13.4. 锚框 — 动手学深度学习 2.0.0 documentation

13.7. 单发多框检测（SSD） — 动手学深度学习 2.0.0 documentation

锚框

一.归一化推导公式

目标检测SSD | Lee的个人博客

之前笔记有点错误 https://mp.csdn.net/mp_blog/creation/editor/129528620

1.未归一化

很普通的公式  ha是指h_a 

 2.普通归一化

只看Wa’和Ha’就行，Wa’是值以W和Wa为标准的从0到1归一化后的值， Ha’只与H和Ha有关，所以Wa’和Ha’的值没直接比较关系，比如都为0.5的时候不能直接比较。

3.d2l的归一化

此处s是长宽缩放比不再是面积的了，宽高比r变成了归一化后的对比。也可以理解，因为代码中处理时候用的是归一化后变小的值。

Ha=hs，Wa=ws

a.归一化之后，两者的值。

b.真实锚框大小需要乘回去

c.因为基准锚框需要是正方形，到时候宽高比变换基于正方形的基准锚框才能变化

c1.所以当输入图像为正方形的时候锚框真实宽高比是Wa/ha=(ws✔r)/(hs/✔r)=r*w/h=r 

c2.不为正方形时候，等于r*w/h ，为了让c2与c1相等 Wa/ha=(ws✔r)/(hs/✔r)=r*w/h,  让Wa需要乘h/w，令结果也等于r。

因为特征图中始终是正方形，h=w所以无影响。

真实图像中若为矩形，则会强制出现正方向基准锚框

二.代码

import torch
from d2l import torch as d2l
torch.set_printoptions(2)  # 精简输出精度
def multibox_prior(data, sizes, ratios):"""生成以每个像素为中心具有不同形状的锚框"""in_height, in_width = data.shape[-2:]device, num_sizes, num_ratios = data.device, len(sizes), len(ratios)boxes_per_pixel = (num_sizes + num_ratios - 1)#n=s+r-1size_tensor = torch.tensor(sizes, device=device)ratio_tensor = torch.tensor(ratios, device=device)# 为了将锚点移动到像素的中心，需要设置偏移量。# 因为一个像素的高为1且宽为1，我们选择偏移我们的中心0.5offset_h, offset_w = 0.5, 0.5steps_h = 1.0 / in_height  # 在y轴上缩放步长steps_w = 1.0 / in_width  # 在x轴上缩放步长# 生成锚框的所有中心点#0.5像素  对应0.5->宽或高像素长度中的一个像素的一半 ，0.5*1像素->0.5*1像素步长#宽和高所有中间像素的坐标值，而xy由meshgrid映射出来 shift_y, shift_x 对应映射列表每个x对应每个ycenter_h = (torch.arange(in_height, device=device) + offset_h) * steps_hcenter_w = (torch.arange(in_width, device=device) + offset_w) * steps_wshift_y, shift_x = torch.meshgrid(center_h, center_w, indexing='ij')shift_y, shift_x = shift_y.reshape(-1), shift_x.reshape(-1)# 生成“boxes_per_pixel”个高和宽，# 之后用于创建锚框的四角坐标(xmin,xmax,ymin,ymax)w = torch.cat((size_tensor * torch.sqrt(ratio_tensor[0]),#不加\\会导致一行无法容纳过多字符 报错sizes[0] * torch.sqrt(ratio_tensor[1:])))\\* in_height / in_width  # 处理矩形输入h = torch.cat((size_tensor / torch.sqrt(ratio_tensor[0]),sizes[0] / torch.sqrt(ratio_tensor[1:])))# 除以2来获得半高和半宽 作为xmin max ymin max的值anchor_manipulations = torch.stack((-w, -h, w, h)).T.repeat(in_height * in_width, 1) / 2#有408,408个像素# 每个中心点都将有“boxes_per_pixel”个锚框，# 所以生成含所有锚框中心的网格，重复了“boxes_per_pixel”次out_grid = torch.stack([shift_x, shift_y, shift_x, shift_y],dim=1).repeat_interleave(boxes_per_pixel, dim=0)#每个像素5个框 备份5次像素  取out_grid[0]因为精度省略了后面 所以0.00output = out_grid + anchor_manipulationsreturn output.unsqueeze(0)img = d2l.plt.imread('../img/catdog.jpg')
h, w = img.shape[:2]print(h, w)
X = torch.rand(size=(1, 3, h, w))
Y = multibox_prior(X, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5])
boxes = Y.reshape(h, w, 5, 4)

#@save
def show_bboxes(axes, bboxes, labels=None, colors=None):"""显示所有边界框"""def _make_list(obj, default_values=None):if obj is None:obj = default_valueselif not isinstance(obj, (list, tuple)):obj = [obj]return objlabels = _make_list(labels)colors = _make_list(colors, ['b', 'g', 'r', 'm', 'c'])for i, bbox in enumerate(bboxes):color = colors[i % len(colors)]rect = d2l.bbox_to_rect(bbox.detach().numpy(), color)axes.add_patch(rect)if labels and len(labels) > i:text_color = 'k' if color == 'w' else 'w'axes.text(rect.xy[0], rect.xy[1], labels[i],va='center', ha='center', fontsize=9, color=text_color,bbox=dict(facecolor=color, lw=0))d2l.set_figsize()
bbox_scale = torch.tensor((w, h, w, h))
fig = d2l.plt.imshow(img)
show_bboxes(fig.axes, boxes[250, 250, :, :] * bbox_scale,#250, 250['s=0.75, r=1', 's=0.5, r=1', 's=0.25, r=1', 's=0.75, r=2','s=0.75, r=0.5'])
#d2l.plt.show()#@save
def box_iou(boxes1, boxes2):"""计算两个锚框或边界框列表中成对的交并比"""box_area = lambda boxes: ((boxes[:, 2] - boxes[:, 0]) *(boxes[:, 3] - boxes[:, 1]))# boxes1,boxes2,areas1,areas2的形状:# boxes1：(boxes1的数量,4),# boxes2：(boxes2的数量,4),# areas1：(boxes1的数量,),# areas2：(boxes2的数量,)areas1 = box_area(boxes1)areas2 = box_area(boxes2)# inter_upperlefts,inter_lowerrights,inters的形状:# (boxes1的数量,boxes2的数量,2)#boxes1[:, None, :2]中的None添加了一个额外的维度到boxes1中，以使其具有与boxes2相同的维数。这允许在计算最大值时进行广播。#4个分别是(xmin,ymin,xmax,ymax)inter_upperlefts = torch.max(boxes1[:, None, :2], boxes2[:, :2])inter_lowerrights = torch.min(boxes1[:, None, 2:], boxes2[:, 2:])inters = (inter_lowerrights - inter_upperlefts).clamp(min=0)# inter_areasandunion_areas的形状:(boxes1的数量,boxes2的数量)inter_areas = inters[:, :, 0] * inters[:, :, 1]union_areas = areas1[:, None] + areas2 - inter_areasreturn inter_areas / union_areas#@save
def assign_anchor_to_bbox(ground_truth, anchors, device, iou_threshold=0.5):"""将最接近的真实边界框分配给锚框"""num_anchors, num_gt_boxes = anchors.shape[0], ground_truth.shape[0]# 位于第i行和第j列的元素x_ij是锚框i和真实边界框j的IoUjaccard = box_iou(anchors, ground_truth)# 对于每个锚框，分配的真实边界框的张量anchors_bbox_map = torch.full((num_anchors,), -1, dtype=torch.long,device=device)#对应num_anchors# 根据阈值，决定是否分配真实边界框max_ious, indices = torch.max(jaccard, dim=1)anc_i = torch.nonzero(max_ious >= iou_threshold).reshape(-1)box_j = indices[max_ious >= iou_threshold]#indices[torch.tensor([False, False,  True, False,  True])] 只拿到true的值anchors_bbox_map[anc_i] = box_j#把13.4.3.1. 第四条做了 所以会增加所有iou大于阈值的 这样的col_discard = torch.full((num_anchors,), -1)row_discard = torch.full((num_gt_boxes,), -1)for _ in range(num_gt_boxes):max_idx = torch.argmax(jaccard)box_idx = (max_idx % num_gt_boxes).long()anc_idx = (max_idx / num_gt_boxes).long()anchors_bbox_map[anc_idx] = box_idxjaccard[:, box_idx] = col_discardjaccard[anc_idx, :] = row_discardreturn anchors_bbox_map#@save
def offset_boxes(anchors, assigned_bb, eps=1e-6):"""对锚框偏移量的转换"""c_anc = d2l.box_corner_to_center(anchors)c_assigned_bb = d2l.box_corner_to_center(assigned_bb)offset_xy = 10 * (c_assigned_bb[:, :2] - c_anc[:, :2]) / c_anc[:, 2:]offset_wh = 5 * torch.log(eps + c_assigned_bb[:, 2:] / c_anc[:, 2:])offset = torch.cat([offset_xy, offset_wh], axis=1)return offset#@save
def multibox_target(anchors, labels):"""使用真实边界框标记锚框"""batch_size, anchors = labels.shape[0], anchors.squeeze(0)batch_offset, batch_mask, batch_class_labels = [], [], []device, num_anchors = anchors.device, anchors.shape[0]for i in range(batch_size):label = labels[i, :, :]anchors_bbox_map = assign_anchor_to_bbox(label[:, 1:], anchors, device)bbox_mask = ((anchors_bbox_map >= 0).float().unsqueeze(-1)).repeat(1, 4)# 将类标签和分配的边界框坐标初始化为零class_labels = torch.zeros(num_anchors, dtype=torch.long,device=device)assigned_bb = torch.zeros((num_anchors, 4), dtype=torch.float32,device=device)# 使用真实边界框来标记锚框的类别。# 如果一个锚框没有被分配，标记其为背景（值为零）indices_true = torch.nonzero(anchors_bbox_map >= 0)bb_idx = anchors_bbox_map[indices_true]class_labels[indices_true] = label[bb_idx, 0].long() + 1assigned_bb[indices_true] = label[bb_idx, 1:]# 偏移量转换offset = offset_boxes(anchors, assigned_bb) * bbox_maskbatch_offset.append(offset.reshape(-1))batch_mask.append(bbox_mask.reshape(-1))batch_class_labels.append(class_labels)bbox_offset = torch.stack(batch_offset)bbox_mask = torch.stack(batch_mask)class_labels = torch.stack(batch_class_labels)return (bbox_offset, bbox_mask, class_labels)ground_truth = torch.tensor([[0, 0.1, 0.08, 0.52, 0.92],[1, 0.55, 0.2, 0.9, 0.88]])
anchors = torch.tensor([[0, 0.1, 0.2, 0.3], [0.15, 0.2, 0.4, 0.4],[0.63, 0.05, 0.88, 0.98], [0.66, 0.45, 0.8, 0.8],[0.57, 0.3, 0.92, 0.9]])fig = d2l.plt.imshow(img)
show_bboxes(fig.axes, ground_truth[:, 1:] * bbox_scale, ['dog', 'cat'], 'k')
show_bboxes(fig.axes, anchors * bbox_scale, ['0', '1', '2', '3', '4']);labels = multibox_target(anchors.unsqueeze(dim=0),ground_truth.unsqueeze(dim=0))labels[2]
labels[1]
labels[0]