YOLOv3学习——损失函数

YOLOv3学习——损失函数

损失函数

上面从概念上将输出特征图上的像素点与预测框关联起来了，那么要对神经网络进行求解，还必须从数学上将网络输出和预测框关联起来，也就是要建立起损失函数跟网络输出之间的关系。下面讨论如何建立起YOLOv3的损失函数。

对于每个预测框，YOLOv3模型会建立三种类型的损失函数：

• 表征是否包含目标物体的损失函数，通过pred_objectness和label_objectness计算。

    loss_obj = paddle.nn.fucntional.binary_cross_entropy_with_logits(pred_objectness, label_objectness)
  

• 表征物体位置的损失函数，通过pred_location和label_location计算。

    pred_location_x = pred_location[:, :, 0, :, :]
    pred_location_y = pred_location[:, :, 1, :, :]
    pred_location_w = pred_location[:, :, 2, :, :]
    pred_location_h = pred_location[:, :, 3, :, :]
    loss_location_x = paddle.nn.fucntional.binary_cross_entropy_with_logits(pred_location_x, label_location_x)
    loss_location_y = paddle.nn.fucntional.binary_cross_entropy_with_logits(pred_location_y, label_location_y)
    loss_location_w = paddle.abs(pred_location_w - label_location_w)
    loss_location_h = paddle.abs(pred_location_h - label_location_h)
    loss_location = loss_location_x + loss_location_y + loss_location_w + loss_location_h
  

• 表征物体类别的损失函数，通过pred_classification和label_classification计算。

    loss_obj = paddle.nn.fucntional.binary_cross_entropy_with_logits(pred_classification, label_classification)
  

我们已经知道怎么计算这些预测值和标签了，但是遗留了一个小问题，就是没有标注出哪些锚框的objectness为-1。为了完成这一步，我们需要计算出所有预测框跟真实框之间的IoU，然后把那些IoU大于阈值的真实框挑选出来。实现代码如下：

# 挑选出跟真实框IoU大于阈值的预测框
def get_iou_above_thresh_inds(pred_box, gt_boxes, iou_threshold):
    batchsize = pred_box.shape[0]
    num_rows = pred_box.shape[1]
    num_cols = pred_box.shape[2]
    num_anchors = pred_box.shape[3]
    ret_inds = np.zeros([batchsize, num_rows, num_cols, num_anchors])
    for i in range(batchsize):
        pred_box_i = pred_box[i]
        gt_boxes_i = gt_boxes[i]
        for k in range(len(gt_boxes_i)): #gt in gt_boxes_i:
            gt = gt_boxes_i[k]
            gtx_min = gt[0] - gt[2] / 2.
            gty_min = gt[1] - gt[3] / 2.
            gtx_max = gt[0] + gt[2] / 2.
            gty_max = gt[1] + gt[3] / 2.
            if (gtx_max - gtx_min < 1e-3) or (gty_max - gty_min < 1e-3):
                continue
            x1 = np.maximum(pred_box_i[:, :, :, 0], gtx_min)
            y1 = np.maximum(pred_box_i[:, :, :, 1], gty_min)
            x2 = np.minimum(pred_box_i[:, :, :, 2], gtx_max)
            y2 = np.minimum(pred_box_i[:, :, :, 3], gty_max)
            intersection = np.maximum(x2 - x1, 0.) * np.maximum(y2 - y1, 0.)
            s1 = (gty_max - gty_min) * (gtx_max - gtx_min)
            s2 = (pred_box_i[:, :, :, 2] - pred_box_i[:, :, :, 0]) * (pred_box_i[:, :, :, 3] - pred_box_i[:, :, :, 1])
            union = s2 + s1 - intersection
            iou = intersection / union
            above_inds = np.where(iou > iou_threshold)
            ret_inds[i][above_inds] = 1
    ret_inds = np.transpose(ret_inds, (0,3,1,2))
    return ret_inds.astype('bool')

上面的函数可以得到哪些锚框的objectness需要被标注为-1，通过下面的程序，对label_objectness进行处理，将IoU大于阈值，但又不是正样本的锚框标注为-1。

def label_objectness_ignore(label_objectness, iou_above_thresh_indices):
    # 注意：这里不能简单的使用 label_objectness[iou_above_thresh_indices] = -1，
    #         这样可能会造成label_objectness为1的点被设置为-1了
    #         只有将那些被标注为0，且与真实框IoU超过阈值的预测框才被标注为-1
    negative_indices = (label_objectness < 0.5)
    ignore_indices = negative_indices * iou_above_thresh_indices
    label_objectness[ignore_indices] = -1
    return label_objectness

下面通过调用这两个函数，实现如何将部分预测框的label_objectness设置为-1。

# 读取数据
reader = paddle.io.DataLoader(train_dataset, batch_size=2, shuffle=True, num_workers=0, drop_last=True)
img, gt_boxes, gt_labels, im_shape = next(reader())
img, gt_boxes, gt_labels, im_shape = img.numpy(), gt_boxes.numpy(), gt_labels.numpy(), im_shape.numpy()
# 计算出锚框对应的标签
label_objectness, label_location, label_classification, scale_location = get_objectness_label(img,
                                                                                              gt_boxes, gt_labels, 
                                                                                              iou_threshold = 0.7,
                                                                                              anchors = [116, 90, 156, 198, 373, 326],
                                                                                              num_classes=7, downsample=32)
                                               
NUM_ANCHORS = 3
NUM_CLASSES = 7
num_filters=NUM_ANCHORS * (NUM_CLASSES + 5)

backbone = DarkNet53_conv_body()
detection = YoloDetectionBlock(ch_in=1024, ch_out=512)
conv2d_pred = paddle.nn.Conv2D(in_channels=1024, out_channels=num_filters,  kernel_size=1)

x = paddle.to_tensor(img)
C0, C1, C2 = backbone(x)
route, tip = detection(C0)
P0 = conv2d_pred(tip)

# anchors包含了预先设定好的锚框尺寸
anchors = [116, 90, 156, 198, 373, 326]
# downsample是特征图P0的步幅
pred_boxes = get_yolo_box_xxyy(P0.numpy(), anchors, num_classes=7, downsample=32)
iou_above_thresh_indices = get_iou_above_thresh_inds(pred_boxes, gt_boxes, iou_threshold=0.7)
label_objectness = label_objectness_ignore(label_objectness, iou_above_thresh_indices)

使用这种方式，就可以将那些没有被标注为正样本，但又与真实框IoU比较大的样本objectness标签设置为-1了，不计算其对任何一种损失函数的贡献。计算总的损失函数的代码如下：

def get_loss(output, label_objectness, label_location, label_classification, scales, num_anchors=3, num_classes=7):
    # 将output从[N, C, H, W]变形为[N, NUM_ANCHORS, NUM_CLASSES + 5, H, W]
    reshaped_output = paddle.reshape(output, [-1, num_anchors, num_classes + 5, output.shape[2], output.shape[3]])

    # 从output中取出跟objectness相关的预测值
    pred_objectness = reshaped_output[:, :, 4, :, :]
    loss_objectness = F.binary_cross_entropy_with_logits(pred_objectness, label_objectness, reduction="none")

    # pos_samples 只有在正样本的地方取值为1.，其它地方取值全为0.
    pos_objectness = label_objectness > 0
    pos_samples = paddle.cast(pos_objectness, 'float32')
    pos_samples.stop_gradient=True

    # 从output中取出所有跟位置相关的预测值
    tx = reshaped_output[:, :, 0, :, :]
    ty = reshaped_output[:, :, 1, :, :]
    tw = reshaped_output[:, :, 2, :, :]
    th = reshaped_output[:, :, 3, :, :]

    # 从label_location中取出各个位置坐标的标签
    dx_label = label_location[:, :, 0, :, :]
    dy_label = label_location[:, :, 1, :, :]
    tw_label = label_location[:, :, 2, :, :]
    th_label = label_location[:, :, 3, :, :]

    # 构建损失函数
    loss_location_x = F.binary_cross_entropy_with_logits(tx, dx_label, reduction="none")
    loss_location_y = F.binary_cross_entropy_with_logits(ty, dy_label, reduction="none")
    loss_location_w = paddle.abs(tw - tw_label)
    loss_location_h = paddle.abs(th - th_label)

    # 计算总的位置损失函数
    loss_location = loss_location_x + loss_location_y + loss_location_h + loss_location_w

    # 乘以scales
    loss_location = loss_location * scales
    # 只计算正样本的位置损失函数
    loss_location = loss_location * pos_samples

    # 从output取出所有跟物体类别相关的像素点
    pred_classification = reshaped_output[:, :, 5:5+num_classes, :, :]

    # 计算分类相关的损失函数
    loss_classification = F.binary_cross_entropy_with_logits(pred_classification, label_classification, reduction="none")
   
    # 将第2维求和
    loss_classification = paddle.sum(loss_classification, axis=2)
    # 只计算objectness为正的样本的分类损失函数
    loss_classification = loss_classification * pos_samples
    total_loss = loss_objectness + loss_location + loss_classification
    # 对所有预测框的loss进行求和
    total_loss = paddle.sum(total_loss, axis=[1,2,3])
    # 对所有样本求平均
    total_loss = paddle.mean(total_loss)

    return total_loss

from paddle.nn import Conv2D

# 计算出锚框对应的标签
label_objectness, label_location, label_classification, scale_location = get_objectness_label(img,
                                                                                              gt_boxes, gt_labels, 
                                                                                              iou_threshold = 0.7,
                                                                                              anchors = [116, 90, 156, 198, 373, 326],
                                                                                              num_classes=7, downsample=32)                                                           

NUM_ANCHORS = 3
NUM_CLASSES = 7
num_filters=NUM_ANCHORS * (NUM_CLASSES + 5)

backbone = DarkNet53_conv_body()
detection = YoloDetectionBlock(ch_in=1024, ch_out=512)
conv2d_pred = Conv2D(in_channels=1024, out_channels=num_filters,  kernel_size=1)

x = paddle.to_tensor(img)
C0, C1, C2 = backbone(x)
route, tip = detection(C0)
P0 = conv2d_pred(tip)
# anchors包含了预先设定好的锚框尺寸
anchors = [116, 90, 156, 198, 373, 326]
# downsample是特征图P0的步幅
pred_boxes = get_yolo_box_xxyy(P0.numpy(), anchors, num_classes=7, downsample=32)
iou_above_thresh_indices = get_iou_above_thresh_inds(pred_boxes, gt_boxes, iou_threshold=0.7)
label_objectness = label_objectness_ignore(label_objectness, iou_above_thresh_indices)

label_objectness = paddle.to_tensor(label_objectness)
label_location = paddle.to_tensor(label_location)
label_classification = paddle.to_tensor(label_classification)
scales = paddle.to_tensor(scale_location)
label_objectness.stop_gradient=True
label_location.stop_gradient=True
label_classification.stop_gradient=True
scales.stop_gradient=True

total_loss = get_loss(P0, label_objectness, label_location, label_classification, scales,
                          num_anchors=NUM_ANCHORS, num_classes=NUM_CLASSES)
total_loss_data = total_loss.numpy()
print(total_loss_data)