Learning a Discriminative Null Space for Person Re-identification (1603.02139v1)

Abstract: Most existing person re-identification (re-id) methods focus on learning the optimal distance metrics across camera views. Typically a person's appearance is represented using features of thousands of dimensions, whilst only hundreds of training samples are available due to the difficulties in collecting matched training images. With the number of training samples much smaller than the feature dimension, the existing methods thus face the classic small sample size (SSS) problem and have to resort to dimensionality reduction techniques and/or matrix regularisation, which lead to loss of discriminative power. In this work, we propose to overcome the SSS problem in re-id distance metric learning by matching people in a discriminative null space of the training data. In this null space, images of the same person are collapsed into a single point thus minimising the within-class scatter to the extreme and maximising the relative between-class separation simultaneously. Importantly, it has a fixed dimension, a closed-form solution and is very efficient to compute. Extensive experiments carried out on five person re-identification benchmarks including VIPeR, PRID2011, CUHK01, CUHK03 and Market1501 show that such a simple approach beats the state-of-the-art alternatives, often by a big margin.

• The paper introduces a discriminative null space method that collapses within-class variance to zero while preserving between-class differences for person re-identification.
• It employs a closed-form NFST solution enhanced with kernelization and a semi-supervised extension, eliminating the need for dimensionality reduction or parameter tuning.
• Extensive experiments on five benchmarks, including VIPeR and Market1501, demonstrate improved rank-1 accuracy and robust performance over state-of-the-art approaches.

Learning a Discriminative Null Space for Person Re-identification

This paper addresses the persistent small sample size (SSS) problem in the domain of person re-identification by proposing a novel method of learning a discriminative null space of the training data. Existing person re-identification approaches often suffer from limitations due to high dimensionality in feature representation and insufficient training data. The proposed technique introduces an innovative approach to distance metric learning by leveraging the null Foley-Sammon transform (NFST), effectively overcoming SSS challenges without needing dimensionality reduction or regularization techniques.

Methodology

The core contribution of the work is to establish that learning a discriminative null space can alleviate the SSS problem by collapsing within-class variance to zero while maintaining a positive between-class variance. The approach ensures that images of the same individual are transformed into a single point within the null space, optimizing the Fisher discriminative criterion. This model leads to a fixed-dimensional, efficient, closed-form solution that does not require parameter tuning.

The NFST method builds upon traditional linear discriminant analysis, aiming to find Null Projecting Directions (NPDs) fulfilling the zero within-class scatter condition. By defining an eigen-problem where the solution lies in the shared space between the null space of the within-class scatter matrix and the orthogonal complement of the total scatter matrix, the approach ensures highly discriminative capabilities while addressing the SSS issue efficiently.

Kernelization of the NFST is also explored to manage non-linearity in the appearance of individuals by projecting the data into a higher-dimensional space. This leads to enhanced matching performance. Furthermore, a semi-supervised extension is proposed, which leverages unlabelled data commonly available in person re-identification tasks to further mitigate SSS effects through an iterative self-training mechanism.

Experimental Evaluation

The paper details extensive experiments conducted across five person re-identification benchmarks: VIPeR, PRID2011, CUHK01, CUHK03, and Market1501. The proposed method consistently outperformed existing state-of-the-art approaches, particularly at low ranks. On the challenging VIPeR dataset, the method achieved a noticeable rank-1 accuracy improvement. On the largest benchmark, Market1501, it significantly outperformed other methods when evaluated with both single-query and multi-query settings.

The paper highlights the robustness of the model in fully supervised learning settings and demonstrates superior performance in semi-supervised scenarios by effectively utilizing unlabelled data. The inclusion of a kernelized variant further underscores the versatility of the method across different data complexities.

Implications and Future Directions

The introduction of discriminative null space learning holds theoretical importance for addressing foundational issues in high-dimensional, small-sample settings. Practically, its efficient computation and lack of tuning make it attractive for real-world re-identification solutions.

Future work could explore the integration of deep learning paradigms with null space learning for enhanced feature representation capabilities. Additionally, examining the method's generalizability to other domains facing the SSS problem could provide valuable insights, particularly in scenarios involving scarce annotated data.

In summary, this paper presents a significant advancement in the domain of person re-identification by offering an efficient and potent solution to a classic problem, demonstrating impressive performance across established benchmarks while maintaining computational efficiency.