani et al. (2016). Extends cross-camera pedestrian matching into end-to-end multi-target multi-camera tracking using large-scale synchronized surveillance footage and identity-preserving evaluation metrics.
Paper: Deep Learning for Person Re-Identification: A Survey and Outlook, Mang Ye et al. (2020). Provides a comprehensive survey synthesizing the transition from traditional descriptor-metric pipelines like LOMO/XQDA to state-of-the-art deep open-world re-identification paradigms.
Paper: Simple online and realtime tracking with a deep association metric, Nicolai Wojke et al. (2017). Integrates learned pedestrian appearance metrics directly into real-time multi-target tracking systems to resolve identity switches during prolonged occlusions.

Keywords

Person Re-identi Cation Metric Metric Learning Local Feature XQDA Proposed Local Maximal Occurrence Representation LOMO

1. Introduction
2. Related Work
3. Local Maximal Occurrence Feature
3.1. Dealing with Illumination Variations
3.2. Dealing with Viewpoint Changes
4. Cross-view Quadratic Discriminant Analysis
4.1. Bayesian Face and KISSME Revisit
4.2. XQDA
4.3. Practical Computation
5. Experiments
5.1. Experiments on VIPeR
5.1.1 Comparison of Metric Learning Algorithms
5.1.2 Comparison of Features
5.1.3 Comparison to the State of the Art
5.2. Experiments on QMUL GRID
5.3. Experiments on CUHK Campus
5.4. Experiments on CUHK03
5.5. Analysis of the Proposed Method
5.5.1 Role of Retinex
5.5.2 Role of Local Maximal Occurrence
5.5.3 Subspace Dimensions
5.5.4 Running Time
6. Summary and Future Work
Acknowledgments
References

Knowls

Knowl 1 — Local Maximal Occurrence (LOMO) Feature Representation
model/method
The Local Maximal Occurrence (LOMO) descriptor extracts a viewpoint-invariant and illumination-robust appearance representation from pedestrian images (normalized to $128 \times 48$ pixels).
1. Illumination Handling: The image is preprocessed using a multiscale center/surround Retinex transform with two Gaussian filter scales ( $\\sigma_1 = 5$ and $\\sigma_2 = 20$ ). Intensities are dynamically stretched to $[0, 255]$ . In addition to Retinex-corrected HSV color, Scale Invariant Local Ternary Patterns (SILTP) are employed to achieve robustness to illumination scale variations and image noise.
2. Local Feature Extraction: A sliding subwindow of size $10 \times 10$ pixels with a stride of 5 pixels is moved across the image. In each subwindow, three histograms are extracted:
- An $8 \times 8 \times 8 = 512$ -bin joint HSV color histogram.
- Two scales of SILTP histograms, $\text{SILTP}_{4,3}^{0.3}$ and $\text{SILTP}_{4,5}^{0.3}$ , each containing $3^4 = 81$ bins (162 bins total).
1. Horizontal Maximal Pooling: To achieve invariance to horizontal viewpoint changes while preserving vertical spatial layout, the maximum occurrence value of each histogram bin $b$ is selected across all subwindows located at the same horizontal band/row: $h_{\text{row}}(b) = \max_{k \in \text{row}} h_k(b)$ where $h_k(b)$ represents the value of bin $b$ in subwindow $k$ of that horizontal row.
2. Multiscale Pyramid and Normalization: A three-scale pyramid is constructed by downsampling the original $128 \times 48$ image via two successive $2 \times 2$ local average pooling operations, yielding images of sizes $128 \times 48$ , $64 \times 24$ , and $32 \times 12$ . The numbers of horizontal subwindow groups at each level are 24, 11, and 5, totaling 40 horizontal bands. The concatenated feature vector has dimensionality: $(512 + 162) \times (24 + 11 + 5) = 674 \times 40 = 26,960$ A logarithmic transform $f(v) = \log(1 + v)$ is applied to suppress large bin counts, and the HSV and SILTP feature subvectors are independently normalized to unit $L_2$ norm.
Knowl 2 — Cross-view Quadratic Discriminant Analysis (XQDA) Formulation and Metric Learning
model/method
Cross-view Quadratic Discriminant Analysis (XQDA) jointly learns a low-dimensional projection subspace $W \in \mathbb{R}^{d \times r}$ ( $r < d$ ) and a quadratic discriminant distance metric for cross-view feature vectors $x \in \mathbb{R}^d$ and $z \in \mathbb{R}^d$ across $c$ identity classes.

Pairwise difference vectors $\Delta = x_i - z_j$ are divided into intrapersonal differences $\Omega_I$ (where identity labels match: $y_i = l_j$ ) and extrapersonal differences $\Omega_E$ (where $y_i \neq l_j$ ). Both classes are assumed to follow zero-mean multivariate Gaussian distributions: $P(\Delta | \Omega_I) = \frac{1}{(2\pi)^{d/2}|\Sigma_I|^{1/2}} \exp\left(-\frac{1}{2} \Delta^T \Sigma_I^{-1} \Delta\right)$ $P(\Delta | \Omega_E) = \frac{1}{(2\pi)^{d/2}|\Sigma_E|^{1/2}} \exp\left(-\frac{1}{2} \Delta^T \Sigma_E^{-1} \Delta\right)$ where $\Sigma_I, \Sigma_E \in \mathbb{R}^{d \times d}$ are the intrapersonal and extrapersonal covariance matrices.

In the projected subspace defined by transformation matrix $W = (w_1, w_2, \dots, w_r) \in \mathbb{R}^{d \times r}$ , the projected covariance matrices are $\Sigma_I' = W^T \Sigma_I W$ and $\Sigma_E' = W^T \Sigma_E W$ . The distance function between $x$ and $z$ in the subspace is: $d_W(x, z) = (x - z)^T W \left( (W^T \Sigma_I W)^{-1} - (W^T \Sigma_E W)^{-1} \right) W^T (x - z)$

Because both $\Omega_I$ and $\Omega_E$ are zero-mean, traditional Fisher linear discriminant analysis is not applicable. Instead, the projection vector $w$ is optimized to maximize the ratio of projected extrapersonal variance $\sigma_E(w) = w^T \Sigma_E w$ to intrapersonal variance $\sigma_I(w) = w^T \Sigma_I w$ , formulated as the Generalized Rayleigh Quotient: $J(w) = \frac{w^T \Sigma_E w}{w^T \Sigma_I w}$ subject to $w^T \Sigma_I w = 1$ . The optimal projection vectors $w_1, \dots, w_r$ are the eigenvectors corresponding to the $r$ largest eigenvalues of $\Sigma_I^{-1} \Sigma_E$ , obtained via generalized eigenvalue decomposition.
Knowl 3 — Closed-Form Covariance Computation for Cross-View Metric Learning
theoretical result
Given cross-view training sets $X = (x_1, x_2, \dots, x_n) \in \mathbb{R}^{d \times n}$ from one camera view and $Z = (z_1, z_2, \dots, z_m) \in \mathbb{R}^{d \times m}$ from another camera view across $c$ classes, where class $k$ contains $n_k$ samples in $X$ and $m_k$ samples in $Z$ , the intrapersonal covariance $\Sigma_I$ and extrapersonal covariance $\Sigma_E$ can be computed without explicitly generating the $n \times m$ difference pairs.

The covariance matrices are given in closed form by: $n_I \Sigma_I = \tilde{X}\tilde{X}^T + \tilde{Z}\tilde{Z}^T - S R^T - R S^T$ $n_E \Sigma_E = m X X^T + n Z Z^T - s r^T - r s^T - n_I \Sigma_I$ where:
- $n_I = \sum_{k=1}^c n_k m_k$ is the total number of intrapersonal sample pairs.
- $n_E = n m - n_I$ is the total number of extrapersonal sample pairs.
- $\tilde{X} = (\sqrt{m_1} x_1, \dots, \sqrt{m_1} x_{n_1}, \dots, \sqrt{m_c} x_n) \in \mathbb{R}^{d \times n}$ .
- $\tilde{Z} = (\sqrt{n_1} z_1, \dots, \sqrt{n_1} z_{m_1}, \dots, \sqrt{n_c} z_m) \in \mathbb{R}^{d \times m}$ .
- $S = \left(\sum_{i: y_i=1} x_i, \sum_{i: y_i=2} x_i, \dots, \sum_{i: y_i=c} x_i\right) \in \mathbb{R}^{d \times c}$ is the matrix of class-wise sums of $X$ .
- $R = \left(\sum_{j: l_j=1} z_j, \sum_{j: l_j=2} z_j, \dots, \sum_{j: l_j=c} z_j\right) \in \mathbb{R}^{d \times c}$ is the matrix of class-wise sums of $Z$ .
- $s = \sum_{i=1}^n x_i \in \mathbb{R}^d$ and $r = \sum_{j=1}^m z_j \in \mathbb{R}^d$ are the total dataset sample sum vectors.
This formulation reduces the computational complexity of evaluating $\Sigma_I$ and $\Sigma_E$ from $O(n m d^2)$ to $O(N d^2)$ , where $N = \max(n, m)$ .
Knowl 4 — Subspace Dimension Selection and Regularization in XQDA
model/method
Cross-view Quadratic Discriminant Analysis (XQDA) includes two specific procedures for numerical stability and automated hyperparameter selection:
1. Covariance Regularization: When $\Sigma_I$ is singular or near-singular, computing $\Sigma_I^{-1}$ is unstable. A positive regularization parameter $\gamma$ is added to the diagonal elements of $\Sigma_I$ : $\Sigma_I \leftarrow \Sigma_I + \gamma I$ When input feature vectors are $L_2$ -normalized to unit length, $\gamma = 0.001$ provides robust and smooth estimation.
2. Automated Dimension Selection Criterion: Each eigenvalue $\lambda_i$ of $\Sigma_I^{-1} \Sigma_E$ equals the variance ratio $\sigma_E(w_i) / \sigma_I(w_i)$ along the corresponding eigenvector $w_i$ . Eigenvalues $\lambda_i \le 1$ correspond to projection directions where extrapersonal variation is smaller than or equal to intrapersonal variation, providing no discriminative capability. Therefore, the subspace dimensionality $r$ is automatically determined by retaining all eigenvectors whose eigenvalues are strictly greater than 1: $r = \sum_i \mathbb{I}(\lambda_i > 1)$

Knowl 5 — Person Re-identification Performance on the CUHK03 Benchmark

data/table

The CUHK03 dataset contains 13,164 images across 1,360 pedestrians observed from 6 camera views. Evaluation follows the standard single-shot protocol with 20 random splits (1,160 training identities, 100 testing identities, $P=100$ ) on both manually labeled bounding boxes and automated pedestrian detector bounding boxes.

Method	Labeled Rank-1 (%)	Detected Rank-1 (%)
LOMO + XQDA (Proposed)	52.20	46.25
DeepReID	20.65	19.89
KISSME	14.17	11.70
LDML	13.51	10.92
eSDC	8.76	7.68
LMNN	7.29	6.25
ITML	5.53	5.14
SDALF	5.60	4.87

LOMO + XQDA achieves 52.20% rank-1 accuracy on labeled boxes and 46.25% on detected boxes, outperforming the prior state-of-the-art DeepReID by 31.55 percentage points (labeled) and 26.36 percentage points (detected).

Knowl 6 — Person Re-identification Performance on the CUHK Campus Benchmark
empirical result
On the CUHK Campus dataset (971 pedestrians captured in two camera views, with Camera A capturing frontal/back views and Camera B capturing side views; images normalized to $160 \times 60$ pixels), the standard multi-shot experimental setting partitions the dataset into 485 training identities and 486 testing identities ( $P=486, M=2$ ).

LOMO + XQDA achieves a rank-1 cumulative matching accuracy of 63.21%, improving over prior state-of-the-art methods by 28.91 percentage points:
- LOMO + XQDA: 63.21%
- Mid-level Filter: 34.30%
- SalMatch: 28.45%
- GenericMetric: 20.00%
- eSDC: 19.67%
- ITML: 15.98%
- LMNN: 13.45%
- $L_1$ -norm: 10.33%
- SDALF: 9.90%
- $L_2$ -norm: 9.84%

Knowl 7 — Person Re-identification Performance on the VIPeR Benchmark

data/table

The VIPeR benchmark consists of 632 person image pairs captured by two cameras outdoors, scaled to $128 \times 48$ pixels. Experiments follow the standard protocol of 10 random 50/50 splits (316 training identities, 316 testing identities, $P=316$ ).

Method	Rank 1 (%)	Rank 10 (%)	Rank 20 (%)
LOMO + XQDA (Proposed)	40.00	80.51	91.08
SCNCD	37.80	81.20	90.40
kBiCov	31.11	70.71	82.45
LADF	30.22	78.92	90.44
SalMatch	30.16	65.54	79.15
Mid-level Filter	29.11	65.95	79.87
MtMCML	28.83	75.82	88.51
RPLM	27.00	69.00	83.00
LDFV	26.53	70.88	84.63
SSCDL	25.60	68.10	83.60
ColorInv	24.21	57.09	69.65
LF	24.18	67.12	82.00
SDALF	19.87	49.37	65.73
KISSME	19.60	62.20	77.00
PCCA	19.27	64.91	80.28
WELF6 + PRDC	16.14	50.98	65.95
PRDC	15.66	53.86	70.09
ELF	12.00	44.00	61.00

LOMO + XQDA achieves 40.00% rank-1 accuracy, outperforming the prior best method (SCNCD at 37.80%) by 2.20 percentage points. Furthermore, fusing LOMO + XQDA with LADF yields a 50.32% rank-1 identification rate on VIPeR.

Knowl 8 — Person Re-identification Performance on the QMUL GRID Benchmark

data/table

The QMUL GRID dataset consists of 250 pedestrian image pairs from 8 camera views in an underground station and 775 distractor gallery images. Evaluation is performed over 10 random trials using 125 pairs for training and 125 pairs plus 775 distractors ( $P=900$ ) for testing.

Without Camera Network Information
Method	Rank 1 (%)	Rank 10 (%)	Rank 20 (%)
ELF6 + L1-norm	4.40	16.24	24.80
ELF6 + RankSVM	10.24	33.28	43.68
ELF6 + PRDC	9.68	32.96	44.32
ELF6 + MRank-RankSVM	12.24	36.32	46.56
ELF6 + MRank-PRDC	11.12	35.76	46.56
ELF6 + XQDA	10.48	38.64	52.56
LOMO + XQDA	16.56	41.84	52.40
With Camera Network Information
Method	Rank 1 (%)	Rank 10 (%)	Rank 20 (%)
ELF6 + MtMCML	14.08	45.84	59.84
ELF6 + XQDA	16.32	40.72	51.76
LOMO + XQDA	18.96	52.56	62.24

When evaluated without camera network information, LOMO + XQDA reaches 16.56% rank-1 accuracy, outperforming the previous best result (12.24% by ELF6 + MRank-RankSVM) by 4.32 percentage points. When camera network pair-specific models are trained, LOMO + XQDA achieves 18.96% rank-1 accuracy.

Knowl 9 — Ablation Analysis of Retinex and Horizontal Max-Pooling in LOMO
empirical result
An ablation study on VIPeR ( $P=316$ ) isolates the effects of Retinex illumination correction and horizontal local maximal pooling under direct Cosine similarity matching and XQDA metric learning:
- Direct Cosine Matching:
  - Full LOMO feature: 20.25% rank-1 identification rate.
  - LOMO without Retinex: 12.97% rank-1 identification rate (a drop of 7.28 percentage points).
  - LOMO without horizontal maximal occurrence pooling: 11.39% rank-1 identification rate (a drop of 8.86 percentage points).
- XQDA Metric Learning:
  - Full LOMO + XQDA: 37.34% rank-1 identification rate.
  - LOMO without Retinex + XQDA: 34.18% rank-1 identification rate.
  - LOMO without horizontal maximal occurrence pooling + XQDA: 28.16% rank-1 identification rate (a drop of 9.18 percentage points).
These results confirm that Retinex improves color consistency across camera viewpoints, and horizontal local maximal pooling provides critical invariance against pose and viewpoint shifts.

Knowl 10 — Computational Efficiency and Metric Learning Training Times

data/table

Computational benchmarks on VIPeR ( $128 \times 48$ images) executed in MATLAB on an Intel Core i5-2400 @ 3.10GHz CPU:

LOMO Feature Extraction Speed: Extracting the 26,960-dimensional LOMO representation takes an average of 0.012 seconds per image.
Metric Learning Training Times (averaged over 10 random trials on VIPeR):

Methods with closed-form generalized eigenvalue solutions (XQDA, KISSME, RLDA) require less than 2 seconds of total training time, whereas iterative optimization techniques (ITML, LMNN) require orders of magnitude more computation.

Coverage note — No substantial contributed material was omitted from the paper.

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Citation

MLA

Liao, S., et al. “Person Re-identification by Local Maximal Occurrence Representation and Metric Learning”. 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2015, pp. 2197–206, https://doi.org/10.1109/CVPR.2015.7298832.

APA

Liao, S., Hu, Y., Xiangyu Zhu, & Li, S. Z. (2015). Person re-identification by Local Maximal Occurrence representation and metric learning. 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2197–2206. https://doi.org/10.1109/CVPR.2015.7298832

Chicago

Liao, S., Y. Hu, Xiangyu Zhu, and S. Z. Li. 2015. “Person Re-identification by Local Maximal Occurrence Representation and Metric Learning”. 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2197–2206. https://doi.org/10.1109/CVPR.2015.7298832.

Harvard

Liao, S. et al. (2015) “Person re-identification by Local Maximal Occurrence representation and metric learning”, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, pp. 2197–2206. Available at: https://doi.org/10.1109/CVPR.2015.7298832.

Vancouver

1. Liao S, Hu Y, Xiangyu Zhu, Li SZ (2015) Person re-identification by Local Maximal Occurrence representation and metric learning. In: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, pp 2197–2206

BibTeX

@inproceedings{Liao_2015, title={Person re-identification by Local Maximal Occurrence representation and metric learning}, url={http://dx.doi.org/10.1109/CVPR.2015.7298832}, DOI={10.1109/cvpr.2015.7298832}, booktitle={2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}, publisher={IEEE}, author={Liao, Shengcai and Hu, Yang and Xiangyu Zhu and Li, Stan Z.}, year={2015}, month=June, pages={2197–2206} }

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Algorithm	Training Time (seconds)
XQDA	1.86
KISSME	1.34
RLDA	1.53
ITML	36.78
LMNN	265.28

Person re-identification by Local Maximal Occurrence representation and metric learning

Keywords

Table of Contents

Knowls

Knowl 1 — Local Maximal Occurrence (LOMO) Feature Representation

Knowl 2 — Cross-view Quadratic Discriminant Analysis (XQDA) Formulation and Metric Learning

Knowl 3 — Closed-Form Covariance Computation for Cross-View Metric Learning

Knowl 4 — Subspace Dimension Selection and Regularization in XQDA

Knowl 5 — Person Re-identification Performance on the CUHK03 Benchmark

Knowl 6 — Person Re-identification Performance on the CUHK Campus Benchmark

Knowl 7 — Person Re-identification Performance on the VIPeR Benchmark

Knowl 8 — Person Re-identification Performance on the QMUL GRID Benchmark

Knowl 9 — Ablation Analysis of Retinex and Horizontal Max-Pooling in LOMO

Knowl 10 — Computational Efficiency and Metric Learning Training Times

References

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