我必须对两个低分辨率图像进行超分辨率以获得高分辨率图像。
拍摄第2张图像作为基本图像，并对其登记第1张图像。我使用SURF算法进行图像配准。 Delaunay三角剖分是 使用内置的MATLAB delaunay在点上构建 功能。 HR网格的大小是 构造用于预先指定的分辨率增强因子R然后HR算法用于内插像素值 接下来总结了人力资源网格。
人力资源算法步骤： 1.构建Delaunay三角剖分 在一组散乱的顶点上 不规则采样的光栅 LR帧。
估算每个梯度向量 通过使用叉积法计算相邻向量的单位法向量，求出三角剖分的顶点。每个三角形的单位法向量乘以其面积的乘积除以所有相邻三角形的面积之和得到顶点法线。
近似每个三角形补丁 连续三角测量， 可能，一个连续可微的 表面，受到一些平滑约束。 二元多项式或样条 可能是解释的近似值 下方。
在代码中提到了使用的二元多项式，使用三角形的每个顶点处的像素值和x和y方向上的对应梯度我计算了与每个三角形相关联的九个常数然后定义了高分辨率网格，计算了像素使用计算的常数
计算每个点的值我正在附加我的代码，我面临的问题是我只是得到一个灰色图像作为输出HR图像，因为我计算的常数有负值导致负像素值
我用代码实现的另一个问题是梯度估计我得到了很多'NaN'作为梯度计算的结果。
如果有人可以花一些时间来帮助我
close all
clear all
K = 2;
P1 = imread('C:\Users\Javeria Farooq\Desktop\project images\a.pgm');
%reads the image to be registered
P2 = imread('C:\Users\Javeria Farooq\Desktop\project images\b.pgm');
%reads the base image
image1_gray = makelr(P1, 1, 100, 1/2);
%image1_gray = P1;
% makes lr image of first
image2_gray= makelr(P2, 1, 100, 1/2);
%image2_gray= P2;
%makes lr image of second
figure(1),imshow(image1_gray)
axis on;
grid on;
title('Unregistered image');
figure(2),imshow(image2_gray)
axis on;
grid on;
title('Base image ');
impixelinfo
% both image displayed with pixel info
hold on
points_image1= detectSURFFeatures(image1_gray, 'NumScaleLevels', 100, 'NumOctaves', 12, 'MetricThreshold', 500 );
%detects surf features of first image
points_image2 = detectSURFFeatures(image2_gray, 'NumScaleLevels', 100, 'NumOctaves', 12, 'MetricThreshold', 500 );
%detects surf features of second image
[features_image1, validPoints_image1] = extractFeatures(image1_gray, points_image1);
[features_image2, validPoints_image2] = extractFeatures(image2_gray, points_image2);
%extracts features of both images
indexPairs = matchFeatures(features_image1, features_image2, 'Prenormalized', true) ;
% get matching points
matched_pts1 = validPoints_image1(indexPairs(:, 1));
matched_pts2 = validPoints_image2(indexPairs(:, 2));
figure; showMatchedFeatures(image1_gray,image2_gray,matched_pts1,matched_pts2,'montage');
%matched features of both images are displayed
legend('matched points 1','matched points 2');
% Compute the transformation matrix
tform = estimateGeometricTransform(matched_pts1,matched_pts2,'projective')
%calculate transformation matrix using projective transform
T=tform.T;
r=[];
A=[];
l=1
[N1 N2]=size(image2_gray)
registeredPts = zeros(N1*N2,2);
% s= zeros(N1*N2,2);
pixelVals = zeros(N1*N2,1);
[N1 N2]=size(image2_gray)
for row = 1:N1
for col = 1:N2
pixNum = (row-1)*N2 + col;
pixelVals(pixNum,1) = image2_gray(row,col);
registeredPts(pixNum,:) = [col,row];
end
end
[r]=transformPointsForward(tform,registeredPts);
%coordinates of base image
image2_gray=double(image2_gray);
R=2;
r1=r(:,1);
r2=r(:,2);
for row = 1:N1
for col = 1:N2
pixNum = N1*N2 + (row-1)*N2 + col;
pixelVals(pixNum,1) = image1_gray(row,col);
registeredPts(pixNum,:) = [r1(row,1),r2(row,1)];
end
end
% all pixel values are saved in pixelVals
%all registered points are saved first base image then unregistered image
%delaunay triangulation of all coordinates passing x and y coordinates from registered Points
tri = delaunay(registeredPts(:,1),registeredPts(:,2));
figure(3), triplot(tri,registeredPts(:,1),registeredPts(:,2))
save tri
% Estimate the gradient vector at each vertex
[totalTris,three] = size(tri);
[totalPoints,two] = size(registeredPts);
vGradientVecs = zeros(totalPoints,2);
triAreas = zeros(totalTris,1);
triUnitNormals = zeros(totalTris,3);
vUnitNormals = zeros(totalPoints,3);
% 1. Find the unit normal vectors and the areas of all triangles,
% then find the product of these two numbers for each triangle
for triNum = 1:totalTris
v = tri(triNum,:);
% 3D triangle points: x,y,pixel
b=pixelVals(v);
b=b(:);
p = [registeredPts(v,:),b];
% triangle area
triAreas(triNum) = polyarea([p(:,1)],[p(:,2)]);
% directional vectors representing the surface of the plane
d1 = p(2,:)-p(1,:);
d2 = p(3,:)-p(1,:);
% cross product of these vectors
crossp = cross(d1,d2);
% If u = [u1 u2 u3] and v = [v1 v2 v3], we know that the product w is defined as w = [(u2v3 – u3v2) (u3v1 - u1v3) (u1v2 - u2v1)]
% normalized cross product = unit normal vector for the triangle
dist = sqrt(sum(crossp.^2));
triUnitNormals(triNum,:) = crossp./dist;
end
% %2. %Estimate the unit normal vector at each vertex
% a. Find the triangle patches that neighbor the vertex
% b. Find the unit normal vectors of these regions
% c. Multiply each of these vectors by the area of the
% associated region, then sum these numbers and divide
% by the total area of all the regions
for pointNum = 1:totalPoints
[neighbors,x] = find(tri==pointNum);
areas = triAreas(neighbors);
areas3 = [areas,areas,areas];
triNormsSum = sum(triUnitNormals(neighbors,:).*areas3);
triAreasSum = sum(areas);
vUnormalized = triNormsSum./triAreasSum;
vUnitNormals(pointNum,:) = ...
vUnormalized./sqrt(sum(vUnormalized.^2));
if( triAreasSum == 0 )
triAreasSum = 0.0001;
vUnormalized = triNormsSum./triAreasSum;
% re-normalize
vUnitNormals(pointNum,:) = ...
vUnormalized./sqrt(sum(vUnormalized.^2));
end
% 3. Find the gradients along the x and y directions for each vertex
% vertex's unit normal: n = [nx,ny,nz]
% x-direction gradient: dz/dx = -nx/nz
% y-direction gradient: dz/dy = -ny/nz
%
for pointNum = 1:totalPoints
nz = vUnitNormals(pointNum,3);
if( nz == 0 )
nz = 0.0001;
end
vGradientVecs(pointNum,1) = -vUnitNormals(pointNum,1)./nz;
vGradientVecs(pointNum,2) = -vUnitNormals(pointNum,2)./nz;
% end
end
end
% 1. Find the 3 equations for each vertex, and
% place them in c_equations matrix;
% c_equations = [A for vertex 1;
% A for vertex 2; ...
% A for vertex totalPoints]
% c(point,row,:) gives one row from an A matrix
Btotal = zeros(3,totalPoints);
c_equations = zeros(3*totalPoints,3,9);
for pointNum = 1:totalPoints
% % B = [pixVal; x gradient; y gradient] at this vertex
z = pixelVals(pointNum);
B = [z; vGradientVecs(pointNum,1); vGradientVecs(pointNum,2)];
%
% % Compile all B matrices into a vector
Btotal(:,pointNum) = B;
% B = Ac to calculate c which is c=[c1 c2 .....c9]' take invA and
% multiply by B
x = registeredPts(pointNum,1);
y = registeredPts(pointNum,2);
A = [1 x y x^2 y^2 x^3 (x^2)*y x*(y^2) y^3; ...
0 1 0 2*x 0 3*(x^2) 2*x*y y^2 0; ...
0 0 1 0 2*y 0 x^2 2*x*y 3*(y^2)];
% Compile all A matrices into a vector
c_equations(pointNum,1,:) = A(1,:);
c_equations(pointNum,2,:) = A(2,:);
c_equations(pointNum,3,:) = A(3,:);
end
% 2. Find the c values for each triangle patch
c = zeros(totalTris,9);
c9 = zeros(9,9);
for triNum = 1:totalTris
p1 = tri(triNum,1);
p2 = tri(triNum,2);
p3 = tri(triNum,3);
B9 = [Btotal(:,p1); Btotal(:,p2); Btotal(:,p3)];
c9 = [(c_equations(p1,1,:)); (c_equations(p1,2,:)); (c_equations(p1,3,:)); ...
(c_equations(p2,1,:)); (c_equations(p2,2,:));( c_equations(p2,3,:)); ...
(c_equations(p3,1,:)); (c_equations(p3,2,:));( c_equations(p3,3,:))];
C9=squeeze(c9);
c(triNum,:) = pinv(C9)*B9; %linsolve(c9,B9);
end
% xc = findBPolyCoefficients1(tri,registeredPts,pixelVals,vGradientVecs);
% save xc
% % 2. For each point on the HR grid, find the associated triangle patch,
% % extract its c values, and use these values as the coefficients
% % in a bivariate polynomial to calculate the HR pixel value at
% % each grid point (x,y)
[N1,N2]=size(image1_gray);
[totalTris,three] = size(tri);
M = N1*R-1;
N = N2*R-1;
HRimage = zeros(M,N);
HRtriangles = zeros(M,N);
[X,Y] = meshgrid(1:1/R:N2,1:1/R:N1);
% Check all the triangles in order noting in which triangle each HR
% grid point occurs.
for triNum = 1:totalTris
pts = registeredPts(tri(triNum,:),:);
IN = inpolygon(X,Y,pts(:,1),pts(:,2)); % NxM
HRtriangles(ind2sub(size(IN),find(IN==1))) = triNum;
end
% there is a problem with this part of code ,
for y = 1:M % row
for x = 1:N % col
% For testing, average the pixels from the vertices of the
% triangle the HR point is in.
% pix = pixelVals(tri(HRtriangles(x,y),:));
% HRimage(x,y) = (pix(1) + pix(2) + pix(3))/3;
% Extract appropriate set of 9 c values
HRptC = c(HRtriangles(x,y),:);
% Bivariate polynomial
HRimage(x,y) = sum(HRptC.*[1,x,y,x^2,y^2,x^3,(x^2)*y,x*(y^2),y^3]);
g(x,y)=HRimage(x,y);
%changd xy with yx
end
end
% HRimage = estimateGridVals1(tri,registeredPts,R,N1,N2,pixelVals);
% %Estimating Grid values at each patch
% %save HRimage
g(g(:,:)<0)=0;
figure(8),imshow(g,[]);