写东西最好中午写，因为早晚不想写

一、论文回顾

论文获取：http://AlignedReID: Surpassing Human-Level Performance in Person Re-Identification

AlignedReID很有意思，提出了动态规划下计算局部最短路径的方法。这条最短路径中的一条边就对应了一对局部特征的匹配，它给出了一种人体对齐的方式，在保证身体个部分相对顺序正确的情况下，这种对齐方式的总距离是最短的。在训练的时候，最短路径的长度被加入到局部损失函数，辅助学习行人的整体特征。

要看懂这张图，我们分几个小问题来一步步分析。

1. 7x7的矩阵是怎么得到的？——用F和G分别代表两张图，其特征分别为 $\mathbf{F}=\left\{\boldsymbol{f}_{1}, \boldsymbol{f}_{2}, \ldots, \boldsymbol{f}_{H}\right\}$ 和 $\mathrm{G}=\left\{\boldsymbol{g}_{1}, \boldsymbol{g}_{2}, \ldots, \boldsymbol{g}_{H}\right\}$ ，在文中H=7，分别计算各部分的相似度（根据公式一），得出7x7=49种相似度，即一个7x7的矩阵。

2. 拐点的含义是什么？——图中拐点表示两张图像切片相对应的位置，比如（2，4）表示Image A的第二块切片和Image B的第四块切片是Aligned

3. 如何理解最短路径？——分黑线和黑箭头两部分理解。首先，第一行黑线横跨矩阵中1-4行，表示Image A的第一块切片与Image B的1-4块切片是corresponding alignment；其次，第一行黑箭头同样横跨矩阵中1-4行，表示Image A的第一块切片与整个Image B的最大相似度（或最短距离），换句话说就是计算机认为A的第一块切片只于B的前四块切片相似，与后面三块完全不相似，所以剩下的三块不属于对应对齐区域，也就无关最短路径的计算。

4. 黑线的最短路径计算公式是什么？（你会说是公式2，没有错，那你能自己推导吗）

Image A的第一块切片与Image B的距离： $d_{1,1}+d_{1,2}+d_{1,3}+d_{1,4}$

Image A的第二块切片与Image B的距离： $d_{2,4}+d_{2,5}$

Image A的第三块切片与Image B的距离： $d_{3,5}$

Image A的第四块切片与Image B的距离： $d_{4,5}+d_{4,6}$

Image A的第五块切片与Image B的距离： $d_{5,6}$

Image A的第六块切片与Image B的距离： $d_{6,6}+d_{6,7}$

Image A的第七块切片与Image B的距离： $d_{7,7}$

二、代码解析

AlignedReID的代码与Triplet loss很相似，由于之前已经详细解析过Triplet loss源码了https://blog.csdn.net/m0_57541899/article/details/122243847?spm=1001.2014.3001.5501https://blog.csdn.net/m0_57541899/article/details/122243847?spm=1001.2014.3001.5501这里直接在代码上解析。先把几个值得注意的函数写在前面：

1. torch.mean(object,dim,keepdim):对指定维度求平均，将指定的那维全变成1。如一个大小为（2，3）的tensor，其中2代表0维，3代表1维，对0维求平均，则tensor大小变为（1，3）

2. permute(dims):将tensor的维度换位。如Imag的size是（28，28，3），就可以利用img.permute(2，0，1）得到一个size为（3，28，28）的张量

3. squzze(a,axis=None):a为输入数组，axis用于删除指定维度

4. clamp(float min-number，float max-number，float parameter):用法为fmin<fp<fmax，则返回fp；fp>fmax，则返回fmax；fp<fmin，则返回fmin

from __future__ import print_function
import torchdef normalize(x, axis=-1):"""Normalizing to unit length along the specified dimension.Args:x: pytorch VariableReturns:x: pytorch Variable, same shape as input      """x = 1. * x / (torch.norm(x, 2, axis, keepdim=True).expand_as(x) + 1e-12)  # torch.norm(input,p,dim):calculate the norm in the specified dimension(p-dim)return xdef euclidean_dist(x, y):"""Args:x: pytorch Variable, with shape [m, d]y: pytorch Variable, with shape [n, d]Returns:dist: pytorch Variable, with shape [m, n]"""m, n = x.size(0), y.size(0)  # n:128  m:128xx = torch.pow(x, 2).sum(1, keepdim=True).expand(m, n)  # 1:means axis=1yy = torch.pow(y, 2).sum(1, keepdim=True).expand(n, m).t()dist = xx + yydist.addmm_(1, -2, x, y.t())  # dist=1*dist-2*(x@y^T);  # Note:dist.addmm_ & dist.addmmdist = dist.clamp(min=1e-12).sqrt()  # gain the distance matrix between samplesreturn distdef batch_euclidean_dist(x, y):  # x,y={Tensor:(128,8,128)}={Tensor:(N,m,d)}"""Args:x(local_feat): pytorch Variable, with shape [N, m, d]=[128,8,128]y(local_feat[p_inds]): pytorch Variable, with shape [N, n, d]=[128,8,128]Returns:dist: pytorch Variable, with shape [N, m, n]"""assert len(x.size()) == 3assert len(y.size()) == 3assert x.size(0) == y.size(0)assert x.size(-1) == y.size(-1)N, m, d = x.size()  # N:128 m:8 d=128N, n, d = y.size()  # n=8# shape [N, m, n]xx = torch.pow(x, 2).sum(-1, keepdim=True).expand(N, m, n)  # xx={Tensor:(128,8,8)}yy = torch.pow(y, 2).sum(-1, keepdim=True).expand(N, n, m).permute(0, 2, 1)  # yy={Tensor:(128,8,8)}dist = xx + yydist.baddbmm_(1, -2, x, y.permute(0, 2, 1))  # dist=1*dist-2*(x@y.permute);  # Note:dist.baddmm_ & dist.baddmmdist = dist.clamp(min=1e-12).sqrt()  # for numerical stabilityreturn distdef shortest_dist(dist_mat):"""Parallel version.Args:dist_mat: pytorch Variable, available shape:1) [m, n]2) [m, n, N], N is batch size3) [m, n, *], * can be arbitrary additional dimensionsReturns:dist: three cases corresponding to `dist_mat`:1) scalar2) pytorch Variable, with shape [N]3) pytorch Variable, with shape [*]"""m, n = dist_mat.size()[:2]# Just offering some reference for accessing intermediate distance.dist = [[0 for _ in range(n)] for _ in range(m)]  # initializationfor i in range(m):for j in range(n):if (i == 0) and (j == 0):dist[i][j] = dist_mat[i, j]elif (i == 0) and (j > 0):dist[i][j] = dist[i][j - 1] + dist_mat[i, j]elif (i > 0) and (j == 0):dist[i][j] = dist[i - 1][j] + dist_mat[i, j]else:dist[i][j] = torch.min(dist[i - 1][j], dist[i][j - 1]) + dist_mat[i, j]dist = dist[-1][-1]return distdef local_dist(x, y):"""Args:x: pytorch Variable, with shape [M, m, d]y: pytorch Variable, with shape [N, n, d]Returns:dist: pytorch Variable, with shape [M, N]"""M, m, d = x.size()N, n, d = y.size()x = x.contiguous().view(M * m, d)y = y.contiguous().view(N * n, d)# shape [M * m, N * n]dist_mat = euclidean_dist(x, y)dist_mat = (torch.exp(dist_mat) - 1.) / (torch.exp(dist_mat) + 1.)# shape [M * m, N * n] -> [M, m, N, n] -> [m, n, M, N]dist_mat = dist_mat.contiguous().view(M, m, N, n).permute(1, 3, 0, 2)# shape [M, N]dist_mat = shortest_dist(dist_mat)return dist_matdef batch_local_dist(x, y):"""Args:x(local_feat): pytorch Variable, with shape [N, m, d]=[128,8,128]y(local_feat[p_inds]): pytorch Variable, with shape [N, n, d]=[128,8,128]Returns:dist: pytorch Variable, with shape [N]"""assert len(x.size()) == 3  # judge the 'x' matrix whether is 3-dim,if not,report errorassert len(y.size()) == 3assert x.size(0) == y.size(0)assert x.size(-1) == y.size(-1)# shape [N, m, n]dist_mat = batch_euclidean_dist(x, y)  # dist_mat={Tensor:(128,8,8)}dist_mat = (torch.exp(dist_mat) - 1.) / (torch.exp(dist_mat) + 1.)  # normalization# shape [N]dist = shortest_dist(dist_mat.permute(1, 2, 0))  # (128,8,8)-->(8,8,128),then calculate the shortest distance under dynamic planningreturn distdef hard_example_mining(dist_mat, labels, return_inds=False):"""For each anchor, find the hardest positive and negative sample.Args:dist_mat: pytorch Variable, pair wise distance between samples, shape [N, N]labels: pytorch LongTensor, with shape [N]return_inds: whether to return the indices. Save time if `False`(?)Returns:dist_ap: pytorch Variable, distance(anchor, positive); shape [N]dist_an: pytorch Variable, distance(anchor, negative); shape [N]p_inds: pytorch LongTensor, with shape [N]; indices of selected hard positive samples; 0 <= p_inds[i] <= N - 1n_inds: pytorch LongTensor, with shape [N];indices of selected hard negative samples; 0 <= n_inds[i] <= N - 1NOTE: Only consider the case in which all labels have same num of samples, thus we can cope with all anchors in parallel."""assert len(dist_mat.size()) == 2  # judge the 'dist_mat' matrix whether is 2-dim,if not,report errorassert dist_mat.size(0) == dist_mat.size(1)  # judge the 'dist_mat' matrix whether is Square matrix,if not,report errorN = dist_mat.size(0)  # gain the 'dist_mat' matrix length i.e.N(N: 128)# shape [N, N]is_pos = labels.expand(N, N).eq(labels.expand(N, N).t())  # gain the positive sampleis_neg = labels.expand(N, N).ne(labels.expand(N, N).t())  # gain the negative sample# `dist_ap` means distance(anchor, positive)# both `dist_ap` and `relative_p_inds` with shape [N, 1]dist_ap, relative_p_inds = torch.max(dist_mat[is_pos].contiguous().view(N, -1), 1, keepdim=True)  # calculate the min similarity(i.e.max distance) between anchor and positive,and return the corresponding serial number# `dist_an` means distance(anchor, negative)# both `dist_an` and `relative_n_inds` with shape [N, 1]dist_an, relative_n_inds = torch.min(dist_mat[is_neg].contiguous().view(N, -1), 1, keepdim=True)  # calculate the max similarity(i.e.min distance) between anchor and negative,and return the corresponding serial number# shape [N]dist_ap = dist_ap.squeeze(1)  # compression dimensiondist_an = dist_an.squeeze(1)if return_inds:# shape [N, N]ind = (labels.new().resize_as_(labels).copy_(torch.arange(0, N).long()).unsqueeze( 0).expand(N, N))# shape [N, 1]p_inds = torch.gather(ind[is_pos].contiguous().view(N, -1), 1, relative_p_inds.data)n_inds = torch.gather(ind[is_neg].contiguous().view(N, -1), 1, relative_n_inds.data)# shape [N]p_inds = p_inds.squeeze(1)n_inds = n_inds.squeeze(1)return dist_ap, dist_an, p_inds, n_indsreturn dist_ap, dist_andef global_loss(tri_loss, global_feat, labels, normalize_feature=True):"""Args:tri_loss: a `TripletLoss` objectglobal_feat: pytorch Variable, shape [N, C]labels: pytorch LongTensor, with shape [N]normalize_feature: whether to normalize feature to unit length along the Channel dimensionReturns:loss: pytorch Variable, with shape [1]p_inds: pytorch LongTensor, with shape [N]; indices of selected hard positive samples; 0 <= p_inds[i] <= N - 1n_inds: pytorch LongTensor, with shape [N];indices of selected hard negative samples; 0 <= n_inds[i] <= N - 1=============For Debugging=============dist_ap: pytorch Variable, distance(anchor, positive); shape [N]dist_an: pytorch Variable, distance(anchor, negative); shape [N]===================For Mutual Learning===================dist_mat: pytorch Variable, pairwise euclidean distance; shape [N, N]"""if normalize_feature:global_feat = normalize(global_feat, axis=-1)# shape [N, N]dist_mat = euclidean_dist(global_feat, global_feat)dist_ap, dist_an, p_inds, n_inds = hard_example_mining(dist_mat, labels, return_inds=True)loss = tri_loss(dist_ap, dist_an)return loss, p_inds, n_inds, dist_ap, dist_an, dist_matdef local_loss(tri_loss,local_feat,p_inds=None,n_inds=None,labels=None,normalize_feature=True):"""Args:tri_loss: a `TripletLoss` objectlocal_feat: pytorch Variable, shape [N, H, c] (NOTE THE SHAPE!)p_inds: pytorch LongTensor, with shape [N]; indices of selected hard positive samples; 0 <= p_inds[i] <= N - 1n_inds: pytorch LongTensor, with shape [N];indices of selected hard negative samples; 0 <= n_inds[i] <= N - 1labels: pytorch LongTensor, with shape [N]normalize_feature: whether to normalize feature to unit length along the Channel dimensionIf hard samples are specified by `p_inds` and `n_inds`, then `labels` is not used. Otherwise, local distance finds its own hard samples independent of global distance.Returns:loss: pytorch Variable,with shape [1]=============For Debugging=============dist_ap: pytorch Variable, distance(anchor, positive); shape [N]dist_an: pytorch Variable, distance(anchor, negative); shape [N]===================For Mutual Learning===================dist_mat: pytorch Variable, pairwise local distance; shape [N, N]"""if normalize_feature:local_feat = normalize(local_feat, axis=-1)  # local_feat={Tensor:(128,8,128)}if p_inds is None or n_inds is None:dist_mat = local_dist(local_feat, local_feat)dist_ap, dist_an = hard_example_mining(dist_mat, labels, return_inds=False)loss = tri_loss(dist_ap, dist_an)return loss, dist_ap, dist_an, dist_matelse:dist_ap = batch_local_dist(local_feat, local_feat[p_inds])  # dist_ap:local_dist_ap;  local_feat[p_inds]:positive_local_featdist_an = batch_local_dist(local_feat, local_feat[n_inds])loss = tri_loss(dist_ap, dist_an)  # loss:local_lossreturn loss, dist_ap, dist_an

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AlignedReID 源码解析

一、论文回顾

二、代码解析

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