发现一个讲解旋转矩阵特别清楚的：旋转矩阵怎么推导_点绕坐标系旋转旋转矩阵推导、理解
代码主要分析masaic数据增强中用到的random_perspective函数
def random_perspective(im, targets=(), segments=(), degrees=10, translate=.1, scale=.1, shear=10, perspective=0.0,
border=(0, 0)):
# torchvision.transforms.RandomAffine(degrees=(-10, 10), translate=(.1, .1), scale=(.9, 1.1), shear=(-10, 10))
# targets = [cls, xyxy]
height = im.shape[0] + border[0] * 2 # shape(h,w,c)
width = im.shape[1] + border[1] * 2
# Center
C = np.eye(3)
C[0, 2] = -im.shape[1] / 2 # x translation (pixels)
C[1, 2] = -im.shape[0] / 2 # y translation (pixels)
# Perspective 透视
P = np.eye(3) # random.uniform(参数1，参数2) 返回参数1和参数2之间的任意值
P[2, 0] = random.uniform(-perspective, perspective) # x perspective (about y)
P[2, 1] = random.uniform(-perspective, perspective) # y perspective (about x)
# Rotation and Scale 旋转和缩放
R = np.eye(3)
a = random.uniform(-degrees, degrees)
# a += random.choice([-180, -90, 0, 90]) # add 90deg rotations to small rotations
s = random.uniform(1 - scale, 1 + scale)
# s = 2 ** random.uniform(-scale, scale)
R[:2] = cv2.getRotationMatrix2D(angle=a, center=(0, 0), scale=s)
# Shear 错切
S = np.eye(3)
S[0, 1] = math.tan(random.uniform(-shear, shear) * math.pi / 180) # x shear (deg)，y不变
S[1, 0] = math.tan(random.uniform(-shear, shear) * math.pi / 180) # y shear (deg)，x不变
# Translation 平移
T = np.eye(3)
T[0, 2] = random.uniform(0.5 - translate, 0.5 + translate) * width # x translation (pixels)
T[1, 2] = random.uniform(0.5 - translate, 0.5 + translate) * height # y translation (pixels)
# Combined rotation matrix @表示矩阵乘法运算
M = T @ S @ R @ P @ C # order of operations (right to left) is IMPORTANT
if (border[0] != 0) or (border[1] != 0) or (M != np.eye(3)).any(): # image changed
if perspective:
#透视变换函数，可保持直线不变形，但是平行线可能不再平行
im = cv2.warpPerspective(im, M, dsize=(width, height), borderValue=(114, 114, 114))
else: # affine
# 仿射变换函数，可实现旋转、平移、缩放；变换后的平行线依旧平行
im = cv2.warpAffine(im, M[:2], dsize=(width, height), borderValue=(114, 114, 114))
# Visualize
# import matplotlib.pyplot as plt
# ax = plt.subplots(1, 2, figsize=(12, 6))[1].ravel()
# ax[0].imshow(im[:, :, ::-1]) # base
# ax[1].imshow(im2[:, :, ::-1]) # warped
# Transform label coordinates
n = len(targets)
if n:
use_segments = any(x.any() for x in segments)
new = np.zeros((n, 4))
if use_segments: # warp segments
segments = resample_segments(segments) # upsample
for i, segment in enumerate(segments):
xy = np.ones((len(segment), 3))
xy[:, :2] = segment
xy = xy @ M.T # transform
xy = xy[:, :2] / xy[:, 2:3] if perspective else xy[:, :2] # perspective rescale or affine
# clip
new[i] = segment2box(xy, width, height)
else: # warp boxes
xy = np.ones((n * 4, 3))
# 1, 2, 3, 4, 1, 4, 3, 2代表 x1 y1 x2 y2 x1 y2 x2 y1
xy[:, :2] = targets[:, [1, 2, 3, 4, 1, 4, 3, 2]].reshape(n * 4, 2) # x1y1, x2y2, x1y2, x2y1
xy = xy @ M.T # transform
xy = (xy[:, :2] / xy[:, 2:3] if perspective else xy[:, :2]).reshape(n, 8) # perspective rescale or affine
# create new boxes
x = xy[:, [0, 2, 4, 6]]
y = xy[:, [1, 3, 5, 7]]
new = np.concatenate((x.min(1), y.min(1), x.max(1), y.max(1))).reshape(4, n).T
# clip
new[:, [0, 2]] = new[:, [0, 2]].clip(0, width)
new[:, [1, 3]] = new[:, [1, 3]].clip(0, height)
# filter candidates
i = box_candidates(box1=targets[:, 1:5].T * s, box2=new.T, area_thr=0.01 if use_segments else 0.10)
targets = targets[i]
targets[:, 1:5] = new[i]
return im, targets