13.1 Image Augmentation
def apply(img, aug, num_rows=2, num_cols=4, scale=1.5):
Y = [aug(img) for _ in range(num_rows * num_cols)]
d2l.show_images(Y, num_rows, num_cols, scale=scale)
apply(img, torchvision.transforms.RandomHorizontalFlip())
apply(img, torchvision.transforms.RandomVerticalFlip())
shape_aug = torchvision.transforms.RandomResizedCrop(
(200, 200), scale=(0.1, 1), ratio=(0.5, 2))
apply(
img,
torchvision.transforms.ColorJitter(brightness=0.5, contrast=0,
saturation=0, hue=0))
augs = torchvision.transforms.Compose([
torchvision.transforms.RandomHorizontalFlip(), color_aug, shape_aug])
train_augs = torchvision.transforms.Compose([
torchvision.transforms.RandomHorizontalFlip(),
torchvision.transforms.ToTensor()])
test_augs = torchvision.transforms.Compose([
torchvision.transforms.ToTensor()])
13.2 Fine-Tuning
应用 迁移学习（transfer learning） 将从 源数据集 学到的知识迁移到 目标数据集。 例如，尽管 ImageNet 数据集中的大多数图像与椅子无关，但在此数据集上训练的模型可能会提取更常规的图像特征，这有助于识别边缘、纹理、形状和对象合成。 这些类似的功能也可能有效地识别椅子。
当目标数据集比源数据集小得多时，微调有助于提高模型的泛化能力。
- 神经网络通常学习有层次的特征表达：
- 低层次的特征更加通用
- 高层次的特征更与数据集有关
- 可以固定底层的一些参数，不参与更新：更强的正则
# 如果 `param_group=True`，输出层中的模型参数将使用十倍的学习率
def train_fine_tuning(net, learning_rate, batch_size=128, num_epochs=5,
param_group=True):
train_iter = torch.utils.data.DataLoader(torchvision.datasets.ImageFolder(
os.path.join(data_dir, 'train'), transform=train_augs),
batch_size=batch_size, shuffle=True)
test_iter = torch.utils.data.DataLoader(torchvision.datasets.ImageFolder(
os.path.join(data_dir, 'test'), transform=test_augs),
batch_size=batch_size)
devices = d2l.try_all_gpus()
loss = nn.CrossEntropyLoss(reduction="none")
if param_group:
params_1x = [param for name, param in net.named_parameters()
if name not in ["fc.weight", "fc.bias"]]
trainer = torch.optim.SGD([{'params': params_1x},
{'params': net.fc.parameters(),
'lr': learning_rate * 10}],
lr=learning_rate, weight_decay=0.001)
else:
trainer = torch.optim.SGD(net.parameters(), lr=learning_rate,
weight_decay=0.001)
d2l.train_ch13(net, train_iter, test_iter, loss, trainer, num_epochs,
devices)
13.3. Object Detection and Bounding Boxes
很多时候图像里有多个我们感兴趣的目标，我们不仅想知道它们的类别，还想得到它们在图像中的具体位置。 Bounding Boxes:
#@save
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
#@save
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 bbox_to_rect(bbox, color):
# 将边界框 (左上x, 左上y, 右下x, 右下y) 格式转换成 matplotlib 格式：
# ((左上x, 左上y), 宽, 高)
return d2l.plt.Rectangle(
xy=(bbox[0], bbox[1]), width=bbox[2]-bbox[0], height=bbox[3]-bbox[1],
fill=False, edgecolor=color, linewidth=2)
13.4. Anchor Boxes
它以每个像素为中心生成多个大小和宽高比（aspect ratio）不同的边界框。 这些边界框被称为锚框（anchor box）。
假设输入图像的高度为 $h$，宽度为 $w$。 我们以图像的每个像素为中心生成不同形状的锚框：比例 为 $s\in (0, 1]$，宽高比（宽高比）为 $r > 0$。 那么[锚框的宽度和高度分别是 $ws\sqrt{r}$ 和 $hs/\sqrt{r}$。] 请注意，当中心位置给定时，已知宽和高的锚框是确定的。
要生成多个不同形状的锚框，让我们设置一系列刻度 $s_1, \ldots, s_n$ 和一系列宽高比 $r_1, \ldots, r_m$。 当使用这些比例和长宽比的所有组合以每个像素为中心时，输入图像将总共有 $whnm$ 个锚框。 尽管这些锚框可能会覆盖所有地面真实边界框，但计算复杂性很容易过高。 在实践中，(我们只考虑)包含 $s_1$ 或 $r_1$ 的(组合：)
\[(s_1, r_1), (s_1, r_2), \ldots, (s_1, r_m), (s_2, r_1), (s_3, r_1), \ldots, (s_n, r_1).\]也就是说，以同一像素为中心的锚框的数量是 $n+m-1$。 对于整个输入图像，我们将共生成 $wh(n+m-1)$ 个锚框。
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 # Scaled steps in y axis
steps_w = 1.0 / in_width # Scaled steps in x axis
# 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)
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 # Handle rectangular inputs
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)
交并比(IoU)：
我们刚刚提到某个锚框“较好地”覆盖了图像中的狗。 如果已知目标的真实边界框，那么这里的 “好”该如何如何量化呢？ 直观地说，我们可以衡量锚框和真实边界框之间的相似性。 我们知道 Jaccard 系数 可以衡量两组之间的相似性。 给定集合 $\mathcal{A}$ 和 $\mathcal{B}$，他们的 Jaccard 系数是他们交集的大小除以他们并集的大小：
\[J(\mathcal{A}, \mathcal{B}) = \frac{\left|\mathcal{A} \cap \mathcal{B}\right|}{\left| \mathcal{A} \cup \mathcal{B}\right|}.\]
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)
# 相交矩形的左下顶点坐标, 就是两个矩形左下坐标的x和y分别取最大值
# xmin = max(gxmin, pxmin)
# ymin = max(gymin, pymin)
# 相交矩形的右上顶点坐标, 就是两个矩形右上坐标的x和y分别取最小值
# xmax = min(gxmax, pxmax)
# ymax = min(gymax, pyxmax)
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_areas` and `union_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
Assigning Ground-Truth Bounding Boxes to Anchor Boxes
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 >= 0.5).reshape(-1)
box_j = indices[max_ious >= 0.5]
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
Labeling Classes and Offsets
现在我们可以为每个锚框标记分类和偏移量了。 假设一个锚框 $A$ 被分配了一个真实边界框 $B$。 一方面，锚框 $A$ 的类将被标记为与 $B$ 相同。 另一方面，锚框 $A$ 的偏移量将根据 $B$ 和 $A$ 中心坐标的相对位置、以及这两个框的相对大小进行标记。 鉴于数据集内不同的框的位置和大小不同，我们可以对那些相对位置和大小应用变换，使其获得更均匀分布、易于适应的偏移量。 在这里，我们介绍一种常见的变换。 给定框 $A$ 和 $B$，中心坐标分别为 $(x_a, y_a)$ 和 $(x_b, y_b)$，宽度分别为 $w_a$ 和 $w_b$，高度分别为 $h_a$ 和 $h_b$。 我们可以将 $A$ 的偏移量标记为
\[\left( \frac{ \frac{x_b - x_a}{w_a} - \mu_x }{\sigma_x}, \frac{ \frac{y_b - y_a}{h_a} - \mu_y }{\sigma_y}, \frac{ \log \frac{w_b}{w_a} - \mu_w }{\sigma_w}, \frac{ \log \frac{h_b}{h_a} - \mu_h }{\sigma_h}\right),\]其中常量的默认值是 $\mu_x = \mu_y = \mu_w = \mu_h = 0, \sigma_x=\sigma_y=0.1$ 和 $\sigma_w=\sigma_h=0.2$。
#@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
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，我们标记其为背景（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)
def offset_boxes(anchors, assigned_bb, eps=1e-6):
"""Transform for anchor box offsets."""
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
def multibox_target(anchors, labels):
"""Label anchor boxes using ground-truth bounding boxes."""
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)
# Initialize class labels and assigned bounding box coordinates with
# zeros
class_labels = torch.zeros(num_anchors, dtype=torch.long,
device=device)
assigned_bb = torch.zeros((num_anchors, 4), dtype=torch.float32,
device=device)
# Label classes of anchor boxes using their assigned ground-truth
# bounding boxes. If an anchor box is not assigned any, we label its
# class as background (the value remains zero)
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:]
# Offset transformation
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)
def offset_inverse(anchors, offset_preds):
"""Predict bounding boxes based on anchor boxes with predicted offsets."""
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
def nms(boxes, scores, iou_threshold):
"""Sort confidence scores of predicted bounding boxes."""
B = torch.argsort(scores, dim=-1, descending=True)
keep = [] # Indices of predicted bounding boxes that will be kept
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):
"""Predict bounding boxes using non-maximum suppression."""
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)
# Find all non-`keep` indices and set the class to background
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]
# Here `pos_threshold` is a threshold for positive (non-background)
# predictions
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)
R-CNN (region-based CNN)
- 对输入图像使用 选择性搜索 来选取多个高质量的提议区域 :cite:
Uijlings. Van-De-Sande. Gevers.ea.2013。这些提议区域通常是在多个尺度下选取的，并具有不同的形状和大小。每个提议区域都将被标注类别和真实边界框。 - 选择一个预训练的卷积神经网络，并将其在输出层之前截断。将每个提议区域变形为网络需要的输入尺寸，并通过前向计算输出抽取的提议区域特征。
- 将每个提议区域的特征连同其标注的类别作为一个样本。训练多个支持向量机对目标分类，其中每个支持向量机用来判断样本是否属于某一个类别。
- 将每个提议区域的特征连同其标注的边界框作为一个样本，训练线性回归模型来预测真实边界框。
