锚框的形状计算公式

假设原图的高为H,宽为W

锚框形状详细公式推导

以每个像素为中心生成不同形状的锚框

# s是缩放比，ratio是宽高比
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:] # 取出最后两个元素，即h和wdevice,num_sizes,num_ratios = data.device,len(sizes),len(ratios)boxes_per_pixel = (num_sizes+num_ratios -1) # 以某个像素坐标为中心的锚框为n+m-1size_tensor = torch.tensor(sizes,device=device) # 将缩放比例列表sizes转为tensor, device参数指定设备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轴上缩放步⻓steps_w = 1.0 / in_width # 在x轴上缩放步⻓print(f'steps_h,steps_w = {steps_h,steps_w}')# 生成锚框的所有中心点center_h = (torch.arange(in_height, device=device) + offset_h) * steps_hcenter_w = (torch.arange(in_width, device=device) + offset_w) * steps_wprint(f'center_h,center_w={center_h,center_w}')#网格化中心点坐标shift_y,shift_x = torch.meshgrid(center_h,center_w)#reshape成一维，shift_y和shift_x坐标一一对应shift_y,shift_x = shift_y.reshape(-1),shift_x.reshape(-1)print(f'shift_y, shift_x={shift_y, shift_x}') ##norm=√(H/W),这个就是个标号，方便计算norm = torch.sqrt(torch.tensor(in_height)/torch.tensor(in_width))# 生成“boxes_per_pixel”个高和宽,#只考虑包含s1或r1的组合,因此S*r1 与s1*R合并即为n+m-1个锚框w = torch.cat((size_tensor * torch.sqrt(ratio_tensor[0]),size_tensor[0] * torch.sqrt(ratio_tensor[1:]))) * normh = torch.cat((size_tensor / torch.sqrt(ratio_tensor[0]),size_tensor[0] / torch.sqrt(ratio_tensor[1:]))) / norm# 获得归一化后的锚框的w,h的一半，形成偏移量，为了让归一化后的锚框根据中心点 + 偏移量找到 左上角和右下角坐标anchor_manipulations = torch.stack((-w, -h, w, h)).T.repeat(in_height * in_width, 1) / 2# 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)#(x_min,y_min,x_max,y_max) =  归一化后的锚框中心点 + 往左上角和右下角走的偏移量output = out_grid + anchor_manipulationsreturn output.unsqueeze(0)

# 将锚框变量Y的形状更改为(图像高度,图像宽度,以同一像素为中心的锚框的数量,4)
boxes = Y.reshape(h, w, 5, 4)#                                                  此处的5由 缩放的数量n + 宽高比的数量m -1 而得
# 访问以(250,250)为中心的第一个锚框。它有四个元素:锚框左上⻆的(x, y)轴坐标和右下⻆的(x, y)轴坐标
boxes[250, 250, 0, :] # 输出的坐标是归一化后的，即归一化前的锚框 w/in_weight 和 h/in_height

img = d2l.plt.imread('../data/images/cat_and_dog.jpg')
h, w = img.shape[:2]
print(h, w)
X = torch.rand(size=(1, 3, h, w))
# 返回的锚框变量Y的形状是(批量大小,锚框的数量,4 (表示锚框的左上角右下角坐标))。
Y = multibox_prior(X, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5])
Y.shape

根据真实框来标注生成的锚框

# 计算IOU
def box_iou(boxes1,boxes2):''':param boxes1: shape = (boxes1的数量,4):param boxes2: shape = (boxes2的数量,4):param areas1: boxes1中每个框的面积 ，shape = (boxes1的数量):param areas2: boxes2中每个框的面积 ，shape = (boxes2的数量):return:'''# 定义一个Lambda函数，输入boxes，内容是计算得到框的面积box_area = lambda  boxes:((boxes[:,2] - boxes[:,0]) * (boxes[:,3] - boxes[:,0]))# 计算面积areas1 = box_area(boxes1)areas2 = box_area(boxes2)# 计算交集 要把所有锚框的左上角坐标 与 真实框的所有左上角坐标 作比较,大的就是交集的左上角 ,加个None 可以让锚框与所有真实框作对比inter_upperlefts = torch.max(boxes1[:,None,:2],boxes2[:,:2])# 把所有锚框的右下角坐标 与 真实框的所有右下角坐标 作比较,小的就是交集的右下角坐标 ,加个None 可以让锚框与所有真实框作对比inter_lowerrights = torch.min(boxes1[:,None,2:],boxes2[:,2:])# 如果右下角-左上角有元素小于0，那就说明没有交集，clamp(min-0)会将每个元素与0比较，小于0的元素将会被替换成0inters = (inter_lowerrights - inter_upperlefts).clamp(min=0) # 得到w和hinter_areas = inters[:,:,0] * inters[:,:,1] # 每个样本的 w*h# 求锚框与真实框的并集# 将所有锚框与真实框相加，他们会多出来一个交集的面积，所以要减一个交集的面积union_areas = areas1[:,None] * areas2 - inter_areasreturn inter_areas/union_areas

# 每个真实框都要跟所有锚框计算iou，Iou数量等于，真实框数量 * 锚框的数量
def assign_anchor_to_bbox(ground_truth,anchors,devices,iou_threshold=0.5):# 得到锚框和真实框的个数num_anchors,num_gt_boxes = anchors.shape[0],ground_truth.shape[0]# jaccard是计算 所有锚框anchors和真实框ground_truth的交并比jaccard = box_iou(anchors,ground_truth)# torch.full(size,fill_value,dtype,device)，如下代码生产成一个一位数组，长度为锚框的个数，值为-1anchors_bbox_map = torch.full((num_anchors,),-1,dtype=torch.long,device=devices)# 对行取最大值，得到每个真实框对应的最大IOU的锚框max_ious,indices = torch.max(jaccard,dim=1)# 返回张量中非0元素的索引，即Max_iou>设定的阈值，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IoUanc_i = torch.nonzero(max_ious>=iou_threshold).reshape(-1)box_j = indices[max_ious>=iou_threshold]anchors_bbox_map[anc_i] = box_jcol_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

# 标注类别和偏移量
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

'''如果一个锚框没有被分配真实边界框,将锚框的类别标记为背景。背景类别的锚框通常被称为负类锚框,其余的被称为正类锚框。我们使用真实边界框(labels参数)实现以下multibox_target函数,来标记锚框的类别和偏移量(anchors参数)。此函数将背景类别的索引设置为零,然后将新类别的整数索引递增一。
'''
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:]# 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)

# 第一个元素表示类别，0代表狗，1代表猫。其余四个元素是左下角坐标和右上角坐标(归一化后的介于0-1之间)，归一化的方法是，x坐标 / 宽，y坐标/高
ground_truth = torch.tensor([[0, 0.1, 0.08, 0.52, 0.92],[1, 0.55, 0.2, 0.9, 0.88]])
# 锚框
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]])
bbox_scale = torch.tensor((w, h, w, h))
# img = d2l.plt.imread('../data/images/cat_dog.png')
img = d2l.plt.imread('../data/images/cat_and_dog.jpg')
fig = d2l.plt.imshow(img)
# 画出真实框 ：(坐标轴，归一化*bbox_scale得到原图规模的坐标，标签，颜色)
show_bboxes(fig.axes,ground_truth[:,1:] * bbox_scale,['dog','cat'],'k') # k最后画出来是黑色
# 画出设置的锚框，把锚框类别标记为0-4
show_bboxes(fig.axes, anchors * bbox_scale, ['0', '1', '2', '3', '4']);
'''labels[0]:labels[1]:掩码，形状为(批量大小，锚框数的4倍)，对应每个锚框的4个偏移量（负类掩码为0），通过元素乘法，将负类的偏移量过滤掉labels[2]:锚框对应的标签
'''
labels = multibox_target(anchors.unsqueeze(dim=0),ground_truth.unsqueeze(dim=0))

非极大值抑制

'''在预测时,我们先为图像生成多个锚框,再为这些锚框一一预测类别和偏移量。一个预测好的边界框则根据其中某个带有预测偏移量的锚框而生成。下面我们实现了offset_inverse函数,该函数将锚框和偏移量预测作为输入,并应用逆偏移变换来返回预测的边界框坐标。输入: 锚框 和 偏移量预测输出：根据锚框的原始坐标和预测的偏移量 计算出的 预测的边界框坐标
'''
def offset_inverse(anchors, offset_preds):"""根据带有预测偏移量的锚框来预测边界框"""anc = d2l.box_corner_to_center(anchors)pred_bbox_xy = (offset_preds[:, :2] * anc[:, 2:] / 10) + anc[:, :2]pred_bbox_wh = torch.exp(offset_preds[:, 2:] / 5) * anc[:, 2:]pred_bbox = torch.cat((pred_bbox_xy, pred_bbox_wh), axis=1)predicted_bbox = d2l.box_center_to_corner(pred_bbox)return predicted_bbox

'''按降序对置信度进行排序并返回其索引'''
#@save
def nms(boxes, scores, iou_threshold):"""对预测边界框的置信度进行排序"""B = torch.argsort(scores, dim=-1, descending=True)keep = []# 保留预测边界框的指标while B.numel() > 0:i = B[0]keep.append(i)if B.numel() == 1: breakiou = box_iou(boxes[i, :].reshape(-1, 4),boxes[B[1:], :].reshape(-1, 4)).reshape(-1)inds = torch.nonzero(iou <= iou_threshold).reshape(-1)B = B[inds + 1]return torch.tensor(keep, device=boxes.device)

def multibox_detection(cls_probs, offset_preds, anchors, nms_threshold=0.5,pos_threshold=0.009999999):"""使用非极大值抑制来预测边界框"""device, batch_size = cls_probs.device, cls_probs.shape[0]anchors = anchors.squeeze(0)num_classes, num_anchors = cls_probs.shape[1], cls_probs.shape[2]out = []for i in range(batch_size):cls_prob, offset_pred = cls_probs[i], offset_preds[i].reshape(-1, 4)conf, class_id = torch.max(cls_prob[1:], 0)'''调用offset_inverse'''predicted_bb = offset_inverse(anchors, offset_pred)'''调用nms'''keep = nms(predicted_bb, conf, nms_threshold)# 找到所有的non_keep索引,并将类设置为背景all_idx = torch.arange(num_anchors, dtype=torch.long, device=device)combined = torch.cat((keep, all_idx))uniques, counts = combined.unique(return_counts=True)non_keep = uniques[counts == 1]all_id_sorted = torch.cat((keep, non_keep))class_id[non_keep] = -1class_id = class_id[all_id_sorted]conf, predicted_bb = conf[all_id_sorted], predicted_bb[all_id_sorted]# pos_threshold是一个用于非背景预测的阈值below_min_idx = (conf < pos_threshold)class_id[below_min_idx] = -1conf[below_min_idx] = 1 - conf[below_min_idx]pred_info = torch.cat((class_id.unsqueeze(1),conf.unsqueeze(1),predicted_bb), dim=1)out.append(pred_info)return torch.stack(out)