鱼眼相机去畸变（图像拉直/展开/矫正）算法及实战总结_鱼眼矫正算法-CSDN博客

安宇雨 - 随手采集
2024-02-29 14:38:37
随手采集
0000-未整理-等待研究

本文介绍两种方法
1、经纬度矫正法
2、棋盘格矫正法

一、经纬度矫正法

1、算法说明

经纬度矫正法，可以把鱼眼图想象成半个地球，然后将地球展开成地图，经纬度矫正法主要是利用几何原理，对图像进行展开矫正。

经过P点的入射光线没有透镜的话，本应交于相机成像平面的e点。然而，经过鱼眼相机的折射，光线会交于相机成像平面的d点，就产生了畸变，因此畸变图像整体上呈现出像素朝图像中心点聚集的态势。
而去畸变，就是将折射到d点的点，重新映射回到e点，因此去畸变之后的图像与原始的鱼眼图像相比，仿佛是把向心聚集的像素又重新向四周铺展开来。
详细的推导流程及公式见地址：AVM环视系统——鱼眼相机去畸变算法 - 知乎

2、代码

import mathfrom PIL import Image  im = Image.open("/Users/Fisheye_photo-600x600.jpg")im.show() width, high = im.sizesqrt_len = min(width, high)im = im.transform((sqrt_len, sqrt_len),                    Image.EXTENT,                    ((width-sqrt_len)/2, (high-sqrt_len)/2,                     sqrt_len+(width-sqrt_len)/2, sqrt_len+(high-sqrt_len)/2)                    )width = high = sqrt_len idata = im.getdata()odata = [] alpha = math.pi/2 out_high = round(high * math.tan(alpha/2))out_width = round(width * math.tan(alpha/2))out_radius = round(high * math.tan(alpha/2))out_center_x = out_width / 2out_center_y = out_high / 2 out_bl_x = 0out_br_x = out_width - 1out_bt_y = 0out_bb_y = out_high - 1 out_bl_cx = out_bl_x - out_center_xout_br_cx = out_br_x - out_center_xout_bt_cy = out_bt_y - out_center_yout_bb_cy = out_bb_y - out_center_y src_radius = round(high * math.sin(alpha/2))src_center_x = width / 2src_center_y = high / 2 for i in range(0, high * width):    ox = math.floor(i / out_width)    oy = i % out_high        cx = ox - out_center_x;    cy = oy - out_center_y;        out_distance = round(math.sqrt(pow(cx, 2) + pow(cy, 2)))    theta = math.atan2(cy, cx)    if (-math.pi/4 <= theta <= math.pi/4):        bx = out_radius * math.cos(math.pi/4)        by = bx * math.tan(theta)    elif (math.pi/4 <= theta <= math.pi*3/4):        by = out_radius * math.sin(math.pi/4)        bx = by / math.tan(theta)    elif (-math.pi*3/4 <= theta <= -math.pi/4):        by = out_radius * math.sin(-math.pi/4)        bx = by / math.tan(theta)    else:        bx = out_radius * math.cos(-math.pi*3/4)        by = bx * math.tan(theta)                bdy_distance = round(math.sqrt(pow(cx, 2) + pow(cy, 2)))    src_distance = src_radius * bdy_distance / out_radius                src_x = round(src_center_x + math.cos(theta) * src_distance)    src_y = round(src_center_y + math.sin(theta) * src_distance)        src_idx = src_x*width + src_y        if(0 < src_idx < high*width):        odata.append(idata[src_idx])    else:        odata.append((0,0,0))      om = Image.new("RGB", (high, width))om.putdata(odata)om.show()

3、代码及图片地址：GitHub - duducosmos/defisheye: Fast Corrects for fisheye distortion in an image.

二、棋盘格矫正方法

1、算法说明

利用棋盘格进行标定，然后计算鱼眼镜头的畸变系数以及内参， opencv中自带有fisheye模块，可以直接根据棋盘格标定结果，采用cv2.fisheye.calibrate计算畸变系数以及内参，然后使用cv2.fisheye.initUndistortRectifyMap函数计算映射矩阵，最后根据映射矩阵，使用cv2.remap进行矫正。

2、代码

import cv2import numpy as npimport mathimport time # 鱼眼有效区域截取def cut(img):    img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)    (_, thresh) = cv2.threshold(img_gray, 20, 255, cv2.THRESH_BINARY)    contours, hierarchy = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)    cnts = sorted(contours, key=cv2.contourArea, reverse=True)[0]    x,y,w,h = cv2.boundingRect(cnts)    r = max(w/ 2, h/ 2)    # 提取有效区域    img_valid = img[y:y+h, x:x+w]    return img_valid, int(r) # 鱼眼矫正def undistort(src,r):    # r： 半径， R: 直径    R = 2*r    # Pi: 圆周率    Pi = np.pi    # 存储映射结果    dst = np.zeros((R, R, 3))    src_h, src_w, _ = src.shape    # 圆心    x0, y0 = src_w//2, src_h//2     for dst_y in range(0, R):         theta =  Pi - (Pi/R)*dst_y        temp_theta = math.tan(theta)**2         for dst_x in range(0, R):            # 取坐标点 p[i][j]            # 计算 sita 和 fi             phi = Pi - (Pi/R)*dst_x            temp_phi = math.tan(phi)**2             tempu = r/(temp_phi+ 1 + temp_phi/temp_theta)**0.5            tempv = r/(temp_theta + 1 + temp_theta/temp_phi)**0.5             if (phi < Pi/2):                u = x0 + tempu            else:                u = x0 - tempu             if (theta < Pi/2):                v = y0 + tempv            else:                v = y0 - tempv             if (u>=0 and v>=0 and u+0.5<src_w and v+0.5<src_h):                dst[dst_y, dst_x, :] = src[int(v+0.5)][int(u+0.5)]                 # 计算在源图上四个近邻点的位置                # src_x, src_y = u, v                # src_x_0 = int(src_x)                # src_y_0 = int(src_y)                # src_x_1 = min(src_x_0 + 1, src_w - 1)                # src_y_1 = min(src_y_0 + 1, src_h - 1)                #                # value0 = (src_x_1 - src_x) * src[src_y_0, src_x_0, :] + (src_x - src_x_0) * src[src_y_0, src_x_1, :]                # value1 = (src_x_1 - src_x) * src[src_y_1, src_x_0, :] + (src_x - src_x_0) * src[src_y_1, src_x_1, :]                # dst[dst_y, dst_x, :] = ((src_y_1 - src_y) * value0 + (src_y - src_y_0) * value1 + 0.5).astype('uint8')     return dst if __name__ == "__main__":    t = time.perf_counter()    frame = cv2.imread('../imgs/pig.jpg')    cut_img,R = cut(frame)    result_img = undistort(cut_img,R)    cv2.imwrite('../imgs/pig_nearest.jpg',result_img)    print(time.perf_counter()-t)

效果图