opencv函数cv2.warpAffine 和 cv2.warpPerspective 的理解和复现

文章目录

• opencv函数cv2.warpAffine 和 cv2.warpPerspective 的理解和复现
• • 1. warpAffine 函数处理仿射变换
  • 2. warp_perspective
  • 3， 实验

opencv函数cv2.warpAffine 和 cv2.warpPerspective 的理解和复现

1. warpAffine 函数处理仿射变换

仿射矩阵是2 * 3的矩阵。

首先进行坐标转换，然后应用插值

具体代码如下, 与opencv一致：

def warp_affine_forward(image, rot_mat, dst_h, dst_w):M = rot_mat.reshape([2, 3])hs, ws, cs = image.shapehh, ww = np.arange(hs), np.arange(ws)xx, yy = np.meshgrid(ww, hh)sx, sy = xx, yy # 不缩放图像tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2], M[1, 0] * sx + M[1, 1] * sy + M[1, 2]# tx = np.sum(M[0, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)# ty = np.sum(M[1, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)dhh, dww = np.arange(dst_h), np.arange(dst_w)dxx, dyy = np.meshgrid(dww, dhh)grid_x, grid_y = dxx, dyypoints = np.dstack((tx, ty))# print(points.shape, image.shape, grid_x.shape)out = griddata(points.reshape(-1, 2), image.reshape(-1, 3), (grid_x, grid_y), method='linear')out[np.isnan(out)] = 0return out

逆变换代码：

def warp_affine(image, rot_mat, dst_h, dst_w):M = rot_mat.reshape([2, 3])hs, ws, cs = image.shapehh, ww = np.arange(dst_h), np.arange(dst_w)xx, yy = np.meshgrid(ww, hh)sx, sy = (xx + 0.5) * (ws / ws) - 0.5, (yy + 0.5) * (hs / hs) - 0.5 # 不缩放图像。# sx, sy = (xx + 0.5) * (ws / dst_w) - 0.5, (yy + 0.5) * (hs / dst_h) - 0.5 # 缩放图像tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2], M[1, 0] * sx + M[1, 1] * sy + M[1, 2]# tx = np.sum(M[0, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)# ty = np.sum(M[1, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)mask = ((tx < 0) + (ty < 0) + (tx > ws - 1) + (ty > hs - 1)) > 0# print(mask.shape, mask.dtype, np.sum(mask))out = interp_linear(image, tx, ty)out[mask] = 0return out

也可以求解转换矩阵的逆后，再正变换，结果相同。

其中用到重查找函数：根据tx,ty坐标位置，获取值
和cv2.remap函数相同。

def interp_linear(image, tx, ty):'''类似 cv2.remap 函数:param image: h,w,c image  np.float:param tx:  dst_h * dst_w, float , 目标位置x方向:param ty:  dst_h * dst_w, float , 目标位置y方向:return:'''h, w, c = image.shapehv, wv = ty, txhh = np.floor(hv).astype(np.int32)ww = np.floor(wv).astype(np.int32)u = hv - hhv = wv - ww# special caseu[hh < 0] = 0hh[hh < 0] = 0u[hh >= h - 1] = 1.0hh[hh >= h - 1] = h - 2v[ww < 0] = 0ww[ww < 0] = 0v[ww >= w - 1] = 1.0ww[ww >= w - 1] = w - 2# v = v.reshape(-1)w00 = (1-u)*(1-v)w01 = u * (1-v)w10 = (1-u) * vw11 = u*vout = w00[..., None] * image[hh, ww] + w10[..., None]  * image[hh, ww + 1] + w01[..., None]  * image[(hh + 1), ww] + w11[..., None]  * image[hh + 1, ww + 1]return out

2. warp_perspective

warpPerspective 和 warpAffine 是类似的。
但是warpPerspective的转换矩阵是3*3的透视变换矩阵，经过变换后平行线可能不在平行

一个逆变换 和 两个正变换的代码如下：

# 逆变换函数
def warp_perspective(image, pers_mat, dst_h, dst_w):M = pers_mat.reshape([3, 3])hs, ws, cs = image.shapehh, ww = np.arange(dst_h), np.arange(dst_w)xx, yy = np.meshgrid(ww, hh)sx, sy = (xx + 0.5) * (ws / ws) - 0.5, (yy + 0.5)* (hs / hs) - 0.5# sx, sy = (xx + 0.5) * (ws / dst_w) - 0.5, (yy + 0.5) * (hs / dst_h) - 0.5  # 缩放图像t = M[2, 0] * sx + M[2, 1] * sy + M[2, 2]tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2] , M[1, 0] * sx + M[1, 1] * sy + M[1, 2]tx, ty = tx / t, ty / t# out = np.zeros_like(image)mask = ((tx < 0 ) + (ty < 0) + (tx > ws - 1) + (ty > hs - 1)) > 0print(mask.shape, mask.dtype, np.sum(mask))# out = interp_linear(image, tx, ty)out = cv2.remap(image, tx.astype(np.float32), ty.astype(np.float32), interpolation=cv2.INTER_LINEAR)out[mask] = 0return out
# 正变化函数
def warp_perspective_forward(image, pers_mat, dst_h, dst_w):M = pers_mat.reshape([3, 3])hs, ws, cs = image.shapehh, ww = np.arange(hs), np.arange(ws)xx, yy = np.meshgrid(ww, hh)sx, sy = xx, yy  # 不缩放图像t = M[2, 0] * sx + M[2, 1] * sy + M[2, 2]tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2] , M[1, 0] * sx + M[1, 1] * sy + M[1, 2]tx, ty = tx / t, ty / t# interpdhh, dww = np.arange(dst_h), np.arange(dst_w)dxx, dyy = np.meshgrid(dww, dhh)grid_x, grid_y = dxx, dyypoints = np.dstack((tx, ty))# print(points.shape, image.shape, grid_x.shape)out = griddata(points.reshape(-1, 2), image.reshape(-1, 3), (grid_x, grid_y), method='linear')out[np.isnan(out)] = 0return out# 正变换函数：这里利用np.linalg.inv 求逆矩阵，然后按照warp_perspective的方式进行
def warp_perspective_forward2(image, pers_mat, dst_h, dst_w):M = pers_mat.reshape([3, 3])M_inv = np.linalg.inv(M)M = M_invhs, ws, cs = image.shapehh, ww = np.arange(dst_h), np.arange(dst_w)xx, yy = np.meshgrid(ww, hh)sx, sy = (xx + 0.5) * (ws / ws) - 0.5, (yy + 0.5) * (hs / hs) - 0.5# sx, sy = (xx + 0.5) * (ws / dst_w) - 0.5, (yy + 0.5) * (hs / dst_h) - 0.5  # 缩放图像t = M[2, 0] * sx + M[2, 1] * sy + M[2, 2]tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2], M[1, 0] * sx + M[1, 1] * sy + M[1, 2]tx, ty = tx / t, ty / t# out = np.zeros_like(image)mask = ((tx < 0) + (ty < 0) + (tx > ws - 1) + (ty > hs - 1)) > 0print(mask.shape, mask.dtype, np.sum(mask))# out = interp_linear(image, tx, ty)out = cv2.remap(image, tx.astype(np.float32), ty.astype(np.float32), interpolation=cv2.INTER_LINEAR)out[mask] = 0return out

3， 实验

验证以上代码和opencv中的一致性

import cv2
import numpy as np
from matplotlib import pyplot as plt
from scipy.interpolate import griddata
def cal_sobel(img):#分别求X,Y方向的梯度grad_X=cv2.Sobel(img,-1,1,0)grad_Y=cv2.Sobel(img,-1,0,1)#求梯度图像grad=cv2.addWeighted(grad_X,0.5,grad_Y,0.5,0)return grad
if __name__ == "__main__":file1 = r'test.jpg'image1 = cv2.imread(file1) / 255image1 = cv2.resize(image1, (0, 0), fx=0.5, fy=0.5)h, w, c = image1.shapeprint(h, w, c)center = (w // 2, h // 2)angle = -50scale = 0.6rot_mat = cv2.getRotationMatrix2D(center, angle, scale)print(rot_mat)dst_h, dst_w = int(image1.shape[0] * 0.7), int(image1.shape[1]* 0.7)image2 = cv2.warpAffine(image1, rot_mat, (dst_w, dst_h))center = (w // 2, h // 2)angle = 50scale = 1 / 0.6rot_mat2 = cv2.getRotationMatrix2D(center, angle, scale)print(rot_mat2)image3 = warp_affine(image1, rot_mat2, dst_h, dst_w)image4 = warp_affine_forward(image1, rot_mat, dst_h, dst_w)plt.figure()plt.subplot(221)plt.imshow(image1)plt.subplot(222)plt.imshow(image2)plt.subplot(223)plt.imshow(image3)plt.subplot(224)plt.imshow(image4)plt.show()# 根据4个点求透视转换pts1 = np.float32([[56, 65], [368, 52], [28, 387], [389, 390]])pts2 = np.float32([[0, 0], [300, 0], [0, 300], [300, 300]])M = cv2.getPerspectiveTransform(pts1, pts2)image2 = cv2.warpPerspective(image1, M, (dst_w, dst_h), flags=cv2.INTER_LINEAR + cv2.WARP_INVERSE_MAP)image3 = warp_perspective(image1, M, dst_h, dst_w)image4 = cv2.warpPerspective(image1, M, (dst_w, dst_h), flags=cv2.INTER_LINEAR)image5 = warp_perspective_forward(image1, M, dst_h, dst_w)image6 = warp_perspective_forward2(image1, M, dst_h, dst_w)plt.figure()plt.subplot(231)plt.imshow(image1)plt.subplot(232)plt.imshow(image2)plt.subplot(233)plt.imshow(image3)plt.subplot(234)plt.imshow(image4)plt.subplot(235)plt.imshow(image5)plt.subplot(236)plt.imshow(image6)plt.show()

运行上面的代码，实验结果如下：
warp affine实验结果：

warp perspective 实验结果

opencv函数cv2.warpAffine 和 cv2.warpPerspective 的理解和复现

文章目录

• opencv函数cv2.warpAffine 和 cv2.warpPerspective 的理解和复现
• • 1. warpAffine 函数处理仿射变换
  • 2. warp_perspective
  • 3， 实验

opencv函数cv2.warpAffine 和 cv2.warpPerspective 的理解和复现

1. warpAffine 函数处理仿射变换

仿射矩阵是2 * 3的矩阵。

首先进行坐标转换，然后应用插值

具体代码如下, 与opencv一致：

def warp_affine_forward(image, rot_mat, dst_h, dst_w):M = rot_mat.reshape([2, 3])hs, ws, cs = image.shapehh, ww = np.arange(hs), np.arange(ws)xx, yy = np.meshgrid(ww, hh)sx, sy = xx, yy # 不缩放图像tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2], M[1, 0] * sx + M[1, 1] * sy + M[1, 2]# tx = np.sum(M[0, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)# ty = np.sum(M[1, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)dhh, dww = np.arange(dst_h), np.arange(dst_w)dxx, dyy = np.meshgrid(dww, dhh)grid_x, grid_y = dxx, dyypoints = np.dstack((tx, ty))# print(points.shape, image.shape, grid_x.shape)out = griddata(points.reshape(-1, 2), image.reshape(-1, 3), (grid_x, grid_y), method='linear')out[np.isnan(out)] = 0return out

逆变换代码：

def warp_affine(image, rot_mat, dst_h, dst_w):M = rot_mat.reshape([2, 3])hs, ws, cs = image.shapehh, ww = np.arange(dst_h), np.arange(dst_w)xx, yy = np.meshgrid(ww, hh)sx, sy = (xx + 0.5) * (ws / ws) - 0.5, (yy + 0.5) * (hs / hs) - 0.5 # 不缩放图像。# sx, sy = (xx + 0.5) * (ws / dst_w) - 0.5, (yy + 0.5) * (hs / dst_h) - 0.5 # 缩放图像tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2], M[1, 0] * sx + M[1, 1] * sy + M[1, 2]# tx = np.sum(M[0, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)# ty = np.sum(M[1, :].reshape([1, 1, 3]) * np.dstack((sx, sy, np.ones_like(sx))), axis=-1)mask = ((tx < 0) + (ty < 0) + (tx > ws - 1) + (ty > hs - 1)) > 0# print(mask.shape, mask.dtype, np.sum(mask))out = interp_linear(image, tx, ty)out[mask] = 0return out

也可以求解转换矩阵的逆后，再正变换，结果相同。

其中用到重查找函数：根据tx,ty坐标位置，获取值
和cv2.remap函数相同。

def interp_linear(image, tx, ty):'''类似 cv2.remap 函数:param image: h,w,c image  np.float:param tx:  dst_h * dst_w, float , 目标位置x方向:param ty:  dst_h * dst_w, float , 目标位置y方向:return:'''h, w, c = image.shapehv, wv = ty, txhh = np.floor(hv).astype(np.int32)ww = np.floor(wv).astype(np.int32)u = hv - hhv = wv - ww# special caseu[hh < 0] = 0hh[hh < 0] = 0u[hh >= h - 1] = 1.0hh[hh >= h - 1] = h - 2v[ww < 0] = 0ww[ww < 0] = 0v[ww >= w - 1] = 1.0ww[ww >= w - 1] = w - 2# v = v.reshape(-1)w00 = (1-u)*(1-v)w01 = u * (1-v)w10 = (1-u) * vw11 = u*vout = w00[..., None] * image[hh, ww] + w10[..., None]  * image[hh, ww + 1] + w01[..., None]  * image[(hh + 1), ww] + w11[..., None]  * image[hh + 1, ww + 1]return out

2. warp_perspective

warpPerspective 和 warpAffine 是类似的。
但是warpPerspective的转换矩阵是3*3的透视变换矩阵，经过变换后平行线可能不在平行

一个逆变换 和 两个正变换的代码如下：

# 逆变换函数
def warp_perspective(image, pers_mat, dst_h, dst_w):M = pers_mat.reshape([3, 3])hs, ws, cs = image.shapehh, ww = np.arange(dst_h), np.arange(dst_w)xx, yy = np.meshgrid(ww, hh)sx, sy = (xx + 0.5) * (ws / ws) - 0.5, (yy + 0.5)* (hs / hs) - 0.5# sx, sy = (xx + 0.5) * (ws / dst_w) - 0.5, (yy + 0.5) * (hs / dst_h) - 0.5  # 缩放图像t = M[2, 0] * sx + M[2, 1] * sy + M[2, 2]tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2] , M[1, 0] * sx + M[1, 1] * sy + M[1, 2]tx, ty = tx / t, ty / t# out = np.zeros_like(image)mask = ((tx < 0 ) + (ty < 0) + (tx > ws - 1) + (ty > hs - 1)) > 0print(mask.shape, mask.dtype, np.sum(mask))# out = interp_linear(image, tx, ty)out = cv2.remap(image, tx.astype(np.float32), ty.astype(np.float32), interpolation=cv2.INTER_LINEAR)out[mask] = 0return out
# 正变化函数
def warp_perspective_forward(image, pers_mat, dst_h, dst_w):M = pers_mat.reshape([3, 3])hs, ws, cs = image.shapehh, ww = np.arange(hs), np.arange(ws)xx, yy = np.meshgrid(ww, hh)sx, sy = xx, yy  # 不缩放图像t = M[2, 0] * sx + M[2, 1] * sy + M[2, 2]tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2] , M[1, 0] * sx + M[1, 1] * sy + M[1, 2]tx, ty = tx / t, ty / t# interpdhh, dww = np.arange(dst_h), np.arange(dst_w)dxx, dyy = np.meshgrid(dww, dhh)grid_x, grid_y = dxx, dyypoints = np.dstack((tx, ty))# print(points.shape, image.shape, grid_x.shape)out = griddata(points.reshape(-1, 2), image.reshape(-1, 3), (grid_x, grid_y), method='linear')out[np.isnan(out)] = 0return out# 正变换函数：这里利用np.linalg.inv 求逆矩阵，然后按照warp_perspective的方式进行
def warp_perspective_forward2(image, pers_mat, dst_h, dst_w):M = pers_mat.reshape([3, 3])M_inv = np.linalg.inv(M)M = M_invhs, ws, cs = image.shapehh, ww = np.arange(dst_h), np.arange(dst_w)xx, yy = np.meshgrid(ww, hh)sx, sy = (xx + 0.5) * (ws / ws) - 0.5, (yy + 0.5) * (hs / hs) - 0.5# sx, sy = (xx + 0.5) * (ws / dst_w) - 0.5, (yy + 0.5) * (hs / dst_h) - 0.5  # 缩放图像t = M[2, 0] * sx + M[2, 1] * sy + M[2, 2]tx, ty = M[0, 0] * sx + M[0, 1] * sy + M[0, 2], M[1, 0] * sx + M[1, 1] * sy + M[1, 2]tx, ty = tx / t, ty / t# out = np.zeros_like(image)mask = ((tx < 0) + (ty < 0) + (tx > ws - 1) + (ty > hs - 1)) > 0print(mask.shape, mask.dtype, np.sum(mask))# out = interp_linear(image, tx, ty)out = cv2.remap(image, tx.astype(np.float32), ty.astype(np.float32), interpolation=cv2.INTER_LINEAR)out[mask] = 0return out

3， 实验

验证以上代码和opencv中的一致性

import cv2
import numpy as np
from matplotlib import pyplot as plt
from scipy.interpolate import griddata
def cal_sobel(img):#分别求X,Y方向的梯度grad_X=cv2.Sobel(img,-1,1,0)grad_Y=cv2.Sobel(img,-1,0,1)#求梯度图像grad=cv2.addWeighted(grad_X,0.5,grad_Y,0.5,0)return grad
if __name__ == "__main__":file1 = r'test.jpg'image1 = cv2.imread(file1) / 255image1 = cv2.resize(image1, (0, 0), fx=0.5, fy=0.5)h, w, c = image1.shapeprint(h, w, c)center = (w // 2, h // 2)angle = -50scale = 0.6rot_mat = cv2.getRotationMatrix2D(center, angle, scale)print(rot_mat)dst_h, dst_w = int(image1.shape[0] * 0.7), int(image1.shape[1]* 0.7)image2 = cv2.warpAffine(image1, rot_mat, (dst_w, dst_h))center = (w // 2, h // 2)angle = 50scale = 1 / 0.6rot_mat2 = cv2.getRotationMatrix2D(center, angle, scale)print(rot_mat2)image3 = warp_affine(image1, rot_mat2, dst_h, dst_w)image4 = warp_affine_forward(image1, rot_mat, dst_h, dst_w)plt.figure()plt.subplot(221)plt.imshow(image1)plt.subplot(222)plt.imshow(image2)plt.subplot(223)plt.imshow(image3)plt.subplot(224)plt.imshow(image4)plt.show()# 根据4个点求透视转换pts1 = np.float32([[56, 65], [368, 52], [28, 387], [389, 390]])pts2 = np.float32([[0, 0], [300, 0], [0, 300], [300, 300]])M = cv2.getPerspectiveTransform(pts1, pts2)image2 = cv2.warpPerspective(image1, M, (dst_w, dst_h), flags=cv2.INTER_LINEAR + cv2.WARP_INVERSE_MAP)image3 = warp_perspective(image1, M, dst_h, dst_w)image4 = cv2.warpPerspective(image1, M, (dst_w, dst_h), flags=cv2.INTER_LINEAR)image5 = warp_perspective_forward(image1, M, dst_h, dst_w)image6 = warp_perspective_forward2(image1, M, dst_h, dst_w)plt.figure()plt.subplot(231)plt.imshow(image1)plt.subplot(232)plt.imshow(image2)plt.subplot(233)plt.imshow(image3)plt.subplot(234)plt.imshow(image4)plt.subplot(235)plt.imshow(image5)plt.subplot(236)plt.imshow(image6)plt.show()

运行上面的代码，实验结果如下：
warp affine实验结果：

warp perspective 实验结果