Summary
(1) Method:
And within the same face of a pedestrian among pedestrian video change video presented within the video and the distance between the video while learning (the SI 2 the DL).
(2) model:
The video (intra-vedio) distance matrix: more compact so that the same video;
Video Inter (intra-vedio) distance matrix: such that the two do not match the video matching video than smaller distance.
Video design triples (vedio triplet), to improve the learning matrix of discrimination.
(3) Data collection:
iLIDS-VID and PRID 2011 image sequence datasets
Introduction
(1) Most of today's methods are mainly heavy pedestrian image recognition (image-based), divided into two categories based on: learning and distance learning features.
Learning Characteristics: extracting features from the pedestrian image, comprising: a significant feature (salience features), wherein middle (mid-level features), significant color characteristics (salient color features).
Distance Learning: distance learning and efficient matrix to maximize matching accuracy, including: LMNN (large margin nearest neighbor), KISSME (keep it simple and straightforward metric), RDC (relative distance comparison).
(2) two video Re-id method recently proposed:
Extracting temporal characteristics (spatial-temporal) to represent each video pedestrian detailed description:
First the video segmentation, generates several fragments (fragments / walking cycles), temporal features extracted from each of the fragment, and using the extracted features to represent the video.
So between video Re-id can also be seen as a set of questions to match (set to set matching) of.
(3) Difficulty:
Posture (POSE), angle of view (Viewpoint), affected by light (Illumination) occlusion (Occlusion), not only there is a change among a plurality of video pedestrians, there is the same change in different frames of a video pedestrian (frame).
No change in the above method (intra-video variations) between the video and the video change (inter-video variations) for simultaneous processing.
Method (4) reduce the variation between the set: Learning (set-based distance learning) based on the set of distance
已提出的方法有：MDA(manifold discriminant analysis)、SBDR(set-based discriminative ranking)、CDL(covariance discriminative learning)、SSDML(set-to-set distance metric learning)、LMKML(localized multi-kernel metric learning).
（5）Motivation：
① major existing Re-id algorithm is based on the picture;
② Based Re-id of the video can be seen as a collection of image processing, but the existing set of methods based on distance learning is not to solve the Re-id-based video and design.
（6）Contribution：
① proposed called the SI 2 Re-ID methods based on the video of the DL;
② design a new model based on a set of distance learning;
③ designed a new model of the relationship between video (video triplet);
④ The iLIDS-VID and PRID 2011 data set evaluated.
The SI 2 the DL
(1) Problem Definition:
① training set: X-= [X- . 1 , ..., X- I , ..., X- K ]
Each video pedestrian X- i is p * n- i -dimensional, i.e., the i-th video containing n- i samples (Sample), p is the dimension of each sample, the j-th sample of the i-th video defined as X ij of .
② can be intuitively understood that, within each video so that if more compact, about separability between video significantly. This leads to the video distance matrix (intra-video distance metric), and the distance between the video matrix (inter-video distance metric ).
③ defines J (V, W):
V: intra-video distance metrics, Specifications: * K the p- 1
W：inter-video distance metrics，规格：K1*K2
V i : i th column of matrix V, specification: p * 1
W i : W i th column of the matrix, size: p * 1
f (V, X): Internal Cohesion video (congregating term)
g (W, V, X): discrimination between the video item (discriminant term)
μ: weight balance factor
The SI 2 frame is DL: training V and W, to reduce the above-described two items:
④ calculate f (V, X):
Using each video sample to represent the average of all the video, i.e. the i-th video X- i mean is:
Cohesion calculated: N represents the number of the data set of all picture frames
Understanding of the formula:
V T (X ij of -m I ) Specification matrix operation: (K . 1 * P) * (P *. 1) = K . 1 *. 1
V T produced here the role of the vector length changes, changes in the distance matrix, so that the video sample were close to about the center.
⑤ defined triplet (video triplet):
Parameters: Video X- I , X- J , X- K , corresponding to m I , m J , m K
Wherein X- J is X- I of correct matches, and X- K is the X- I mismatched,
Satisfy
He said X- I , X- J , X- K is triplet, referred to as <i, j, k>.
⑥ calculates g (W, V, X): | D | represents the number of triples.
Calculation discrimination items:
Where ρ is the penalty term:
两个范式之间的差值可以理解为：正确匹配的距离和错误匹配的距离之差，期望的结果是正确匹配的距离更小，错误匹配的距离更大，也就是这个差值更小.
为什么要加这个惩罚项？个人的理解是：为了保证区分度项始终是正值.
简写 ρ = exp(- b 式/ a 式)，ρ < 1. 若 a 式的值比 b 式小很多，那么 ρ 会很小，b 式会被削弱，(a式 - ρ*b式)结果为正；若 a 式的值比 b 式大很多，那么 ρ 会接近1，那么(a式 - ρ*b式)结果也为正.
⑦目标函数：
（2）SI2DL的优化：
① 由于上面的公式不是凸的，需要将问题进行转化：
其中 M1 和 M2 矩阵的元素分别为：
和
，其中<i,j,k>属于D.
(为什么？可能是凸优化方面的问题，还没有去学习，对这个公式的转化也不理解)
【注】Frobenius范式的计算方式：
② 确定 V、W 来更新 A、B：
初始化 V：
通过构建拉格朗日函数，并对其求导，得到结果：
其中 
个人推导过程【不一定准确】：
问题转化为了特征分解问题，选取 K1 个特征向量作为 V 的初始化.
初始化W：
采用同样的方法，选取 K2 个特征向量作为 W 的初始化.
当 V 和 W 确定后，通过优化下面的公式来获得 A 和 B ：
③ 确定 A、B、W 来更新 V：
当 A、B、W 确定后，优化问题转化为：
其中：
使用 ADMM算法 对上述的公式进一步转化：
首先引入变量S：
ADMM算法：
（ADMM算法这步没有理解，待查阅资料）
④ 确定 A、B、V 来更新W：
当 A、B、W 确定后，优化问题转化为：
同样使用ADMM算法把问题进一步优化，求解出 W.
⑤ SI2DL 算法总结：
（3）使用 V，W 矩阵对结果进行预测：
视频库(gallery video)：Y = [Y1, ..., Yi, ..., Yn]
第 i 个视频为 Yi，规格为：p * li，其中 li 为 Yi 中的样本数量.
待测视频 Zi 的规格为：p * ni，其中 ni 为 Zi 中的样本数量.
Yi / Zi 的第 j 个样本记为 yij / zij.
识别过程：
① 计算 Zi 和 Yi 的一阶表示：
② 计算两者间的距离：
③ 在视频库中挑选出距离最近的视频，作为 Zi 的匹配结果.
实验结果
（1）实验设置：
① 对比试验：
discriminative video fragments selection and ranking (DVR)
改进版：Salience+DVR 、 MSColour&LBP+DVR
spatial-temporal fisher vector representation (STFV3D)
改进版：STFV3D+KISSME
② 参数设置：
对于iLIDS-VID数据集(K1,K2) = (2200,80)，μ = 0.00005、τ1 = 0.2、τ2 = 0.2；
对于PRID数据集(K1,K2) = (2500,100)，μ = 0.00005、τ1 = 0.1、τ2 = 0.1；
③ 评估设置：
数据集50%用作训练集，50%用作测试集.
测试集中第1个相机的数据用作测试组，第2个相机的数据用作视频库.
使用CMC曲线评测，CMC曲线的介绍：【传送门】
（2）在iLIDS-VID数据集上的评测结果：
该数据集含有300个行人的600个图像序列，每个行人都有来自两个相机拍摄的图像序列.
每个图像序列含有22-192帧，平均还有71帧.
（3）在PRID2011数据集上的测评结果：
Cam-A含有385个行人的图像序列，Cam-B含有749个行人的图像序列.
每个序列含有5-675帧，平均含有84帧.（低于20帧的需要被忽略）
