.. _sec_anchor:
Hộp neo
=======
Thuật toán phát hiện đối tượng thường lấy mẫu một số lượng lớn các vùng
trong hình ảnh đầu vào, xác định xem các vùng này có chứa các đối tượng
quan tâm hay không, và điều chỉnh ranh giới của các vùng để dự đoán *hộp
giới hạn đất-truth* of the objects các đối tượng more accurately chính
xác. Các mô hình khác nhau có thể áp dụng các sơ đồ lấy mẫu khu vực khác
nhau. Ở đây chúng tôi giới thiệu một trong những phương pháp như vậy: nó
tạo ra nhiều hộp giới hạn với tỷ lệ khác nhau và tỷ lệ khung hình tập
trung vào mỗi pixel. Các hộp giới hạn này được gọi là hộp neo \*. Chúng
tôi sẽ thiết kế một mô hình phát hiện đối tượng dựa trên các hộp neo
trong :numref:`sec_ssd`.
Đầu tiên, chúng ta hãy sửa đổi độ chính xác in ấn chỉ để kết quả đầu ra
ngắn gọn hơn.
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%matplotlib inline
from mxnet import gluon, image, np, npx
from d2l import mxnet as d2l
np.set_printoptions(2) # Simplify printing accuracy
npx.set_np()
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%matplotlib inline
import torch
from d2l import torch as d2l
torch.set_printoptions(2) # Simplify printing accuracy
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#@save
def multibox_prior(data, sizes, ratios):
"""Generate anchor boxes with different shapes centered on each pixel."""
in_height, in_width = data.shape[-2:]
device, num_sizes, num_ratios = data.ctx, len(sizes), len(ratios)
boxes_per_pixel = (num_sizes + num_ratios - 1)
size_tensor = np.array(sizes, ctx=device)
ratio_tensor = np.array(ratios, ctx=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 = (np.arange(in_height, ctx=device) + offset_h) * steps_h
center_w = (np.arange(in_width, ctx=device) + offset_w) * steps_w
shift_x, shift_y = np.meshgrid(center_w, center_h)
shift_x, shift_y = shift_x.reshape(-1), shift_y.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 = np.concatenate((size_tensor * np.sqrt(ratio_tensor[0]),
sizes[0] * np.sqrt(ratio_tensor[1:]))) \
* in_height / in_width # Handle rectangular inputs
h = np.concatenate((size_tensor / np.sqrt(ratio_tensor[0]),
sizes[0] / np.sqrt(ratio_tensor[1:])))
# Divide by 2 to get half height and half width
anchor_manipulations = np.tile(np.stack((-w, -h, w, h)).T,
(in_height * in_width, 1)) / 2
# Each center point will have `boxes_per_pixel` number of anchor boxes, so
# generate a grid of all anchor box centers with `boxes_per_pixel` repeats
out_grid = np.stack([shift_x, shift_y, shift_x, shift_y],
axis=1).repeat(boxes_per_pixel, axis=0)
output = out_grid + anchor_manipulations
return np.expand_dims(output, axis=0)
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#@save
def multibox_prior(data, sizes, ratios):
"""Generate anchor boxes with different shapes centered on each pixel."""
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)
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
# Each center point will have `boxes_per_pixel` number of anchor boxes, so
# generate a grid of all anchor box centers with `boxes_per_pixel` repeats
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)
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img = image.imread('../img/catdog.jpg').asnumpy()
h, w = img.shape[:2]
print(h, w)
X = np.random.uniform(size=(1, 3, h, w)) # Construct input data
Y = multibox_prior(X, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5])
Y.shape
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561 728
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(1, 2042040, 4)
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img = d2l.plt.imread('../img/catdog.jpg')
h, w = img.shape[:2]
print(h, w)
X = torch.rand(size=(1, 3, h, w)) # Construct input data
Y = multibox_prior(X, sizes=[0.75, 0.5, 0.25], ratios=[1, 2, 0.5])
Y.shape
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561 728
/home/d2l-worker/miniconda3/envs/d2l-vi-release-1/lib/python3.8/site-packages/torch/functional.py:568: UserWarning: torch.meshgrid: in an upcoming release, it will be required to pass the indexing argument. (Triggered internally at ../aten/src/ATen/native/TensorShape.cpp:2228.)
return _VF.meshgrid(tensors, **kwargs) # type: ignore[attr-defined]
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torch.Size([1, 2042040, 4])
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boxes = Y.reshape(h, w, 5, 4)
boxes[250, 250, 0, :]
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array([0.06, 0.07, 0.63, 0.82])
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boxes = Y.reshape(h, w, 5, 4)
boxes[250, 250, 0, :]
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tensor([0.06, 0.07, 0.63, 0.82])
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#@save
def show_bboxes(axes, bboxes, labels=None, colors=None):
"""Show bounding boxes."""
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 = d2l.bbox_to_rect(bbox.asnumpy(), 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))
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#@save
def show_bboxes(axes, bboxes, labels=None, colors=None):
"""Show bounding boxes."""
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 = 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))
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d2l.set_figsize()
bbox_scale = np.array((w, h, w, h))
fig = d2l.plt.imshow(img)
show_bboxes(fig.axes, boxes[250, 250, :, :] * bbox_scale,
['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'])
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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,
['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'])
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#@save
def box_iou(boxes1, boxes2):
"""Compute pairwise IoU across two lists of anchor or bounding boxes."""
box_area = lambda boxes: ((boxes[:, 2] - boxes[:, 0]) *
(boxes[:, 3] - boxes[:, 1]))
# Shape of `boxes1`, `boxes2`, `areas1`, `areas2`: (no. of boxes1, 4),
# (no. of boxes2, 4), (no. of boxes1,), (no. of boxes2,)
areas1 = box_area(boxes1)
areas2 = box_area(boxes2)
# Shape of `inter_upperlefts`, `inter_lowerrights`, `inters`: (no. of
# boxes1, no. of boxes2, 2)
inter_upperlefts = np.maximum(boxes1[:, None, :2], boxes2[:, :2])
inter_lowerrights = np.minimum(boxes1[:, None, 2:], boxes2[:, 2:])
inters = (inter_lowerrights - inter_upperlefts).clip(min=0)
# Shape of `inter_areas` and `union_areas`: (no. of boxes1, no. of boxes2)
inter_areas = inters[:, :, 0] * inters[:, :, 1]
union_areas = areas1[:, None] + areas2 - inter_areas
return inter_areas / union_areas
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#@save
def box_iou(boxes1, boxes2):
"""Compute pairwise IoU across two lists of anchor or bounding boxes."""
box_area = lambda boxes: ((boxes[:, 2] - boxes[:, 0]) *
(boxes[:, 3] - boxes[:, 1]))
# Shape of `boxes1`, `boxes2`, `areas1`, `areas2`: (no. of boxes1, 4),
# (no. of boxes2, 4), (no. of boxes1,), (no. of boxes2,)
areas1 = box_area(boxes1)
areas2 = box_area(boxes2)
# Shape of `inter_upperlefts`, `inter_lowerrights`, `inters`: (no. of
# boxes1, no. of boxes2, 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)
# Shape of `inter_areas` and `union_areas`: (no. of boxes1, no. of boxes2)
inter_areas = inters[:, :, 0] * inters[:, :, 1]
union_areas = areas1[:, None] + areas2 - inter_areas
return inter_areas / union_areas
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#@save
def assign_anchor_to_bbox(ground_truth, anchors, device, iou_threshold=0.5):
"""Assign closest ground-truth bounding boxes to anchor boxes."""
num_anchors, num_gt_boxes = anchors.shape[0], ground_truth.shape[0]
# Element x_ij in the i-th row and j-th column is the IoU of the anchor
# box i and the ground-truth bounding box j
jaccard = box_iou(anchors, ground_truth)
# Initialize the tensor to hold the assigned ground-truth bounding box for
# each anchor
anchors_bbox_map = np.full((num_anchors,), -1, dtype=np.int32, ctx=device)
# Assign ground-truth bounding boxes according to the threshold
max_ious, indices = np.max(jaccard, axis=1), np.argmax(jaccard, axis=1)
anc_i = np.nonzero(max_ious >= 0.5)[0]
box_j = indices[max_ious >= 0.5]
anchors_bbox_map[anc_i] = box_j
col_discard = np.full((num_anchors,), -1)
row_discard = np.full((num_gt_boxes,), -1)
for _ in range(num_gt_boxes):
max_idx = np.argmax(jaccard) # Find the largest IoU
box_idx = (max_idx % num_gt_boxes).astype('int32')
anc_idx = (max_idx / num_gt_boxes).astype('int32')
anchors_bbox_map[anc_idx] = box_idx
jaccard[:, box_idx] = col_discard
jaccard[anc_idx, :] = row_discard
return anchors_bbox_map
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#@save
def assign_anchor_to_bbox(ground_truth, anchors, device, iou_threshold=0.5):
"""Assign closest ground-truth bounding boxes to anchor boxes."""
num_anchors, num_gt_boxes = anchors.shape[0], ground_truth.shape[0]
# Element x_ij in the i-th row and j-th column is the IoU of the anchor
# box i and the ground-truth bounding box j
jaccard = box_iou(anchors, ground_truth)
# Initialize the tensor to hold the assigned ground-truth bounding box for
# each anchor
anchors_bbox_map = torch.full((num_anchors,), -1, dtype=torch.long,
device=device)
# Assign ground-truth bounding boxes according to the threshold
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) # Find the largest IoU
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
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#@save
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 * np.log(eps + c_assigned_bb[:, 2:] / c_anc[:, 2:])
offset = np.concatenate([offset_xy, offset_wh], axis=1)
return offset
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#@save
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
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#@save
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.ctx, 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 = np.tile((np.expand_dims((anchors_bbox_map >= 0),
axis=-1)), (1, 4)).astype('int32')
# Initialize class labels and assigned bounding box coordinates with
# zeros
class_labels = np.zeros(num_anchors, dtype=np.int32, ctx=device)
assigned_bb = np.zeros((num_anchors, 4), dtype=np.float32,
ctx=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 = np.nonzero(anchors_bbox_map >= 0)[0]
bb_idx = anchors_bbox_map[indices_true]
class_labels[indices_true] = label[bb_idx, 0].astype('int32') + 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 = np.stack(batch_offset)
bbox_mask = np.stack(batch_mask)
class_labels = np.stack(batch_class_labels)
return (bbox_offset, bbox_mask, class_labels)
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#@save
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)
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ground_truth = np.array([[0, 0.1, 0.08, 0.52, 0.92],
[1, 0.55, 0.2, 0.9, 0.88]])
anchors = np.array([[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']);
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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']);
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labels = multibox_target(np.expand_dims(anchors, axis=0),
np.expand_dims(ground_truth, axis=0))
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labels = multibox_target(anchors.unsqueeze(dim=0),
ground_truth.unsqueeze(dim=0))
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labels[2]
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array([[0, 1, 2, 0, 2]], dtype=int32)
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labels[2]
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tensor([[0, 1, 2, 0, 2]])
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labels[1]
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array([[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1]],
dtype=int32)
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labels[1]
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tensor([[0., 0., 0., 0., 1., 1., 1., 1., 1., 1., 1., 1., 0., 0., 0., 0., 1., 1.,
1., 1.]])
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labels[0]
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:class: output
array([[-0.00e+00, -0.00e+00, -0.00e+00, -0.00e+00, 1.40e+00, 1.00e+01,
2.59e+00, 7.18e+00, -1.20e+00, 2.69e-01, 1.68e+00, -1.57e+00,
-0.00e+00, -0.00e+00, -0.00e+00, -0.00e+00, -5.71e-01, -1.00e+00,
4.17e-06, 6.26e-01]])
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labels[0]
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:class: output
tensor([[-0.00e+00, -0.00e+00, -0.00e+00, -0.00e+00, 1.40e+00, 1.00e+01,
2.59e+00, 7.18e+00, -1.20e+00, 2.69e-01, 1.68e+00, -1.57e+00,
-0.00e+00, -0.00e+00, -0.00e+00, -0.00e+00, -5.71e-01, -1.00e+00,
4.17e-06, 6.26e-01]])
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#@save
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 = np.exp(offset_preds[:, 2:] / 5) * anc[:, 2:]
pred_bbox = np.concatenate((pred_bbox_xy, pred_bbox_wh), axis=1)
predicted_bbox = d2l.box_center_to_corner(pred_bbox)
return predicted_bbox
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#@save
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
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#@save
def nms(boxes, scores, iou_threshold):
"""Sort confidence scores of predicted bounding boxes."""
B = scores.argsort()[::-1]
keep = [] # Indices of predicted bounding boxes that will be kept
while B.size > 0:
i = B[0]
keep.append(i)
if B.size == 1: break
iou = box_iou(boxes[i, :].reshape(-1, 4),
boxes[B[1:], :].reshape(-1, 4)).reshape(-1)
inds = np.nonzero(iou <= iou_threshold)[0]
B = B[inds + 1]
return np.array(keep, dtype=np.int32, ctx=boxes.ctx)
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#@save
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)
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#@save
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.ctx, cls_probs.shape[0]
anchors = np.squeeze(anchors, axis=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 = np.max(cls_prob[1:], 0), np.argmax(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 = np.arange(num_anchors, dtype=np.int32, ctx=device)
combined = np.concatenate((keep, all_idx))
unique, counts = np.unique(combined, return_counts=True)
non_keep = unique[counts == 1]
all_id_sorted = np.concatenate((keep, non_keep))
class_id[non_keep] = -1
class_id = class_id[all_id_sorted].astype('float32')
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 = np.concatenate((np.expand_dims(class_id, axis=1),
np.expand_dims(conf, axis=1),
predicted_bb), axis=1)
out.append(pred_info)
return np.stack(out)
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#@save
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)
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anchors = np.array([[0.1, 0.08, 0.52, 0.92], [0.08, 0.2, 0.56, 0.95],
[0.15, 0.3, 0.62, 0.91], [0.55, 0.2, 0.9, 0.88]])
offset_preds = np.array([0] * d2l.size(anchors))
cls_probs = np.array([[0] * 4, # Predicted background likelihood
[0.9, 0.8, 0.7, 0.1], # Predicted dog likelihood
[0.1, 0.2, 0.3, 0.9]]) # Predicted cat likelihood
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anchors = torch.tensor([[0.1, 0.08, 0.52, 0.92], [0.08, 0.2, 0.56, 0.95],
[0.15, 0.3, 0.62, 0.91], [0.55, 0.2, 0.9, 0.88]])
offset_preds = torch.tensor([0] * anchors.numel())
cls_probs = torch.tensor([[0] * 4, # Predicted background likelihood
[0.9, 0.8, 0.7, 0.1], # Predicted dog likelihood
[0.1, 0.2, 0.3, 0.9]]) # Predicted cat likelihood
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fig = d2l.plt.imshow(img)
show_bboxes(fig.axes, anchors * bbox_scale,
['dog=0.9', 'dog=0.8', 'dog=0.7', 'cat=0.9'])
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fig = d2l.plt.imshow(img)
show_bboxes(fig.axes, anchors * bbox_scale,
['dog=0.9', 'dog=0.8', 'dog=0.7', 'cat=0.9'])
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output = multibox_detection(np.expand_dims(cls_probs, axis=0),
np.expand_dims(offset_preds, axis=0),
np.expand_dims(anchors, axis=0),
nms_threshold=0.5)
output
.. parsed-literal::
:class: output
array([[[ 1. , 0.9 , 0.55, 0.2 , 0.9 , 0.88],
[ 0. , 0.9 , 0.1 , 0.08, 0.52, 0.92],
[-1. , 0.8 , 0.08, 0.2 , 0.56, 0.95],
[-1. , 0.7 , 0.15, 0.3 , 0.62, 0.91]]])
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output = multibox_detection(cls_probs.unsqueeze(dim=0),
offset_preds.unsqueeze(dim=0),
anchors.unsqueeze(dim=0),
nms_threshold=0.5)
output
.. parsed-literal::
:class: output
tensor([[[ 0.00, 0.90, 0.10, 0.08, 0.52, 0.92],
[ 1.00, 0.90, 0.55, 0.20, 0.90, 0.88],
[-1.00, 0.80, 0.08, 0.20, 0.56, 0.95],
[-1.00, 0.70, 0.15, 0.30, 0.62, 0.91]]])
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fig = d2l.plt.imshow(img)
for i in output[0].asnumpy():
if i[0] == -1:
continue
label = ('dog=', 'cat=')[int(i[0])] + str(i[1])
show_bboxes(fig.axes, [np.array(i[2:]) * bbox_scale], label)
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fig = d2l.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)
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`Discussions `__
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`Discussions `__
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