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三十四、锚框
import torch
import matplotlib.pyplot as plt
from matplotlib_inline import backend_inline
torch.set_printoptions(2) # 精简输出精度
def show_images(imgs, titles=None):
plt.imshow(imgs)
backend_inline.set_matplotlib_formats('svg')
plt.rcParams['figure.figsize'] = (10.5, 8.5)
plt.rcParams['font.sans-serif'] = ['Microsoft YaHei']
plt.title(titles)
plt.show()
def box_corner_to_center(boxes):
"""从（左上，右下）转换到（中间，宽度，高度）"""
x1, y1, x2, y2 = boxes[:, 0], boxes[:, 1], boxes[:, 2], boxes[:, 3]
cx = (x1 + x2) / 2
cy = (y1 + y2) / 2
w = x2 - x1
h = y2 - y1
boxes = torch.stack((cx, cy, w, h), axis=-1)
return boxes
def box_center_to_corner(boxes):
"""从（中间，宽度，高度）转换到（左上，右下）"""
cx, cy, w, h = boxes[:, 0], boxes[:, 1], boxes[:, 2], boxes[:, 3]
x1 = cx - 0.5 * w
y1 = cy - 0.5 * h
x2 = cx + 0.5 * w
y2 = cy + 0.5 * h
boxes = torch.stack((x1, y1, x2, y2), axis=-1)
return boxes
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)
size_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0.5
offset_h, offset_w = 0.5, 0.5
steps_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
center_h = (torch.arange(in_height, device=device) + offset_h) * steps_h
center_w = (torch.arange(in_width, device=device) + offset_w) * steps_w
shift_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]),
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
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)
output = out_grid + anchor_manipulations
return output.unsqueeze(0)
img = plt.imread('E:\\cat\\catdog.jpg')
h, w = img.shape[:2]
show_images(img, titles='原图')
print(f'图像的高为 {h} px,图像的宽为 {w} px')
X = torch.rand(size=(1, 3, h, w))
Y = multibox_prior(X, sizes=[0.60, 0.5, 0.25], ratios=[1, 2, 0.5])
print(f'锚框变量 Y 的形状是 : {Y.shape}')
boxes = Y.reshape(h, w, 5, 4) # ( 图像高度, 图像宽度, 以同一像素为中心的锚框的数量, 4 )
print("第一个锚框左上角和右下角坐标分别为: ", boxes[425, 350, 0, :] * torch.tensor([w, h, w, h]))
def bbox_to_rect(bbox, color):
# Convert the bounding box (upper-left x, upper-left y, lower-right x,
# lower-right y) format to the matplotlib format: ((upper-left x,
# upper-left y), width, height)
return plt.Rectangle(
xy=(bbox[0], bbox[1]), width=bbox[2]-bbox[0], height=bbox[3]-bbox[1],
fill=False, edgecolor=color, linewidth=2)
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_values
elif not isinstance(obj, (list, tuple)):
obj = [obj]
return obj
labels = _make_list(labels)
colors = _make_list(colors, ['b', 'g', 'r', 'm', 'c'])
for i, bbox in enumerate(bboxes):
color = colors[i % len(colors)]
rect = 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))
def set_figsize(figsize=(6.5, 3.5)):
backend_inline.set_matplotlib_formats('svg')
plt.rcParams['figure.figsize'] = figsize
set_figsize()
bbox_scale = torch.tensor((w, h, w, h))
fig = plt.imshow(img)
show_bboxes(fig.axes, boxes[425, 350, :, :] * bbox_scale,
['s=0.60, r=1', 's=0.5, r=1', 's=0.25, r=1', 's=0.60, r=2',
's=0.60, r=0.5'])
plt.title('绘制出图像中以 (425, 350) 为中心的锚框')
plt.show()
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)
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_areas
return inter_areas / union_areas
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IoU
jaccard = 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)
# 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]
anchors_bbox_map[anc_i] = box_j
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_idx
jaccard[:, box_idx] = col_discard
jaccard[anc_idx, :] = row_discard
return anchors_bbox_map
def offset_boxes(anchors, assigned_bb, eps=1e-6):
"""对锚框偏移量的转换"""
c_anc = box_corner_to_center(anchors)
c_assigned_bb = 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
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() + 1
assigned_bb[indices_true] = label[bb_idx, 1:]
# 偏移量转换
offset = offset_boxes(anchors, assigned_bb) * bbox_mask
batch_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, 0.06, 0.44, 0.27, 0.98], [1, 0.24, 0.31, 0.47, 0.99],
[0, 0.42, 0.03, 0.68, 0.98], [1, 0.68, 0.38, 0.95, 0.98]])
anchors = torch.tensor([[0.08, 0.28, 0.22, 0.92], [0.32, 0.28, 0.52, 0.89],
[0.43, 0.15, 0.67, 0.68], [0.66, 0.23, 0.89, 0.88]])
fig = plt.imshow(img)
show_bboxes(fig.axes, ground_truth[:, 1:] * bbox_scale, ['dog', 'cat', 'dog', 'cat'], 'k')
show_bboxes(fig.axes, anchors * bbox_scale, ['0', '1', '2', '3'])
plt.title('另外构建了四个锚框')
plt.show()
labels = multibox_target(anchors.unsqueeze(dim=0), ground_truth.unsqueeze(dim=0))
print(f'标记的输入锚框的类别 : {labels[2]}\n'
f'掩码（mask）变量 : {labels[1]}\n' # 形状为（批量大小，锚框数的四倍）
f'为每个锚框标记的四个偏移值 : {labels[0]}') # 负类锚框的偏移量被标记为零
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 = 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 = box_center_to_corner(pred_bbox)
return predicted_bbox
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: break
iou = 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)
predicted_bb = offset_inverse(anchors, offset_pred)
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] = -1
class_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] = -1
conf[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)
anchors = torch.tensor([[0.06, 0.44, 0.27, 0.98], [0.24, 0.31, 0.47, 0.99],
[0.42, 0.03, 0.68, 0.98], [0.68, 0.38, 0.95, 0.98],
[0.08, 0.28, 0.22, 0.92], [0.32, 0.28, 0.52, 0.89],
[0.43, 0.15, 0.67, 0.68], [0.66, 0.23, 0.89, 0.88]])
offset_preds = torch.tensor([0] * anchors.numel())
cls_probs = torch.tensor([[0] * 8, # 背景的预测概率
[0.9, 0.1, 0.9, 0.1, 0.4, 0.2, 0.6, 0.3], # 狗的预测概率
[0.1, 0.9, 0.1, 0.9, 0.6, 0.8, 0.4, 0.7]]) # 猫的预测概率
fig = plt.imshow(img)
show_bboxes(fig.axes, anchors * bbox_scale,
['dog=0.9', 'cat=0.9', 'dog=0.9', 'cat=0.9', 'dog=0.6', 'cat=0.8', 'dog=0.6', 'cat=0.7'])
plt.title('在图像上绘制这些预测边界框和置信度')
plt.show()
output = multibox_detection(cls_probs.unsqueeze(dim=0),
offset_preds.unsqueeze(dim=0),
anchors.unsqueeze(dim=0),
nms_threshold=0.45)
""" 第一个元素是预测的类索引，从0开始（0代表狗，1代表猫），值 -1 表示背景或在非极大值抑制中被移除了。
第二个元素是预测的边界框的置信度。 其余四个元素分别是预测边界框左上角和右下角的轴坐标 """
print(f'[ 预测的类索引, 预测的边界框的置信度, left_x, left_y, right_x, right_y ] :\n{output}')
fig = plt.imshow(img)
for i in output[0].detach().numpy():
if i[0] == -1:
continue
label = ('dog=', 'cat=')[int(i[0])] + str(i[1])
show_bboxes(fig.axes, [torch.tensor(i[2:]) * bbox_scale], label)
plt.title('输出由非极大值抑制保存的最终预测边界框')
plt.show()
三十五、多尺度锚框
import torch
import matplotlib.pyplot as plt
from matplotlib_inline import backend_inline
def bbox_to_rect(bbox, color):
return plt.Rectangle(
xy=(bbox[0], bbox[1]), width=bbox[2]-bbox[0], height=bbox[3]-bbox[1],
fill=False, edgecolor=color, linewidth=2)
def show_bboxes(axes, bboxes, labels=None, colors=None):
def make_list(obj, default_values=None):
if obj is None:
obj = default_values
elif not isinstance(obj, (list, tuple)):
obj = [obj]
return obj
numpy = lambda x, *args, **kwargs: x.detach().numpy(*args, **kwargs)
labels = make_list(labels)
colors = make_list(colors, ['b', 'g', 'r', 'm', 'c'])
for i, bbox in enumerate(bboxes):
color = colors[i % len(colors)]
rect = bbox_to_rect(numpy(bbox), 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))
def multibox_prior(data, sizes, ratios):
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)
size_tensor = torch.tensor(sizes, device=device)
ratio_tensor = torch.tensor(ratios, device=device)
# Offsets are required to move the anchor to the center of a pixel. Since
# a pixel has height=1 and width=1, we choose to offset our centers by 0.5
offset_h, offset_w = 0.5, 0.5
steps_h = 1.0 / in_height # Scaled steps in y axis
steps_w = 1.0 / in_width # Scaled steps in x axis
# Generate all center points for the anchor boxes
center_h = (torch.arange(in_height, device=device) + offset_h) * steps_h
center_w = (torch.arange(in_width, device=device) + offset_w) * steps_w
shift_y, shift_x = torch.meshgrid(center_h, center_w, indexing='ij')
shift_y, shift_x = shift_y.reshape(-1), shift_x.reshape(-1)
# Generate `boxes_per_pixel` number of heights and widths that are later
# used to create anchor box corner coordinates (xmin, xmax, ymin, ymax)
w = torch.cat((size_tensor * torch.sqrt(ratio_tensor[0]),
sizes[0] * torch.sqrt(ratio_tensor[1:])))\
* in_height / in_width # Handle rectangular inputs
h = torch.cat((size_tensor / torch.sqrt(ratio_tensor[0]),
sizes[0] / torch.sqrt(ratio_tensor[1:])))
# Divide by 2 to get half height and half width
anchor_manipulations = torch.stack((-w, -h, w, h)).T.repeat(
in_height * in_width, 1) / 2
out_grid = torch.stack([shift_x, shift_y, shift_x, shift_y],
dim=1).repeat_interleave(boxes_per_pixel, dim=0)
output = out_grid + anchor_manipulations
return output.unsqueeze(0)
img = plt.imread('E:\\cat\\catdog.jpg')
h, w = img.shape[:2]
print(f'图像的高度为 {h} px, 图像的宽度为 {w} px')
def display_anchors(fmap_w, fmap_h, s):
backend_inline.set_matplotlib_formats('svg')
plt.rcParams['figure.figsize'] = (8.5, 5.5)
# 前两个维度上的值不影响输出
fmap = torch.zeros((1, 10, fmap_h, fmap_w))
anchors = multibox_prior(fmap, sizes=s, ratios=[1, 2, 0.5])
bbox_scale = torch.tensor((w, h, w, h))
show_bboxes(plt.imshow(img).axes, anchors[0] * bbox_scale)
plt.rcParams['font.sans-serif'] = ['Microsoft YaHei']
plt.title(f'锚框的尺度设置为{s}，特征图的高度设置为{fmap_h}，特征图的宽度设置为{fmap_w}')
plt.show()
display_anchors(fmap_w=5, fmap_h=3, s=[0.15])
display_anchors(fmap_w=2, fmap_h=2, s=[0.3])
display_anchors(fmap_w=1, fmap_h=1, s=[0.6])
文中部分知识参考：B 站 —— 跟李沐学AI；百度百科
