我在Matlab下从2D图像重建3D场景有些困难。 我想创建一个删除透视的场景的顶视图，换句话说，实现逆透视映射。
让我们假设我们知道相机的位置，方向及其参数。此外，我们认为所有捕获点都位于同一平面XY上。 然后，很容易证明图像中（u，v）位置的像素将移动到3D空间中的坐标（X，Y，0）：
X=-((u*P(3,4)-P(1,4))*(v*P(3,1)-P(2,1)) + (v*P(3,4)-P(2,4))*(P(1,1)-u*P(3,1)))/((u*P(3,2)-P(1,2))*(v*P(3,1)-P(2,1)) + (v*P(3,2)-P(2,2))*(P(1,1)-u*P(3,1)));
Y=(X*(u*P(3,2)-P(1,2)) + (u*P(3,4)-P(1,4)))/(P(1,1)-u*P(3,1));
P是投影矩阵，使得：P = [KR KT]，其中K，R和T分别是内禀，旋转和平移矩阵。
一旦计算了每个像素的所有3D位置，我想用原始像素的颜色信息显示XY平面，就像它是2D图像一样。
然而，像素（u，v）可以在3D空间中映射到非整数位置，这意味着我得到非常规散点图，每个（X，Y）点包含颜色信息。 我试图将XY平面划分为小窗口，然后计算每个方块中所有点的平均颜色，但速度非常慢。
请在下面找到我的代码。 一些帮助将不胜感激。
提前谢谢你， PM
% This program aims to convert a 2D image into a 3D scenario. Let's assume that
% all the points in the image lie on the same plan in the 3D space.
% Program:
% 1-Generate the 3D scenario with 4 squares from diferrent colors
% 2-Take a picture of these squares by projecting the scene into an image 2D space
% 3-Reconstruct the 3D scene from the 2D picture
% Author: Pierre-Marie Damon
clear all; close all; clc;
%% 4 SQUARES DEFINITION
c=10;
sq1_3D = [ 0 0 0;
0 c 0;
c c 0;
c 0 0];
sq2_3D = [ 0 0 0;
c 0 0;
c -c 0;
0 -c 0];
sq3_3D = [ 0 0 0;
0 -c 0;
-c -c 0;
-c 0 0];
sq4_3D = [ 0 0 0;
-c 0 0;
-c c 0;
0 c 0];
SQ_3D = [sq1_3D;
sq2_3D;
sq3_3D;
sq4_3D];
%% CAMERA DEFINITION
% Image resolution:
image_size = [640,480];
% Intrinsic matrix:
fx=150; fy=150; % fx, fy: focal lengths in pixel
x0=image_size(1)/2; y0=image_size(2)/2; % x0, y0: optical center projection coordinates in the 2D cxamera space
K = [fx 0 x0 ;
0 fy y0 ;
0 0 1 ];
% 3D camera orientation:
Rot_cam = [ 0 0 1;
-1 0 0;
0 -1 0]';
% 3D camera rotations:
yaw = -20*pi/180;
roll = -0*pi/180;
pitch = -20*pi/180;
% 3D camera position:
O_Rcam = [-20;0;10];
h_cam = O_Rcam(3); % camera height
% Projection & transformation matrices
R = rotationVectorToMatrix([pitch,yaw,roll])*Rot_cam; % Rotation matrix
T = -R*O_Rcam; % Translation matrix
P = [K*R K*T; zeros(1,3) 1]; %Projection Matrix
%% PROJECTION FROM 3D TO THE 2D IMAGE
SQ_2D = (P*[SQ_3D ones(size(SQ_3D,1),1)]')'; % homogeneous coordinates
SQ_2D = SQ_2D(:,1:2)./repmat(SQ_2D(:,3),1,2); % Normalization
% Square splits:
sq1_2D = SQ_2D(1:4,:);
sq2_2D = SQ_2D(5:8,:);
sq3_2D = SQ_2D(9:12,:);
sq4_2D = SQ_2D(13:16,:);
%% PLOT THE 3D SCENARIO
figure('units','normalized','outerposition',[0 0 1 1]);
f1=subplot(1,2,1);hold on; grid on; view(50, 30); axis equal;
xlabel('X');ylabel('Y');zlabel('Z'); title('3D Scene');
% Plot the camera
cam = plotCamera('Location',O_Rcam,'Orientation',R,'Size',1,'AxesVisible',0);
% Plot the squares
patch([sq1_3D(:,1)],[sq1_3D(:,2)],'r','EdgeColor','k');
patch([sq2_3D(:,1)],[sq2_3D(:,2)],'g','EdgeColor','k');
patch([sq3_3D(:,1)],[sq3_3D(:,2)],'b','EdgeColor','k');
patch([sq4_3D(:,1)],[sq4_3D(:,2)],'m','EdgeColor','k');
%% PLOT THE 2D IMAGE
f2=subplot(1,2,2); hold on; grid on; axis equal; set(gca,'YDir','Reverse'); title('2D Image'); axis off;
xlim([0 image_size(1)]); ylim([0 image_size(2)]);
% plot the projected squares
patch ([sq1_2D(:,1)],[sq1_2D(:,2)],'r','EdgeColor','none');
patch ([sq2_2D(:,1)],[sq2_2D(:,2)],'g','EdgeColor','none');
patch ([sq3_2D(:,1)],[sq3_2D(:,2)],'b','EdgeColor','none');
patch ([sq4_2D(:,1)],[sq4_2D(:,2)],'m','EdgeColor','none');
% Plot the image borders
plot([0 image_size(1)],[0 0],'k','linewidth',3);
plot([image_size(1) image_size(1)],[0 image_size(2)],'k','linewidth',3);
plot([0 image_size(1)],[image_size(2) image_size(2)],'k','linewidth',3);
plot([0 0],[0 image_size(2)],'k','linewidth',3);
%% GENERATE A JPG IMAGE
figure; hold on; grid on; set(gca,'YDir','Reverse'); axis off;
hFig = gcf; hAx = gca; % get the figure and axes handles
set(hFig,'units','normalized','outerposition',[0 0 1 1]); % set the figure to full screen
set(hAx,'Unit','normalized','Position',[0 0 1 1]); % set the axes to full screen
set(hFig,'menubar','none'); % hide the toolbar
set(hFig,'NumberTitle','off'); % to hide the title
xlim([0 image_size(1)]); ylim([0 image_size(2)]);
% Plot the squares
patch ([sq1_2D(:,1)],[sq1_2D(:,2)],'r','EdgeColor','none');
patch ([sq2_2D(:,1)],[sq2_2D(:,2)],'g','EdgeColor','none');
patch ([sq3_2D(:,1)],[sq3_2D(:,2)],'b','EdgeColor','none');
patch ([sq4_2D(:,1)],[sq4_2D(:,2)],'m','EdgeColor','none');
% Create the image
set(gcf,'PaperUnits','inches','PaperPosition',[0 0 image_size(1)/100 image_size(2)/100])
print -djpeg Image.jpg -r100
save('ImageParam.mat', 'K','R','T','P','O_Rcam' )
%% 3D RECONSTRUCTION FROM 2D IMAGE
clear all;
close all;
clc;
load('ImageParam');
I=imread('Image.jpg');
I1 = rgb2gray(I);
figure;imshow(I1);impixelinfo;
I2 = zeros(size(I1));
k=1; i=1; j=1;
tic
for y=size(I2,1):-1:1
for x=1:size(I2,2)
% The formula below comes from the projection equations of
% the camera and the additional constraint that all the points lie on the XY
% plane
X(k)=-((x*P(3,4)-P(1,4))*(y*P(3,1)-P(2,1)) + (y*P(3,4)-P(2,4))*(P(1,1)-x*P(3,1)))/((x*P(3,2)-P(1,2))*(y*P(3,1)-P(2,1)) + (y*P(3,2)-P(2,2))*(P(1,1)-x*P(3,1)));
Y(k)=(X(k)*(x*P(3,2)-P(1,2)) + (x*P(3,4)-P(1,4)))/(P(1,1)-x*P(3,1));
Z(k)=0;
C(k)=I1(y,x); % Color (gray intensity) information
k=k+1;
end
end
toc
figure;hold on;axis equal;
plot(X,Y,'.');
grid on;