.. _sec_anchor:
Caixas de Âncora
================
Os algoritmos de detecção de objetos geralmente amostram um grande
número de regiões na imagem de entrada, determinam se essas regiões
contêm objetos de interesse e ajustam as bordas das regiões de modo a
prever a caixa delimitadora da verdade terrestre do alvo com mais
precisão. Diferentes modelos podem usar diferentes métodos de amostragem
de região. Aqui, apresentamos um desses métodos: ele gera várias caixas
delimitadoras com diferentes tamanhos e proporções de aspecto, enquanto
é centralizado em cada pixel. Essas caixas delimitadoras são chamadas de
caixas de âncora. Praticaremos a detecção de objetos com base em caixas
de âncora nas seções a seguir.
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Primeiro, importe os pacotes ou módulos necessários para esta seção.
Aqui, modificamos a precisão de impressão do NumPy. Como os tensores de
impressão, na verdade, chamam a função de impressão de NumPy, os números
de ponto flutuante nos tensores impressos nesta seção são mais concisos.
.. code:: python
%matplotlib inline
from mxnet import gluon, image, np, npx
from d2l import mxnet as d2l
np.set_printoptions(2)
npx.set_np()
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Primeiro, importe os pacotes ou módulos necessários para esta seção.
Aqui, modificamos a precisão de impressão do PyTorch. Como os tensores
de impressão, na verdade, chamam a função de impressão de PyTorch, os
números de ponto flutuante nos tensores impressos nesta seção são mais
concisos.
.. code:: python
%matplotlib inline
import torch
from d2l import torch as d2l
torch.set_printoptions(2)
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#@save
def multibox_prior(data, sizes, ratios):
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 center of a pixel
# Since pixel (height=1, 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 which are later
# used to create anchor box corner coordinates (xmin, xmax, ymin, ymax)
# concat (various sizes, first ratio) and (first size, various ratios)
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 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):
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 center of a pixel
# Since pixel (height=1, 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 which are later
# used to create anchor box corner coordinates (xmin, xmax, ymin, ymax)
# cat (various sizes, first ratio) and (first size, various ratios)
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 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[0:2]
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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:class: output
(1, 2042040, 4)
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img = d2l.plt.imread('../img/catdog.jpg')
h, w = img.shape[0:2]
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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:class: output
561 728
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:class: output
torch.Size([1, 2042040, 4])
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.. code:: python
boxes = Y.reshape(h, w, 5, 4)
boxes[250, 250, 0, :]
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:class: output
array([0.06, 0.07, 0.63, 0.82])
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.. code:: python
boxes = Y.reshape(h, w, 5, 4)
boxes[250, 250, 0, :]
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:class: output
tensor([0.06, 0.07, 0.63, 0.82])
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.. code:: python
#@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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.. code:: python
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 IOU between two sets of boxes of shape (N,4) and (M,4)."""
# Compute box areas
box_area = lambda boxes: ((boxes[:, 2] - boxes[:, 0]) *
(boxes[:, 3] - boxes[:, 1]))
area1 = box_area(boxes1)
area2 = box_area(boxes2)
lt = np.maximum(boxes1[:, None, :2], boxes2[:, :2]) # [N,M,2]
rb = np.minimum(boxes1[:, None, 2:], boxes2[:, 2:]) # [N,M,2]
wh = (rb - lt).clip(min=0) # [N,M,2]
inter = wh[:, :, 0] * wh[:, :, 1] # [N,M]
unioun = area1[:, None] + area2 - inter
return inter / unioun
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#@save
def box_iou(boxes1, boxes2):
"""Compute IOU between two sets of boxes of shape (N,4) and (M,4)."""
# Compute box areas
box_area = lambda boxes: ((boxes[:, 2] - boxes[:, 0]) *
(boxes[:, 3] - boxes[:, 1]))
area1 = box_area(boxes1)
area2 = box_area(boxes2)
lt = torch.max(boxes1[:, None, :2], boxes2[:, :2]) # [N,M,2]
rb = torch.min(boxes1[:, None, 2:], boxes2[:, 2:]) # [N,M,2]
wh = (rb - lt).clamp(min=0) # [N,M,2]
inter = wh[:, :, 0] * wh[:, :, 1] # [N,M]
unioun = area1[:, None] + area2 - inter
return inter / unioun
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#@save
def match_anchor_to_bbox(ground_truth, anchors, device, iou_threshold=0.5):
"""Assign ground-truth bounding boxes to anchor boxes similar to them."""
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 `anc_i` to the ground-truth bounding box `box_j`
jaccard = box_iou(anchors, ground_truth)
# Initialize the tensor to hold assigned ground truth bbox for each anchor
anchors_bbox_map = np.full((num_anchors,), -1, dtype=np.int32, ctx=device)
# Assign ground truth bounding box 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
# Find the largest iou for each bbox
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)
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 match_anchor_to_bbox(ground_truth, anchors, device, iou_threshold=0.5):
"""Assign ground-truth bounding boxes to anchor boxes similar to them."""
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 `anc_i` to the ground-truth bounding box `box_j`
jaccard = box_iou(anchors, ground_truth)
# Initialize the tensor to hold assigned ground truth bbox for each anchor
anchors_bbox_map = torch.full((num_anchors,), -1, dtype=torch.long,
device=device)
# Assign ground truth bounding box 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
# Find the largest iou for each bbox
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
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#@save
def offset_boxes(anchors, assigned_bb, eps=1e-6):
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
#@save
def multibox_target(anchors, labels):
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 = match_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 bbox 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)
# Assign class labels to the anchor boxes using matched gt bbox labels
# If no gt bbox is assigned to an anchor box, then let the
# class_labels and assigned_bb remain zero, i.e the background class
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 transformations
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 offset_boxes(anchors, assigned_bb, eps=1e-6):
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):
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 = match_anchor_to_bbox(label[:, 1:], anchors, device)
bbox_mask = ((anchors_bbox_map >= 0).float().unsqueeze(-1)).repeat(1, 4)
# Initialize class_labels and assigned bbox 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)
# Assign class labels to the anchor boxes using matched gt bbox labels
# If no gt bbox is assigned to an anchor box, then let the
# class_labels and assigned_bb remain zero, i.e the background class
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 transformations
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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Adicionamos dimensões de exemplo às caixas de âncora e às caixas
delimitadoras de verdade e construímos resultados preditos aleatórios
com uma forma de (tamanho do lote, número de categorias incluindo plano
de fundo, número de caixas de âncora) usando a função ``expand_dims``.
.. code:: python
labels = multibox_target(np.expand_dims(anchors, axis=0),
np.expand_dims(ground_truth, axis=0))
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Adicionamos dimensões de exemplo às caixas de âncora e caixas
delimitadoras de verdade e construímos resultados preditos aleatórios
com uma forma de (tamanho do lote, número de categorias incluindo fundo,
número de caixas de âncora) usando a função ``unsqueeze``.
.. code:: python
labels = multibox_target(anchors.unsqueeze(dim=0),
ground_truth.unsqueeze(dim=0))
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labels[2]
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:class: output
array([[0, 1, 2, 0, 2]], dtype=int32)
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labels[2]
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:class: output
tensor([[0, 1, 2, 0, 2]])
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labels[1]
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:class: output
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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:class: output
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]
.. parsed-literal::
: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]
.. parsed-literal::
: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):
c_anc = d2l.box_corner_to_center(anchors)
c_pred_bb_xy = (offset_preds[:, :2] * c_anc[:, 2:] / 10) + c_anc[:, :2]
c_pred_bb_wh = np.exp(offset_preds[:, 2:] / 5) * c_anc[:, 2:]
c_pred_bb = np.concatenate((c_pred_bb_xy, c_pred_bb_wh), axis=1)
predicted_bb = d2l.box_center_to_corner(c_pred_bb)
return predicted_bb
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#@save
def offset_inverse(anchors, offset_preds):
c_anc = d2l.box_corner_to_center(anchors)
c_pred_bb_xy = (offset_preds[:, :2] * c_anc[:, 2:] / 10) + c_anc[:, :2]
c_pred_bb_wh = torch.exp(offset_preds[:, 2:] / 5) * c_anc[:, 2:]
c_pred_bb = torch.cat((c_pred_bb_xy, c_pred_bb_wh), axis=1)
predicted_bb = d2l.box_center_to_corner(c_pred_bb)
return predicted_bb
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#@save
def nms(boxes, scores, iou_threshold):
# sorting scores by the descending order and return their indices
B = scores.argsort()[::-1]
keep = [] # boxes indices 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)
#@save
def multibox_detection(cls_probs, offset_preds, anchors, nms_threshold=0.5,
pos_threshold=0.00999999978):
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, 0.5)
# Find all non_keep indices and set the class_id 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]
# threshold to be a positive prediction
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 nms(boxes, scores, iou_threshold):
# sorting scores by the descending order and return their indices
B = torch.argsort(scores, dim=-1, descending=True)
keep = [] # boxes indices 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)
#@save
def multibox_detection(cls_probs, offset_preds, anchors, nms_threshold=0.5,
pos_threshold=0.00999999978):
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, 0.5)
# Find all non_keep indices and set the class_id 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]
# threshold to be a positive prediction
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 probability for background
[0.9, 0.8, 0.7, 0.1], # Predicted probability for dog
[0.1, 0.2, 0.3, 0.9]]) # Predicted probability for cat
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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 probability for background
[0.9, 0.8, 0.7, 0.1], # Predicted probability for dog
[0.1, 0.2, 0.3, 0.9]]) # Predicted probability for cat
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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'])
.. figure:: output_anchor_f592d1_163_0.svg
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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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`Discussões `__
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`Discussões `__
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