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I'm trying to write an image compression script in MATLAB using multilayer 3D DWT(color image). along the way, I want to apply thresholding on coefficient matrices, both global and local thresholds.
I like to use the formula below to calculate my local threshold:
where sigma is variance and N is the number of elements.
Global thresholding works fine; but my problem is that the calculated local threshold is (most often!) greater than the maximum band coefficient, therefore no thresholding is applied.
Everything else works fine and I get a result too, but I suspect the local threshold is miscalculated. Also, the resulting image is larger than the original!
I'd appreciate any help on the correct way to calculate the local threshold, or if there's a pre-set MATLAB function.
here's an example output:
here's my code:
clear;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% COMPRESSION %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% read base image
% dwt 3/5-L on base images
% quantize coeffs (local/global)
% count zero value-ed coeffs
% calculate mse/psnr
% save and show result
% read images
base = imread('circ.jpg');
fam = 'haar'; % wavelet family
lvl = 3; % wavelet depth
% set to 1 to apply global thr
thr_type = 0;
% global threshold value
gthr = 180;
% convert base to grayscale
%base = rgb2gray(base);
% apply dwt on base image
dc = wavedec3(base, lvl, fam);
% extract coeffs
ll_base = dc.dec{1};
lh_base = dc.dec{2};
hl_base = dc.dec{3};
hh_base = dc.dec{4};
ll_var = var(ll_base, 0);
lh_var = var(lh_base, 0);
hl_var = var(hl_base, 0);
hh_var = var(hh_base, 0);
% count number of elements
ll_n = numel(ll_base);
lh_n = numel(lh_base);
hl_n = numel(hl_base);
hh_n = numel(hh_base);
% find local threshold
ll_t = ll_var * (sqrt(2 * log2(ll_n)));
lh_t = lh_var * (sqrt(2 * log2(lh_n)));
hl_t = hl_var * (sqrt(2 * log2(hl_n)));
hh_t = hh_var * (sqrt(2 * log2(hh_n)));
% global
if thr_type == 1
ll_t = gthr; lh_t = gthr; hl_t = gthr; hh_t = gthr;
end
% count zero values in bands
ll_size = size(ll_base);
lh_size = size(lh_base);
hl_size = size(hl_base);
hh_size = size(hh_base);
% count zero values in new band matrices
ll_zeros = sum(ll_base==0,'all');
lh_zeros = sum(lh_base==0,'all');
hl_zeros = sum(hl_base==0,'all');
hh_zeros = sum(hh_base==0,'all');
% initiate new matrices
ll_new = zeros(ll_size);
lh_new = zeros(lh_size);
hl_new = zeros(lh_size);
hh_new = zeros(lh_size);
% apply thresholding on bands
% if new value < thr => 0
% otherwise, keep the previous value
for id=1:ll_size(1)
for idx=1:ll_size(2)
if ll_base(id,idx) < ll_t
ll_new(id,idx) = 0;
else
ll_new(id,idx) = ll_base(id,idx);
end
end
end
for id=1:lh_size(1)
for idx=1:lh_size(2)
if lh_base(id,idx) < lh_t
lh_new(id,idx) = 0;
else
lh_new(id,idx) = lh_base(id,idx);
end
end
end
for id=1:hl_size(1)
for idx=1:hl_size(2)
if hl_base(id,idx) < hl_t
hl_new(id,idx) = 0;
else
hl_new(id,idx) = hl_base(id,idx);
end
end
end
for id=1:hh_size(1)
for idx=1:hh_size(2)
if hh_base(id,idx) < hh_t
hh_new(id,idx) = 0;
else
hh_new(id,idx) = hh_base(id,idx);
end
end
end
% count zeros of the new matrices
ll_new_size = size(ll_new);
lh_new_size = size(lh_new);
hl_new_size = size(hl_new);
hh_new_size = size(hh_new);
% count number of zeros among new values
ll_new_zeros = sum(ll_new==0,'all');
lh_new_zeros = sum(lh_new==0,'all');
hl_new_zeros = sum(hl_new==0,'all');
hh_new_zeros = sum(hh_new==0,'all');
% set new band matrices
dc.dec{1} = ll_new;
dc.dec{2} = lh_new;
dc.dec{3} = hl_new;
dc.dec{4} = hh_new;
% count how many coeff. were thresholded
ll_zeros_diff = ll_new_zeros - ll_zeros;
lh_zeros_diff = lh_zeros - lh_new_zeros;
hl_zeros_diff = hl_zeros - hl_new_zeros;
hh_zeros_diff = hh_zeros - hh_new_zeros;
% show coeff. matrices vs. thresholded version
figure
colormap(gray);
subplot(2,4,1); imagesc(ll_base); title('LL');
subplot(2,4,2); imagesc(lh_base); title('LH');
subplot(2,4,3); imagesc(hl_base); title('HL');
subplot(2,4,4); imagesc(hh_base); title('HH');
subplot(2,4,5); imagesc(ll_new); title({'LL thr';ll_zeros_diff});
subplot(2,4,6); imagesc(lh_new); title({'LH thr';lh_zeros_diff});
subplot(2,4,7); imagesc(hl_new); title({'HL thr';hl_zeros_diff});
subplot(2,4,8); imagesc(hh_new); title({'HH thr';hh_zeros_diff});
% idwt to reconstruct compressed image
cmp = waverec3(dc);
cmp = uint8(cmp);
% calculate mse/psnr
D = abs(cmp - base) .^2;
mse = sum(D(:))/numel(base);
psnr = 10*log10(255*255/mse);
% show images and mse/psnr
figure
subplot(1,2,1);
imshow(base); title("Original"); axis square;
subplot(1,2,2);
imshow(cmp); colormap(gray); axis square;
msg = strcat("MSE: ", num2str(mse), " | PSNR: ", num2str(psnr));
title({"Compressed";msg});
% save image locally
imwrite(cmp, 'compressed.png');
I solved the question.
the sigma in the local threshold formula is not variance, it's the standard deviation. I applied these steps:
used stdfilt() std2() to find standard deviation of my coeff. matrices (thanks to #Rotem for pointing this out)
used numel() to count the number of elements in coeff. matrices
this is a summary of the process. it's the same for other bands (LH, HL, HH))
[c, s] = wavedec2(image, wname, level); %apply dwt
ll = appcoeff2(c, s, wname); %find LL
ll_std = std2(ll); %find standard deviation
ll_n = numel(ll); %find number of coeffs in LL
ll_t = ll_std * (sqrt(2 * log2(ll_n))); %local the formula
ll_new = ll .* double(ll > ll_t); %thresholding
replace the LL values in c in a for loop
reconstruct by applying IDWT using waverec2
this is a sample output:
I = imread('Sub1.png');
figure, imshow(I);
I = imcomplement(I);
I = double(I)/255;
I = adapthisteq(I,'clipLimit',0.0003,'Distribution','exponential');
k = 12;
beta = 2;
maxIter = 100;
for i=1:length(beta)
[seg,prob,mu,sigma,it(i)] = ICM(I, k, beta(i), maxIter,5);
pr(i) = prob(end);
hold on;
end
figure, imshow(seg,[]);
and ICM function is defined as
function [segmented_image,prob,mu,sigma,iter] = ICM(image, k, beta, max_iterations, neigh)
[width, height, bands] = size(image);
image = imstack2vectors(image);
segmented_image = init(image,k,1);
clear c;
iter = 0;
seg_old = segmented_image;
while(iter < max_iterations)
[mu, sigma] = stats(image, segmented_image, k);
E1 = energy1(image,mu,sigma,k);
E2 = energy2(segmented_image, beta, width, height, k);
E = E1 + E2;
[p2,~] = min(E2,[],2);
[p1,~] = min(E1,[],2);
[p,segmented_image] = min(E,[],2);
prob(iter+1) = sum(p);
%find mismatch with previous step
[c,~] = find(seg_old~=segmented_image);
mismatch = (numel(c)/numel(segmented_image))*100;
if mismatch<0.1
iter
break;
end
iter = iter + 1;
seg_old = segmented_image;
end
segmented_image = reshape(segmented_image,[width height]);
end
Output of my algorithm is a logical matrix (seg) of size 305-by-305. When I use
imshow(seg,[]);
I am able to display the image. It shows different component with varying gray value. But bwlabel returns 1. I want to display the connected components. I think bwlabel thresholds the image to 1. unique(seg) returns values 1 to 10 since number of classes used in k-means is 10. I used
[label n] = bwlabel(seg);
RGB = label2rgb(label);
figure, imshow(RGB);
I need all the ellipse-like structures which are in between the two squares close to the middle of the image. I don't know the number of classes present in it.
Input image:
Ground truth:
My output:
If you want to explode the label image to different connected components you need to use a loop to extract labels for each class and sum label images to get the out label image.
u = unique(seg(:));
out = zeros(size(seg));
num_objs = 0;
for k = 1: numel(u)
mask = seg==u(k);
[L,N] = bwlabel(mask);
L(mask) = L(mask) + num_objs;
out = out + L;
num_objs = num_objs + N ;
end
mp = jet(num_objs);
figure,imshow(out,mp)
Something like this is produced:
I have tried to do everything out of scratch. I wish it is of some help.
I have a treatment chain that get at first contours with parameters tuned on a trial-and-error basis, I confess. The last "image" is given at the bottom ; with it, you can easily select the connected components and do for example a reconstruction by markers using "imreconstruct" operator.
clear all;close all;
I = imread('C:\Users\jean-marie.becker\Desktop\imagesJPG10\spinalchord.jpg');
figure,imshow(I);
J = I(:,:,1);% select the blue channel because jpg image
J=double(J<50);% I haven't inverted the image
figure, imshow(J);
se = strel('disk',5);
J=J-imopen(J,se);
figure, imshow(J);
J=imopen(J,ones(1,15));% privilegizes long horizontal strokes
figure, imshow(J);
K=imdilate(J,ones(20,1),'same');
% connects verticaly not-to-far horizontal "segments"
figure, imshow(K);
I am estimating ridge orientation of an fingerprint image by dividing it into blocks of 41*41..image is of size 240*320..here is my code and the problem is that I am getting output image size different than input image.
% matalb code for orientation
im =imread('D:\project\116_2_5.jpg');
im = double(im);
[m,n] = size(im);
% to normalise image
nor = im - mean(im(:));
im = nor/std(nor(:));
w = 41;
% To calculate x and y gradient component using 3*3 sobel mask
[delx,dely] = gradient(im);
% Ridge orientation
for i=21:w:240-41
for j=21:w:320-41
A = delx(i-20:i+20,j-20:j+20);
B = dely(i-20:i+20,j-20:j+20);
Gxy = sum(sum(A.*B));
Gxx = sum(sum(A.*A));
Gyy = sum(sum(B.*B));
diff = Gxx-Gyy;
theta(i-20:i+20,j-20:j+20) = (pi/2) + 0.5*atan2(2*Gxy,diff);
end;
end;
but in this process i am loosing the pixels at the boundries so as to avoid the "index exceed" error i.e size of theta is m = 240-41 = 199 and n = 320-41=279..Thus my input image size is 240*320 and output image size is size 199*279..How can i get output image same as size of input image.
one more thing that i dnt have to use "blockproc" function...Thanks in advance
You can use padarray to add zeros onto your matrix:
A1 = padarray(A,[7 8],'post'); % 240+7=41*7, 320+8=41*8
B1 = padarray(B,[7 8],'post');
then generate Gxx, Gyy, and Gxy with A1 and B1.
Method 2:
Besides, I tried to simplify your code a little bit by removing the loops, for your reference:
% Ridge orientation
Gxy = delx .* dely;
Gxx = delx .* delx;
Gyy = dely .* dely;
fun = #(x) sum(x(:))*ones(size(x));
theta_Gxy = blockproc(Gxy,[41 41],fun, 'PadPartialBlocks', true);
theta_diff = blockproc(Gxx-Gyy,[41 41],fun, 'PadPartialBlocks', true);
theta0 = pi/2 + 0.5 * atan2(2 * theta_Gxy, theta_diff);
theta = theta0(1:240, 1:320);
You may check blockproc for more details.
Normally, a Gabor filter, as its name suggests, is used to filter an image and extract everything that it is oriented in the same direction of the filtering.
In this question, you can see more efficient code than written in this Link
Assume 16 scales of Filters at 4 orientations, so we get 64 gabor filters.
scales=[7:2:37], 7x7 to 37x37 in steps of two pixels, so we have 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29, 31x31, 33x33, 35x35 and 37x37.
directions=[0, pi/4, pi/2, 3pi/4].
The equation of Gabor filter in the spatial domain is:
The equation of Gabor filter in the frequency domain is:
In the spatial domain:
function [fSiz,filters,c1OL,numSimpleFilters] = init_gabor(rot, RF_siz)
image=imread('xxx.jpg');
image_gray=rgb2gray(image);
image_gray=imresize(image_gray, [100 100]);
image_double=double(image_gray);
rot = [0 45 90 135]; % we have four orientations
RF_siz = [7:2:37]; %we get 16 scales (7x7 to 37x37 in steps of two pixels)
minFS = 7; % the minimum receptive field
maxFS = 37; % the maximum receptive field
sigma = 0.0036*RF_siz.^2 + 0.35*RF_siz + 0.18; %define the equation of effective width
lambda = sigma/0.8; % it the equation of wavelength (lambda)
G = 0.3; % spatial aspect ratio: 0.23 < gamma < 0.92
numFilterSizes = length(RF_siz); % we get 16
numSimpleFilters = length(rot); % we get 4
numFilters = numFilterSizes*numSimpleFilters; % we get 16x4 = 64 filters
fSiz = zeros(numFilters,1); % It is a vector of size numFilters where each cell contains the size of the filter (7,7,7,7,9,9,9,9,11,11,11,11,......,37,37,37,37)
filters = zeros(max(RF_siz)^2,numFilters); % Matrix of Gabor filters of size %max_fSiz x num_filters, where max_fSiz is the length of the largest filter and num_filters the total number of filters. Column j of filters matrix contains a n_jxn_j filter (reshaped as a column vector and padded with zeros).
for k = 1:numFilterSizes
for r = 1:numSimpleFilters
theta = rot(r)*pi/180; % so we get 0, pi/4, pi/2, 3pi/4
filtSize = RF_siz(k);
center = ceil(filtSize/2);
filtSizeL = center-1;
filtSizeR = filtSize-filtSizeL-1;
sigmaq = sigma(k)^2;
for i = -filtSizeL:filtSizeR
for j = -filtSizeL:filtSizeR
if ( sqrt(i^2+j^2)>filtSize/2 )
E = 0;
else
x = i*cos(theta) - j*sin(theta);
y = i*sin(theta) + j*cos(theta);
E = exp(-(x^2+G^2*y^2)/(2*sigmaq))*cos(2*pi*x/lambda(k));
end
f(j+center,i+center) = E;
end
end
f = f - mean(mean(f));
f = f ./ sqrt(sum(sum(f.^2)));
p = numSimpleFilters*(k-1) + r;
filters(1:filtSize^2,p)=reshape(f,filtSize^2,1);
fSiz(p)=filtSize;
end
end
% Rebuild all filters (of all sizes)
nFilts = length(fSiz);
for i = 1:nFilts
sqfilter{i} = reshape(filters(1:(fSiz(i)^2),i),fSiz(i),fSiz(i));
%if you will use conv2 to convolve an image with this gabor, so you should also add the equation below. But if you will use imfilter instead of conv2, so do not add the equation below.
sqfilter{i} = sqfilter{i}(end:-1:1,end:-1:1); %flip in order to use conv2 instead of imfilter (%bug_fix 6/28/2007);
convv=imfilter(image_double, sqfilter{i}, 'same', 'conv');
figure;
imagesc(convv);
colormap(gray);
end
phi = ij*pi/4; % ij = 0, 1, 2, 3
theta = 3;
sigma = 0.65*theta;
filterSize = 7; % 7:2:37
G = zeros(filterSize);
for i=(0:filterSize-1)/filterSize
for j=(0:filterSize-1)/filterSize
xprime= j*cos(phi);
yprime= i*sin(phi);
K = exp(2*pi*theta*sqrt(-1)*(xprime+ yprime));
G(round((i+1)*filterSize),round((j+1)*filterSize)) =...
exp(-(i^2+j^2)/(sigma^2))*K;
end
end
As of R2015b release of the Image Processing Toolbox, you can create a Gabor filter bank using the gabor function in the image processing toolbox, and you can apply it to an image using imgaborfilt.
In the frequency domain:
sigma_u=1/2*pi*sigmaq;
sigma_v=1/2*pi*sigmaq;
u0=2*pi*cos(theta)*lambda(k);
v0=2*pi*sin(theta)*lambda(k);
for u = -filtSizeL:filtSizeR
for v = -filtSizeL:filtSizeR
if ( sqrt(u^2+v^2)>filtSize/2 )
E = 0;
else
v_theta = u*cos(theta) - v*sin(theta);
u_theta = u*sin(theta) + v*cos(theta);
E=(1/2*pi*sigma_u*sigma_v)*((exp((-1/2)*(((u_theta-u0)^2/sigma_u^2))+((v_theta-v0)^2/sigma_v^2))) + (exp((-1/2)*(((u_theta+u0)^2/sigma_u^2))+((v_theta+v0)^2/sigma_v^2))));
end
f(v+center,u+center) = E;
end
end
My idea is simple here. I am using mexopencv and trying to see whether there is any object present in my current that matches with any image stored in my database.I am using OpenCV DescriptorMatcher function to train my images.
Here is a snippet, I am wishing to build on top of this, which is one to one one image matching using mexopencv, and can also be extended for image stream.
function hello
detector = cv.FeatureDetector('ORB');
extractor = cv.DescriptorExtractor('ORB');
matcher = cv.DescriptorMatcher('BruteForce-Hamming');
train = [];
for i=1:3
train(i).img = [];
train(i).points = [];
train(i).features = [];
end;
train(1).img = imread('D:\test\1.jpg');
train(2).img = imread('D:\test\2.png');
train(3).img = imread('D:\test\3.jpg');
for i=1:3
frameImage = train(i).img;
framePoints = detector.detect(frameImage);
frameFeatures = extractor.compute(frameImage , framePoints);
train(i).points = framePoints;
train(i).features = frameFeatures;
end;
for i = 1:3
boxfeatures = train(i).features;
matcher.add(boxfeatures);
end;
matcher.train();
camera = cv.VideoCapture;
pause(3);%Sometimes necessary
window = figure('KeyPressFcn',#(obj,evt)setappdata(obj,'flag',true));
setappdata(window,'flag',false);
while(true)
sceneImage = camera.read;
sceneImage = rgb2gray(sceneImage);
scenePoints = detector.detect(sceneImage);
sceneFeatures = extractor.compute(sceneImage,scenePoints);
m = matcher.match(sceneFeatures);
%{
%Comments in
img_no = m.imgIdx;
img_no = img_no(1);
%I am planning to do this based on the fact that
%on a perfect match imgIdx a 1xN will be filled
%with the index of the training
%example 1,2 or 3
objPoints = train(img_no+1).points;
boxImage = train(img_no+1).img;
ptsScene = cat(1,scenePoints([m.queryIdx]+1).pt);
ptsScene = num2cell(ptsScene,2);
ptsObj = cat(1,objPoints([m.trainIdx]+1).pt);
ptsObj = num2cell(ptsObj,2);
%This is where the problem starts here, assuming the
%above is correct , Matlab yells this at me
%index exceeds matrix dimensions.
end [H,inliers] = cv.findHomography(ptsScene,ptsObj,'Method','Ransac');
m = m(inliers);
imgMatches = cv.drawMatches(sceneImage,scenePoints,boxImage,boxPoints,m,...
'NotDrawSinglePoints',true);
imshow(imgMatches);
%Comment out
%}
flag = getappdata(window,'flag');
if isempty(flag) || flag, break; end
pause(0.0001);
end
Now the issue here is that imgIdx is a 1xN matrix , and it contains the index of different training indices, which is obvious. And only on a perfect match is the matrix imgIdx is completely filled with the matched image index. So, how do I use this matrix to pick the right image index. Also
in these two lines, I get the error of index exceeding matrix dimension.
ptsObj = cat(1,objPoints([m.trainIdx]+1).pt);
ptsObj = num2cell(ptsObj,2);
This is obvious since while debugging I saw clearly that the size of m.trainIdx is greater than objPoints, i.e I am accessing points which I should not, hence index exceeds
There is scant documentation on use of imgIdx , so anybody who has knowledge on this subject, I need help.
These are the images I used.
Image1
Image2
Image3
1st update after #Amro's response:
With the ratio of min distance to distance at 3.6 , I get the following response.
With the ratio of min distance to distance at 1.6 , I get the following response.
I think it is easier to explain with code, so here it goes :)
%% init
detector = cv.FeatureDetector('ORB');
extractor = cv.DescriptorExtractor('ORB');
matcher = cv.DescriptorMatcher('BruteForce-Hamming');
urls = {
'http://i.imgur.com/8Pz4M9q.jpg?1'
'http://i.imgur.com/1aZj0MI.png?1'
'http://i.imgur.com/pYepuzd.jpg?1'
};
N = numel(urls);
train = struct('img',cell(N,1), 'pts',cell(N,1), 'feat',cell(N,1));
%% training
for i=1:N
% read image
train(i).img = imread(urls{i});
if ~ismatrix(train(i).img)
train(i).img = rgb2gray(train(i).img);
end
% extract keypoints and compute features
train(i).pts = detector.detect(train(i).img);
train(i).feat = extractor.compute(train(i).img, train(i).pts);
% add to training set to match against
matcher.add(train(i).feat);
end
% build index
matcher.train();
%% testing
% lets create a distorted query image from one of the training images
% (rotation+shear transformations)
t = -pi/3; % -60 degrees angle
tform = [cos(t) -sin(t) 0; 0.5*sin(t) cos(t) 0; 0 0 1];
img = imwarp(train(3).img, affine2d(tform)); % try all three images here!
% detect fetures in query image
pts = detector.detect(img);
feat = extractor.compute(img, pts);
% match against training images
m = matcher.match(feat);
% keep only good matches
%hist([m.distance])
m = m([m.distance] < 3.6*min([m.distance]));
% sort by distances, and keep at most the first/best 200 matches
[~,ord] = sort([m.distance]);
m = m(ord);
m = m(1:min(200,numel(m)));
% naive classification (majority vote)
tabulate([m.imgIdx]) % how many matches each training image received
idx = mode([m.imgIdx]);
% matches with keypoints belonging to chosen training image
mm = m([m.imgIdx] == idx);
% estimate homography (used to locate object in query image)
ptsQuery = num2cell(cat(1, pts([mm.queryIdx]+1).pt), 2);
ptsTrain = num2cell(cat(1, train(idx+1).pts([mm.trainIdx]+1).pt), 2);
[H,inliers] = cv.findHomography(ptsTrain, ptsQuery, 'Method','Ransac');
% show final matches
imgMatches = cv.drawMatches(img, pts, ...
train(idx+1).img, train(idx+1).pts, ...
mm(logical(inliers)), 'NotDrawSinglePoints',true);
% apply the homography to the corner points of the training image
[h,w] = size(train(idx+1).img);
corners = permute([0 0; w 0; w h; 0 h], [3 1 2]);
p = cv.perspectiveTransform(corners, H);
p = permute(p, [2 3 1]);
% show where the training object is located in the query image
opts = {'Color',[0 255 0], 'Thickness',4};
imgMatches = cv.line(imgMatches, p(1,:), p(2,:), opts{:});
imgMatches = cv.line(imgMatches, p(2,:), p(3,:), opts{:});
imgMatches = cv.line(imgMatches, p(3,:), p(4,:), opts{:});
imgMatches = cv.line(imgMatches, p(4,:), p(1,:), opts{:});
imshow(imgMatches)
The result:
Note that since you did not post any testing images (in your code you are taking input from the webcam), I created one by distorting one the training images, and using it as a query image. I am using functions from certain MATLAB toolboxes (imwarp and such), but those are non-essential to the demo and you could replace them with equivalent OpenCV ones...
I must say that this approach is not the most robust one.. Consider using other techniques such as the bag-of-word model, which OpenCV already implements.