Semi-Supervised Ranking for Re-identification with Few Labeled Image Pairs

Abstract

In many person re-identification applications, typically only a small number of labeled image pairs are available for training. To address this serious practical issue, we propose a novel semi-supervised ranking method which makes use of unlabeled data to improve the re-identification performance. It is shown that low density separation or graph propagation assumption is not valid under some conditions in person re-identification. Thus, we propose to iteratively select the most confident matched (positive) image pairs from the unlabeled data. Since the number of positive matches is greatly smaller than that of negative ones, we increase the positive prior by selecting positive data from the top-ranked matching subset among all unlabeled data. The optimal model is learnt by solving a regression based ranking problem. Experimental results show that our method significantly outperforms state-of-the-art distance learning algorithms on three publicly available datasets using only few labeled matched image pairs for training.

Appendix: Proof of Equation (12)

Suppose there are $N_i^a$ images for person $i$ under camera $a$ and $N_j^b$ images for person $j$ under $b$. The number of positive matches for person $i$ in both camera views is $N_i^a N_i^b$. Since the total numbers of images are $\sum _{i=1}^{J^a} N_i^a$ under camera view $a$ and $\sum _{j=1}^{J^b} N_j^b$ under camera view $b$, the positive prior $\tau$ is calculated by

$$\begin{aligned} \tau = \frac{\sum _{i=1}^{J} N_i^a N_i^b}{\sum _{i=1}^{J^a} N_i^a \sum _{j=1}^{J^b} N_j^b} \end{aligned}$$

(17)

The total number of image pairs in $E_1$ is equal to the number of groups $G_{m\cdot }$ and $G_{\cdot n}$, i.e., $\sum _{i=1}^{J^a} N_i^a + \sum _{j=1}^{J^b} N_j^b$. There are $\sum _{i=1}^{J} N_i^a$ groups $G_{m\cdot }$ and $\sum _{j=1}^{J} N_j^b$ groups $G_{\cdot n}$ containing at least one positive ADV. However, the classification function $f$ may wrongly select a negative ADV from $G_{m\cdot }$ or $G_{\cdot n}$ that contains positive ADV(s). Thus, the number of ADVs in $E_1$ is $(\sum _{i=1}^{J} N_i^a + \sum _{j=1}^{J} N_j^b) c_1$, where $c_1$ is the rank one accuracy measuring the performance of $f$. Then, the positive prior $\tau _1$ in $E_1$ is given by the following equation,

$$\begin{aligned} \tau _1 = \frac{(\sum _{i=1}^{J} N_i^a + \sum _{j=1}^{J} N_j^b) c_1}{\sum _{i=1}^{J^a} N_i^a + \sum _{j=1}^{J^b} N_j^b} \end{aligned}$$

(18)

Since it is difficult to compare $\tau$ and $\tau _1$ by (17) and (18) directly, we approximate them by assuming $N_i^a \approx \sum _{i'=1}^{J^a} N_{i'}^a / J^a$ and $N_j^b \approx \sum _{j'=1}^{J^b} N_{j'}^b / J^b$. Substituting the approximations of $N_i^a$ and $N_j^b$ into (17) and (18), respectively, $\tau$ and $\tau _1$ become

$$\begin{aligned} \tau = \frac{J}{J^a J^b}, \tau _1 = \frac{(\frac{J}{J^a} \sum _{i=1}^{J^a} N_i^a + \frac{J}{J^b} \sum _{j=1}^{J^b} N_j^b) c_1}{\sum _{i=1}^{J^a} N_i^a + \sum _{j=1}^{J^b} N_j^b} \ge \frac{J c_1}{\max (J^a, J^b)} \end{aligned}$$

(19)

If $\max (1 / J^a, 1 / J^b) \ll c_1$, multiplying $J^a J^b$ on both sides, we obtain $\max (J^a, J^b) \ll J^a J^b c_1$. Thus, $\tau \ll \tau _1$, which leads to (12).