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IOU（Intersection over Union）：
- 作用：IOU是最常用的边界框重叠度量方法，用于衡量两个边界框之间的重叠程度。
- 优点：简单直观，易于计算和理解。
- 缺点：不考虑形状信息，对大小和方向不敏感。
- 计算公式：IOU = (Intersection Area) / (Union Area)
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GIOU（Generalized Intersection over Union）：
- 作用：GIOU是对IOU的改进，它在边界框重叠度量中考虑了形状信息。它通过计算交集面积、并集面积和最小闭合矩形的面积来进行度量。
- 优点：对形状差异较大的边界框提供了更准确的度量结果。
- 缺点：对形状变化敏感度不一致，不具备方向信息，对大小不敏感。
- 计算公式：GIOU = IOU - (C - Union Area) / C, C为最小包闭区面积
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DIOU（Distance-IoU）：
- 作用：在GIOU的基础上考虑了边界框中心点之间的距离。
- 优点：对中心点距离的变化更加敏感，可以更好地处理边界框的位置偏移。
- 缺点：仍然不具备方向信息，对大小不敏感。
- 计算公式：DIOU = IOU - (ρ2(b, bgt) / c2), ρ为预测框与gt框中心点距离，c为最小包闭区对角线长度。
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CIOU（Complete-IoU）：
- 作用：在DIOU的基础上进一步考虑了宽高的相似性。
- 优点：综合考虑了位置、形状、尺寸等因素，对边界框的重叠度量更加准确。
- 缺点：仍然不具备方向信息。
- 计算公式：
ν = 4 / pi2 * ( arctan( wgt / hgt ) - arctan(w / h))2
α = ν / (1 - IoU + ν) PS：ν不变时，iou越大，α越大，loss越大
CIOU = DIOU - αv - 当iou很小时，v的权重小，更多关心把iou变大；当iou很大时，权重大，更多关心是否相似
- α - IOU
在计算iou损失时,将iou项变为α指数。对小数据集和噪声的鲁棒性更好
eg. LIOU = 1 - IOU Lα - IOU = 1 - IOUα
LGIOU = 1- IOU + (C - U) / C, Lα-GIOU = 1 - IOUα + (C - U) / C)α
当iou>0.5时，梯度>1，加速学习
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EIOU：
- 将CIOU的长宽比例拆分为长比例、宽比例，收敛更快
- EIOU = IOU - (ρ2(b, bgt) / c2) - (ρ2(w, wgt) / cw2) - (ρ2(h, hgt) / ch2) , cw、ch最小包闭区w、h
- 引入Focal - EIOU缓解样品不平衡问题
- LFocal-EIOU = IOUλLEIOU
- 简单的任务框（即iou较大）回归不需要用过大的权重来学习，而复杂的任务框回归需要大权重来学习
class WIoU_Scale:
''' monotonous: {
None: origin v1
True: monotonic FM v2
False: non-monotonic FM v3
}
momentum: The momentum of running mean'''
iou_mean = 1.
monotonous = False
_momentum = 1 - 0.5 ** (1 / 7000)
_is_train = True
def __init__(self, iou):
self.iou = iou
self._update(self)
@classmethod
def _update(cls, self):
if cls._is_train: cls.iou_mean = (1 - cls._momentum) * cls.iou_mean + \
cls._momentum * self.iou.detach().mean().item()
@classmethod
def _scaled_loss(cls, self, gamma=1.9, delta=3):
if isinstance(self.monotonous, bool):
if self.monotonous:
return (self.iou.detach() / self.iou_mean).sqrt()
else:
beta = self.iou.detach() / self.iou_mean
alpha = delta * torch.pow(gamma, beta - delta)
return beta / alpha
return 1
def bbox_iou(box1, box2, xywh=True, GIoU=False, DIoU=False, CIoU=False, SIoU=False, EIoU=False, WIoU=False, Focal=False,
alpha=1, gamma=0.5, scale=False, eps=1e-7):
# Returns Intersection over Union (IoU) of box1(1,4) to box2(n,4)
# Get the coordinates of bounding boxes
if xywh: # transform from xywh to xyxy
(x1, y1, w1, h1), (x2, y2, w2, h2) = box1.chunk(4, -1), box2.chunk(4, -1)
w1_, h1_, w2_, h2_ = w1 / 2, h1 / 2, w2 / 2, h2 / 2
b1_x1, b1_x2, b1_y1, b1_y2 = x1 - w1_, x1 + w1_, y1 - h1_, y1 + h1_
b2_x1, b2_x2, b2_y1, b2_y2 = x2 - w2_, x2 + w2_, y2 - h2_, y2 + h2_
else: # x1, y1, x2, y2 = box1
b1_x1, b1_y1, b1_x2, b1_y2 = box1.chunk(4, -1)
b2_x1, b2_y1, b2_x2, b2_y2 = box2.chunk(4, -1)
w1, h1 = b1_x2 - b1_x1, (b1_y2 - b1_y1).clamp(eps)
w2, h2 = b2_x2 - b2_x1, (b2_y2 - b2_y1).clamp(eps)
# Intersection area
inter = (torch.min(b1_x2, b2_x2) - torch.max(b1_x1, b2_x1)).clamp(0) * \
(torch.min(b1_y2, b2_y2) - torch.max(b1_y1, b2_y1)).clamp(0)
# Union Area
union = w1 * h1 + w2 * h2 - inter + eps
if scale:
self = WIoU_Scale(1 - (inter / union))
# IoU
# iou = inter / union # ori iou
iou = torch.pow(inter / (union + eps), alpha) # alpha iou
if CIoU or DIoU or GIoU or EIoU or SIoU or WIoU:
cw = torch.max(b1_x2, b2_x2) - torch.min(b1_x1, b2_x1) # convex (smallest enclosing box) width
ch = torch.max(b1_y2, b2_y2) - torch.min(b1_y1, b2_y1)
# convex height
if CIoU or DIoU or EIoU or SIoU or WIoU: # Distance or Complete IoU https://arxiv.org/abs/1911.08287v1
c2 = (cw ** 2 + ch ** 2) ** alpha + eps # convex diagonal squared
rho2 = (((b2_x1 + b2_x2 - b1_x1 - b1_x2) ** 2 + (
b2_y1 + b2_y2 - b1_y1 - b1_y2) ** 2) / 4) ** alpha # center dist ** 2
if CIoU: # https://github.com/Zzh-tju/DIoU-SSD-pytorch/blob/master/utils/box/box_utils.py#L47
v = (4 / math.pi ** 2) * (torch.atan(w2 / h2) - torch.atan(w1 / h1)).pow(2)
with torch.no_grad():
alpha_ciou = v / (v - iou + (1 + eps))
if Focal:
return iou - (rho2 / c2 + torch.pow(v * alpha_ciou + eps, alpha)), torch.pow(inter / (union + eps),
gamma) # Focal_CIoU
else:
return iou - (rho2 / c2 + torch.pow(v * alpha_ciou + eps, alpha)) # CIoU
elif EIoU:
rho_w2 = ((b2_x2 - b2_x1) - (b1_x2 - b1_x1)) ** 2
rho_h2 = ((b2_y2 - b2_y1) - (b1_y2 - b1_y1)) ** 2
cw2 = torch.pow(cw ** 2 + eps, alpha)
ch2 = torch.pow(ch ** 2 + eps, alpha)
if Focal:
return iou - (rho2 / c2 + rho_w2 / cw2 + rho_h2 / ch2), torch.pow(inter / (union + eps),
gamma) # Focal_EIou
else:
return iou - (rho2 / c2 + rho_w2 / cw2 + rho_h2 / ch2) # EIou
elif SIoU:
# SIoU Loss https://arxiv.org/pdf/2205.12740.pdf
s_cw = (b2_x1 + b2_x2 - b1_x1 - b1_x2) * 0.5 + eps
s_ch = (b2_y1 + b2_y2 - b1_y1 - b1_y2) * 0.5 + eps
sigma = torch.pow(s_cw ** 2 + s_ch ** 2, 0.5)
sin_alpha_1 = torch.abs(s_cw) / sigma
sin_alpha_2 = torch.abs(s_ch) / sigma
threshold = pow(2, 0.5) / 2
sin_alpha = torch.where(sin_alpha_1 > threshold, sin_alpha_2, sin_alpha_1)
angle_cost = torch.cos(torch.arcsin(sin_alpha) * 2 - math.pi / 2)
rho_x = (s_cw / cw) ** 2
rho_y = (s_ch / ch) ** 2
gamma = angle_cost - 2
distance_cost = 2 - torch.exp(gamma * rho_x) - torch.exp(gamma * rho_y)
omiga_w = torch.abs(w1 - w2) / torch.max(w1, w2)
omiga_h = torch.abs(h1 - h2) / torch.max(h1, h2)
shape_cost = torch.pow(1 - torch.exp(-1 * omiga_w), 4) + torch.pow(1 - torch.exp(-1 * omiga_h), 4)
if Focal:
return iou - torch.pow(0.5 * (distance_cost + shape_cost) + eps, alpha), torch.pow(
inter / (union + eps), gamma) # Focal_SIou
else:
return iou - torch.pow(0.5 * (distance_cost + shape_cost) + eps, alpha) # SIou
elif WIoU:
if Focal:
raise RuntimeError("WIoU do not support Focal.")
elif scale:
return getattr(WIoU_Scale, '_scaled_loss')(self), (1 - iou) * torch.exp(
(rho2 / c2)), iou # WIoU https://arxiv.org/abs/2301.10051
else:
return iou, torch.exp((rho2 / c2)) # WIoU v1
if Focal:
return iou - rho2 / c2, torch.pow(inter / (union + eps), gamma) # Focal_DIoU
else:
return iou - rho2 / c2 # DIoU
c_area = cw * ch + eps # convex area
if Focal:
return iou - torch.pow((c_area - union) / c_area + eps, alpha), torch.pow(inter / (union + eps),
gamma) # Focal_GIoU https://arxiv.org/pdf/1902.09630.pdf
else:
return iou - torch.pow((c_area - union) / c_area + eps, alpha) # GIoU https://arxiv.org/pdf/1902.09630.pdf
if Focal:
return iou, torch.pow(inter / (union + eps), gamma) # Focal_IoU
else:
return iou # IoU标签：IoU,torch,eps,b1,b2,alpha,iou From： https://www.cnblogs.com/lbclyc/p/17458788.html