I have written a code that reads an image and does scaling of 2 units in x-axis direction. Scaling matrix is filled by values that are read from a text file.
Scaling Matrix looks like
2 0 0
0 1 0
0 0 1
Original Image
Transformed Image (Scaling of 2 units in X-direction)
Code
file = importdata('transform_c.txt');
fileData = file.data;
image = imread('mecca06.pgm');
[row, col] = size(image);
scalingMatrix = zeros(3,3);
scalingMatrix(1,1) = fileData(2);
scalingMatrix(1,2) = fileData(3);
scalingMatrix(1,3) = fileData(4);
scalingMatrix(2,1) = fileData(5);
scalingMatrix(2,2) = fileData(6);
scalingMatrix(2,3) = fileData(7);
scalingMatrix(3,1) = fileData(8);
scalingMatrix(3,2) = fileData(9);
scalingMatrix(3,3) = fileData(10);
m1Inverse = inv(scalingMatrix);
outputImage = applyTransformation(image, row, col, m1Inverse);
figure
imshow(outputImage);
function outImage = applyTransformation(image, row, col, m1Inverse)
points = zeros(3,1);
for i=1:row
for j=1:col
points(1,1) = i;
points(2,1) = j;
points(3,1) = 1;
m2 = m1Inverse * points;
x = m2(1,1);
y = m2(2,1);
xlb = floor(x);
ylb = floor(y);
if(xlb <= 0)
xlb = 1;
end
if(xlb > row)
xlb = row;
end
if(ylb <= 0)
ylb = 1;
end
if(ylb > col)
ylb = col;
end
xub = xlb+1;
yub = ylb+1;
if(xub <= 0)
xub = 1;
end
if(xub > row)
xub = row;
end
if(yub <= 0)
yub = 1;
end
if(yub > col)
yub = col;
end
exub = xub-x;
eyub = yub-y;
exlb = x-xlb;
eylb = y-ylb;
outImage(i,j) = (exub*eyub*image(xlb,ylb))+(exlb*eyub*image(xub,ylb))+(exub*eylb*image(xlb,yub))+(exlb*eylb*image(xub,yub));
end
end
end
My question is how can i modify the above code to get uncropped image ?
I want to get following image
Try to see if this code produces the result you need:
img = imread('aSxLS.png');
scale = [
2 0 0
0 1 0
0 0 1
];
tform = maketform('affine',inv(scale));
img_tform = imtransform(img,tform,'bilinear');
figure();
imshow(img);
figure();
imshow(img_tform);
Related
The picture with noise is like this.
Noised picture: Image3.bmp
I was doing image processing in MatLab with some built-in and self-implemented filters.
I have already tried a combination of bilateral, median and gaussian. bilateral and gaussian code are at the end of this post.
img3 = double(imread('Image3.bmp')); % this is the noised image
lena = double(imread('lena_gray.jpg')); % this is the original one
img3_com = bilateral(img3, 3, 2, 80);
img3_com = medfilt2(img3_com, [3 3], 'symmetric');
img3_com = gaussian(img3_com, 3, 0.5);
img3_com = bilateral(double(img3_com), 6, 100, 13);
SNR3_com = snr(img3_com,img3_com - lena); % 17.1107
However, the result is not promising with SNR of only 17.11.
Filtered image: img3_com
The original picture is like this.
Clean original image: lena_gray.jpg
Could you please give me any possible ideas about how to process it? Like what noise generators generated the noised image and what filtering methods or image processing method I can use to deal with it. Appreciate!!!
My bilateral function bilateral.m
function img_new = bilateral(img_gray, window, sigmaS, sigmaI)
imgSize = size(img_gray);
img_new = zeros(imgSize);
for i = 1:imgSize(1)
for j = 1:imgSize(2)
sum = 0;
simiSum = 0;
for a = -window:window
for b = -window:window
x = i + a;
y = j + b;
p = img_gray(i,j);
q = 0;
if x < 1 || y < 1 || x > imgSize(1) || y > imgSize(2)
% q=0;
continue;
else
q = img_gray(x,y);
end
gaussianFilter = exp( - double((a)^2 + (b)^2)/ (2 * sigmaS^2 ) - (double(p-q)^2)/ (2 * sigmaI^2 ));
% gaussianFilter = gaussian((a^2 + b^2)^(1/2), sigma) * gaussian(abs(p-q), sigma);
sum = sum + gaussianFilter * q;
simiSum = simiSum + gaussianFilter;
end
end
img_new(i,j) = sum/simiSum;
end
end
% disp SNR
lena = double(imread('lena_gray.jpg'));
SNR1_4_ = snr(img_new,img_new - lena);
disp(SNR1_4_);
My gaussian implementation gaussian.m
function img_gau = gaussian(img, hsize, sigma)
h = fspecial('gaussian', hsize, sigma);
img_gau = conv2(img,h,'same');
% disp SNR
lena = double(imread('lena_gray.jpg'));
SNR1_4_ = snr(img_gau,img_gau - lena);
disp(SNR1_4_);
I am getting an error when I run this code for disc waves. The code is attached.
The Error is in line 137 and 292. Please help in resolving issue.
function waves
% WAVES Wave equation in one and two space dimensions.
% The two-dimensional domains include a pi-by-pi square, a unit disc,
% a three-quarter circular sector and the L-shaped union of three squares.
% The eigenfunctions of the square are sin(m*x)*sin(n*y). With polar
% coordinates, the eigenfunctions of the disc and the sector involve Bessel
% functions. The eigenfunctions of the L-shaped domain also involve
% Bessel functions and are computed by the MATLAB function membranetx.m.
% 2-D eigenvalues and eigenfunctions
m = 11; % Determines number of grid points
speed = 1;
bvals = [1; 0; 0; 0; 0];
t = 0;
while bvals(5) == 0
% Initialize figure
shg
clf reset
set(gcf,'doublebuffer','on','menubar','none','tag','', ...
'numbertitle','off','name','Waves','colormap',hot(64));
for k= 1:5
b(k) = uicontrol('style','toggle','value',bvals(k), ...
'units','normal','position',[.15*k .01 .14 .05]);
end
set(b(1),'style','pop','string', ...
{'1-d','square','disc','sector'})
set(b(2),'string','modes/wave')
set(b(3),'string','slower')
set(b(4),'string','faster')
set(b(5),'string','close')
if bvals(3)==1
speed = speed/sqrt(2);
set(b(3),'value',0);
end
if bvals(4)==1
speed = speed*sqrt(2);
set(b(4),'value',0);
end
bvals = cell2mat(get(b,'value'));
region = bvals(1);
modes = bvals(2)==0;
if region == 1
% 1-D
x = (0:4*m)/(4*m)*pi;
orange = [1 1/3 0];
gray = get(gcf,'color');
if modes
% 1-D modes
for k = 1:4
subplot(2,2,k)
h(k) = plot(x,zeros(size(x)));
axis([0 pi -3/2 3/2])
set(h(k),'color',orange,'linewidth',3)
set(gca,'color',gray','xtick',[],'ytick',[])
end
delta = 0.005*speed;
bvs = bvals;
while all(bvs == bvals)
t = t + delta;
for k = 1:4
u = sin(k*t)*sin(k*x);
set(h(k),'ydata',u)
end
drawnow
bvs = cell2mat(get(b,'value'));
end
else
% 1-D wave
h = plot(x,zeros(size(x)));
axis([0 pi -9/4 9/4])
set(h,'color',orange,'linewidth',3)
set(gca,'color',gray','xtick',[],'ytick',[])
delta = 0.005*speed;
a = 1./(1:4);
bvs = bvals;
while all(bvs == bvals)
t = t + delta;
u = zeros(size(x));
for k = 1:4
u = u + a(k)*sin(k*t)*sin(k*x);
end
set(h,'ydata',u)
drawnow
bvs = cell2mat(get(b,'value'));
end
end
elseif region <= 5
switch region
case 2
% Square
x = (0:2*m)/(2*m)*pi;
y = x';
lambda = zeros(4,1);
V = cell(4,1);
k = 0;
for i = 1:2
for j = 1:2
k = k+1;
lambda(k) = i^2 + j^2;
V{k} = sin(i*y)*sin(j*x);
end
end
ax = [0 pi 0 pi -1.75 1.75];
case 3
% Disc, mu = zeros of J_0(r) and J_1(r)
mu = [bjzeros(0,2) bjzeros(1,2)];
[r,theta] = meshgrid((0:m)/m,(-m:m)/m*pi);
x = r.*cos(theta);
y = r.*sin(theta);
V = cell(4,1);
k = 0;
for j = 0:1
for i = 1:2
k = k+1;
if j == 0
V{k} = besselj(0,mu(k)*r);
else
V{k} = besselj(j,mu(k)*r).*sin(j*theta);
end
V{k} = V{k}/max(max(abs(V{k})));
end
end
lambda = mu.^2;
ax = [-1 1 -1 1 -1.75 1.75];
case 4
% Circular sector , mu = zeros of J_(2/3)(r) and J_(4/3)(r)
mu = [bjzeros(2/3,2) bjzeros(4/3,2)];
[r,theta] = meshgrid((0:m)/m,(3/4)*(0:2*m)/m*pi);
x = r.*cos(theta+pi);
y = r.*sin(theta+pi);
V = cell(4,1);
k = 0;
for j = 1:2
for i = 1:2
k = k+1;
alpha = 2*j/3;
V{k} = besselj(alpha,mu(k)*r).*sin(alpha*theta);
V{k} = V{k}/max(max(abs(V{k})));
end
end
lambda = mu.^2;
ax = [-1 1 -1 1 -1.75 1.75];
case 5\
% L-membrane
x = (-m:m)/m;
y = x';
lambda = zeros(4,1);
V = cell(4,1);
for k = 1:4
[L lambda(k)] = membranetx(k,m,9,9);
L(m+2:2*m+1,m+2:2*m+1) = NaN;
V{k} = rot90(L,-1);
end
ax = [-1 1 -1 1 -1.75 1.75];
end
if modes
% 2-D modes
p = [.02 .52 .02 .52];
q = [.52 .52 .02 .02];
for k = 1:4
axes('position',[p(k) q(k) .46 .46]);
h(k) = surf(x,y,zeros(size(V{k})));
axis(ax)
axis off
view(225,30);
caxis([-1.5 1]);
end
delta = .08*speed;
mu = sqrt(lambda(:));
bvs = bvals;
while all(bvs == bvals)
t = t + delta;
for k = 1:4
U = 1.5*sin(mu(k)*t)*V{k};
set(h(k),'zdata',U)
set(h(k),'cdata',U)
end
drawnow
bvs = cell2mat(get(b,'value'));
end
else
% 2-D wave
h = surf(x,y,zeros(size(V{1})));
axis(ax);
axis off
view(225,30);
caxis([-1.5 1]);
delta = .02*speed;
mu = sqrt(lambda(:));
a = 1.25./(1:4);
bvs = bvals;
while all(bvs == bvals)
t = t + delta;
U = zeros(size(V{1}));
for k = 1:4
U = U + a(k)*sin(mu(k)*t)*V{k};
end
set(h,'zdata',U)
set(h,'cdata',U)
drawnow
bvs = cell2mat(get(b,'value'));
end
end
elseif region == 6
figure
bizcard
set(b(1),'value',1)
end
% Retain uicontrol values
bvals = cell2mat(get(b,'value'));
end
close
% -------------------------------
function z = bjzeros(n,k)
% BJZEROS Zeros of the Bessel function.
% z = bjzeros(n,k) is the first k zeros of besselj(n,x)
% delta must be chosen so that the linear search can take
% steps as large as possible without skipping any zeros.
% delta is approx bjzero(0,2)-bjzero(0,1)
delta = .99*pi;
Jsubn = inline('besselj(n,x)''x','n');
a = n+1;
fa = besselj(n,a);
z = zeros(1,k);
j = 0;
while j < k
b = a + delta;
fb = besselj(n,b);
if sign(fb) ~= sign(fa)
j = j+1;
z(j) = fzerotx(Jsubn,[a b],n);
end
a = b;
fa = fb;
end
I'm using the next code to plot in a pie chart the percentage of values in a matrix that are greater/smaller than 1. The thing is that when I want to put the title above the graph, it overlaps with the label of one of the groups.
I tried replacing it with text() but it didn't worked, and Documentation on pie say nothing to this. How can I avoid this overlap?
eigen = []; % Modes array
c2 = 170; % Sound speed divided by 2
%% Room dimensions
lx = 5.74;
ly = 8.1;
lz = 4.66;
i = 1; % Index for modes array
for nz = 0:50
for ny = 0:50
for nx = 0:50
aux = c2 * sqrt((nx/lx)^2+(ny/ly)^2+(nz/lz)^2);
if aux < 400 %% If value is into our range of interest
eigen(i) = aux;
i=i+1;
end
end
end
end
eigen = round(sort(eigen'),1);
eigen
% dif = eigen(2:end)-eigen(1:end-1); % Distance between modes
x = 0; %% dif >= 1
y = 0; %% dif <= 1
dif = [];
for i=2:length(eigen)
if eigen(i)-eigen(i-1) >= 1
x = x+1;
else
y = y+1;
end
end
figure
dif = [x,y];
explode = [1 1];
graf = pie(dif,explode);
hText = findobj(graf,'Type','text');
percentValues = get(hText,'String');
txt = {'Smaller than 1 Hz: ';'Greater than 1 Hz: '};
combinedtxt = strcat(txt,percentValues);
oldExtents_cell = get(hText,'Extent');
oldExtents = cell2mat(oldExtents_cell);
hText(1).String = combinedtxt(1);
hText(2).String = combinedtxt(2);
title('Distance between modes')
You can rotate the pie chart so that the figure look better. Further, you can use position to allocate your text as follows,
figure
dif = [x,y];
explode = [1 1];
graf = pie(dif,explode);
hText = findobj(graf,'Type','text');
percentValues = get(hText,'String');
txt = {'Smaller than 1 Hz: ';'Greater than 1 Hz: '};
combinedtxt = strcat(txt,percentValues);
oldExtents_cell = get(hText,'Extent');
oldExtents = cell2mat(oldExtents_cell);
hText(1).String = combinedtxt(1);
hText(2).String = combinedtxt(2);
view([90 90]) % this is to rotate the chart
textPositions_cell = get(hText,{'Position'});
textPositions = cell2mat(textPositions_cell);
textPositions(:,1) = textPositions(:,1) + 0.2; % replace 0.2 with any offset value you want
hText(1).Position = textPositions(1,:);
hText(2).Position = textPositions(2,:);
title('Distance between modes')
You can change only the text position (without rotation) by deleting view command.
I have a problem that I can't seem to solve. I want a query to determine whether a given value lies within a predefined range, but my loop is very slow for big datasets. Is there a more efficient way?
clear all
close all
Regression(1,1) = 1.001415645694801;
Regression(1,2) = 0.043822386790753;
FF_Value(:,1) = [24.24 30.77 31.37 29.05 29.20 29.53 29.67 27.78];
FF_Value(:,2) = [24.16 30.54 31.15 29.53 29.39 29.34 29.53 28.17];
FF_Distance = FF_Value(:,2)-(Regression(1,2)+Regression(1,1)*FF_Value(:,1));
FF_Distance_Positiv = sort(FF_Distance(FF_Distance > 0));
FF_Distance_Positiv(FF_Distance_Positiv == 0) = [];
FF_Distance_Negativ = sort(FF_Distance(FF_Distance < 0),'descend');
FF_Distance_Negativ(FF_Distance_Negativ == 0) = [];
A = repmat(FF_Distance_Positiv,length(FF_Distance_Negativ),1);
B = repmat(FF_Distance_Negativ',length(FF_Distance_Positiv),1);
C = reshape(B,[length(FF_Distance_Positiv)*length(FF_Distance_Negativ),1]);
Recognition(:,1) = A;
Recognition(:,2) = C;
FF_Recognition = zeros(length(FF_Value),1);
for i = 1:length(Recognition)
for j = 1:length(FF_Value)
if (Regression(1,2)+Recognition(i,1))+Regression(1,1)*FF_Value(j,1) >= FF_Value(j,2) &&...
(Regression(1,2)+Recognition(i,2))+Regression(1,1)*FF_Value(j,1) <= FF_Value(j,2)
FF_Recognition(j,1) = 1;
end
end
end
Welcome to the world of bsxfun's replacing your world of repmats -
%------------ Original code -----------------------------------------
FF_Distance = FF_Value(:,2)-(Regression(1,2)+Regression(1,1)*FF_Value(:,1));
FF_Distance_Positiv = sort(FF_Distance(FF_Distance > 0));
FF_Distance_Positiv(FF_Distance_Positiv == 0) = [];
%// Note for Performance: If number of elements satisfying `FF_Distance_Positiv == 0`
%// is a lot, consider doing this instead -
%// `FF_Distance_Positiv = FF_Distance_Positiv(FF_Distance_Positiv~=0)`.
%// Follow this strategy for `FF_Distance_Negativ` too.
FF_Distance_Negativ = sort(FF_Distance(FF_Distance < 0),'descend');
FF_Distance_Negativ(FF_Distance_Negativ == 0) = [];
%------- Added vectorization replacing `repmats` and nested loops ------------
mult = Regression(1,1)*FF_Value(:,1);
y1 = bsxfun(#plus,Regression(1,2),FF_Distance_Positiv);
y2 = bsxfun(#plus,y1.',mult); %//'
mc1 = bsxfun(#ge,y2,FF_Value(:,2));
z1 = bsxfun(#plus,Regression(1,2),FF_Distance_Negativ);
z2 = bsxfun(#plus,z1.',mult); %//'
mc2 = bsxfun(#le,z2,FF_Value(:,2));
FF_Recognition = all([any(mc1,2) any(mc2,2)],2);
I am trying to implement my own Thinning Algorithm in Matlab to understand the thinning algorithm. I am following http://fourier.eng.hmc.edu/e161/lectures/morphology/node2.html and implementing my own code, but the result is incorrect.
Here is my code:
%for the sake of simplicity, the outermost pixels are ignored.
for x = 2:1:511
for y = 2:1:511
% if this pixel is not black, then, proceed in.
if (frame2(y,x) > 0)
% the pos(1 to 8) here are for the surrounding pixels.
pos(1) = frame2(y-1,x-1);
pos(2) = frame2(y, x-1);
pos(3) = frame2(y+1, x+1);
pos(4) = frame2(y+1, x);
pos(5) = frame2(y+1, x-1);
pos(6) = frame2(y, x-1);
pos(7) = frame2(y-1, x-1);
pos(8) = frame2(y-1, x);
nonZeroNeighbor = 0;
transitSequence = 0;
change = 0;
for n = 1:1:8
% for N(P1)
if (pos(n) >= 1)
nonZeroNeighbor = nonZeroNeighbor + 1;
end
% for S(P1)
if (n > 1)
if (pos(n) ~= change)
change = pos(n);
transitSequence = transitSequence + 1;
end
else
change = pos(n);
end
end
% also for S(P1)
if ((nonZeroNeighbor > 1 && nonZeroNeighbor < 7) || transitSequence >= 2)
markMatrix(y,x) = 1;
fprintf(1, '(%d,%d) nonzero: %d transit: %d\n', y,x, nonZeroNeighbor, transitSequence);
else %this else here is for the reverse.
end
end
end
end
for x = 2:1:511
for y = 2:1:511
if (markMatrix(y,x) > 0)
frame2(y,x) = 0;
end
end
end
savePath = [path header number2 '.bmp'];
imwrite(frame2, savePath, 'bmp'); %output image here, replacing the original
From the site above, it states the function S(P1) as:
"S(P1): number of 0 to 1 (or 1 to 0) transitions in the sequence (P2, P3, ..., P9)"
For this part, my codes are below "% for S(P1)" and "% also for S(P1)" comments. Am I implementing this function correctly? The output image I got is simply blank. Nothing at all.
For the correct output, I am aware that there is a logical problem. Regarding the site, it states:
When part of the shape is only 2-pixel wide, all pixels are boundary points and will be marked and then deleted.
This problem is to be ignored for now.
I've had a go at the problem and think I managed to get the algorithm to work. I've made several small edits along the way (please see the code below for details), but also found two fundamental problems with your initial implementation.
Firstly, you assumed all would be done in the first pass of step 1 and 2, but really you need to let the algorithm work away at the image for some time. This is typical for iterative morphological steps 'eating' away at the image. This is the reason for the added while loop.
Secondly, your way of calculating S() was wrong; it counted both steps from 0 to 1 and 1 to 0, counting twice when it shouldn't and it didn't take care of the symmetry around P(2) and P(9).
My code:
%Preliminary setups
close all; clear all;
set(0,'DefaultFigureWindowStyle','Docked')
%Read image
frame2 = imread('q1.jpg');
%Code for spesific images
%frame2(:,200:end) = [];
%frame2 = rgb2gray(frame2);
%Make binary
frame2(frame2 < 128) = 1;
frame2(frame2 >= 128) = 0;
%Get sizes and set up mark
[Yn Xn] = size(frame2);
markMatrix = zeros(Yn,Xn);
%First visualization
figure();imagesc(frame2);colormap(gray)
%%
%While loop control
cc = 0;
changed = 1;
while changed && cc < 50;
changed = 0;
cc = cc + 1;
markMatrix = zeros(Yn,Xn);
for x = 2:1:Xn-1
for y = 2:1:Yn-1
% if this pixel is not black, then, proceed in.
if (frame2(y,x) > 0)
% the pos(2 to 9) here are for the surrounding pixels.
pos(1) = frame2(y, x);
pos(2) = frame2(y-1, x);
pos(3) = frame2(y-1, x+1);
pos(4) = frame2(y, x+1);
pos(5) = frame2(y+1, x+1);
pos(6) = frame2(y+1, x);
pos(7) = frame2(y+1, x-1);
pos(8) = frame2(y, x-1);
pos(9) = frame2(y-1, x-1);
nonZeroNeighbor = 0;
transitSequence = 0;
change = pos(9);
for n = 2:1:9
%N()
nonZeroNeighbor = sum(pos(2:end));
%S()
if (double(pos(n)) - double(change)) < 0
transitSequence = transitSequence + 1;
end
change = pos(n);
end
%Test if pixel is to be removed
if ~( nonZeroNeighbor == 0 || nonZeroNeighbor == 1 ...
||nonZeroNeighbor == 7 || nonZeroNeighbor == 8 ...
||transitSequence >= 2)
markMatrix(y,x) = 1;
fprintf(1, '(%d,%d) nonzero: %d transit: %d\n', ...
y,x, nonZeroNeighbor, transitSequence);
end
end
end
end
%Mask out all pixels found to be deleted
frame2(markMatrix > 0) = 0;
%Check if anything has changed
if sum(markMatrix(:)) > 0;changed = 1;end
end
%Final visualization
figure();imagesc(frame2);colormap(gray)