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undistortImageForDivisionModel.m
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undistortImageForDivisionModel.m
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function [J,camIntrinsic,mapX,mapY,newOrigin] = undistortImageForDivisionModel(I,lambda,x_center,y_center,options)
% Brief: 使用除法模型distortion division model已知的三个参数(lambda,x_center,y_center)对畸变图像I进行去畸变，适用略微和严重畸变类型。
% Details:
% 对畸变图像I使用distortion division model中包含一阶畸变系数lambda和畸变
% 中心x_center,y_center进行去畸变，得对应camIntrinsic的无畸变图J。
%
% Syntax:
% [J,camIntrinsic,mapX,mapY] = undistortImageForDivisionModel(I,lambda,x_center,y_center)
%
% Inputs:
% I - [m,n] size,any image type,畸变图像
% lambda - [1,1] size,[double] type,畸变系数
% x_center - [1,1] size,[double] type,畸变中心横坐标
% y_center - [1,1] size,[double] type,畸变中心纵坐标
% options.OutputView和options.OutputViewROI必须仅有一个参数输入，其中
% OutputViewROI参数输入形如[x,y,width,height],前2个值代表输出图像undistortImg
% 的(1,1)坐标在原图像I上几何/畸变中心为原点的像素坐标。
%
% Outputs:
% J - [M,N] size,any image type,去畸变图像
% camIntrinsic - [1,1] size,[cameraIntrinsics] type,build-in cameraIntrinsics (https://ww2.mathworks.cn/help/vision/ref/cameraintrinsics.html)
% mapX - [M,N] size,[double] type,映射X坐标
% mapY - [M,N] size,[double] type,映射Y坐标
% newOrigin - [1,2] size, [double] type,代表输出图像undistortImg的(1,1)坐
% 标在原图像I上几何/畸变中心为原点的像素坐标。
%
% References:
% https://www.wikiwand.com/en/Distortion_(optics)
%
% Example:
% None
%
% See also: None
% Release Note:
% 2023.12.5
% 1、valid模式和full模式只适用于入射角小于90度的情况，如果有大于90度
% 况，则应当指定NewOrigin输入参数。
% Author: cuixingxing
% Email: cuixingxing150@gmail.com
% Created: 13-Jun-2023 08:46:34
% Version history revision notes:
% None
% Implementation In Matlab R2023b
% Copyright © 2023 TheMatrix.All Rights Reserved.
%
arguments
I
lambda (1,1) double
x_center (1,1) double
y_center (1,1) double
options.OutputView (1,:) char {mustBeMember(options.OutputView,["full","valid","same"])}
options.OutputViewROI (1,4) double
end
flag1 = isfield(options,"OutputView");
flag2 = isfield(options,"OutputViewROI");
if (flag1&&flag2)|| (~flag1&&~flag2)
error("options:OutputView and NewOrigin must only occur once");
end
[H,W,~] = size(I);
% recovery undistorted image,参考维基百科Distortion_(optics)的reverse-distortion公式
if flag1
if strcmpi(options.OutputView,"same")
newOrigin = -[x_center,y_center];
[x_u,y_u] = meshgrid(1:W,1:H);
elseif strcmpi(options.OutputView,"full")
xEdges = [1:W,W*ones(1,H),1:W,ones(1,H)];
yEdges = [ones(1,W),1:H,H*ones(1,W),1:H];
conersEdgePts = [xEdges(:),yEdges(:)];
x_d = conersEdgePts(:,1);
y_d = conersEdgePts(:,2);
r = sqrt((x_d-x_center).^2+(y_d-y_center).^2);
x_u = x_center+(x_d-x_center)./(1+lambda*r.^2);
y_u = y_center+(y_d-y_center)./(1+lambda*r.^2);
[minA,maxA] = bounds([x_u,y_u]);
newOrigin = [minA(1),minA(2)]-[x_center,y_center];
[x_u,y_u] = meshgrid(minA(1):maxA(1),minA(2):maxA(2));
else
% 参考来源：本项目中的undistortFisheyeFromTable/undistortFisheyeImgFromTable.m实现
% 求不规则四条曲线边轮廓的最大内接矩形
xEdges = [1:W,W*ones(1,H),W:-1:1,ones(1,H)]';% top,right,down,left edge order
yEdges = [ones(1,W),1:H,H*ones(1,W),H:-1:1]';
conersEdgePts = [xEdges(:),yEdges(:)];
x_d = conersEdgePts(:,1);
y_d = conersEdgePts(:,2);
r = sqrt((x_d-x_center).^2+(y_d-y_center).^2);
x_u = x_center+(x_d-x_center)./(1+lambda*r.^2);
y_u = y_center+(y_d-y_center)./(1+lambda*r.^2);
undistortPts = [x_u,y_u];
topEdgePoints = undistortPts(1:W,:);
rightEdgePoints = undistortPts(W+1:W+H,:);
bottomEdgePoints = undistortPts(W+H+1:2*W+H,:);
leftEdgePoints = undistortPts(2*W+H+1:end,:);
% [xmin,xmax,ymin,ymax] = largetstInscribedAxisRectangle(topEdgePoints,...
% rightEdgePoints,bottomEdgePoints,leftEdgePoints);
xmin = max(leftEdgePoints(:,1));
xmax = min(rightEdgePoints(:,1));
ymin = max(topEdgePoints(:,2));
ymax = min(bottomEdgePoints(:,2));
assert((xmin<xmax)&&(ymin<ymax),"Invalid parameter lambda, too small or too large a value");
newOrigin = [xmin,ymin]-[x_center,y_center];
[x_u,y_u] = meshgrid(xmin:xmax,ymin:ymax);
end
else
x0 = options.OutputViewROI(1);
y0 = options.OutputViewROI(2);
width = options.OutputViewROI(3);
height = options.OutputViewROI(4);
xx = (x0:x0+width-1)+x_center;
yy = (y0:y0+height-1)+y_center;
newOrigin = [x0,y0];
[x_u,y_u] = meshgrid(xx,yy);
end
r_u = sqrt((x_u-x_center).^2+(y_u-y_center).^2);
x_d = x_center+(x_u-x_center).*(1-sqrt(1-4*lambda.*r_u.^2))./(2*lambda.*r_u.^2);
y_d = y_center+(y_u-y_center).*(1-sqrt(1-4*lambda.*r_u.^2))./(2*lambda.*r_u.^2);
mapX = fillmissing(x_d,"constant",1);
mapY = fillmissing(y_d,"constant",1);
J = images.internal.interp2d(I,mapX,mapY,...
"linear",0, false);
% 以下等价无畸变图像内参矩阵,其计算参考官方undistortFisheyeImage函数源码
imageSize = size(J,[1,2]);
f = min(size(I,[1,2]))/2;
principalPoint = -newOrigin + 0.5;
K = [f,0,principalPoint(1);
0,f,principalPoint(2);
0,0,1];
camIntrinsic = cameraIntrinsics([K(1,1),K(2,2)],principalPoint,imageSize);
end
function mustBeExclusive(options)
flag1 = isfield(options,"OutputView");
flag2 = isfield(options,"NewOrigin");
if (flag1&&flag2)|| (~flag1&&~flag2)
error("options:OutputView and NewOrigin only occur once");
end
end