IMAGE PROCESSING

Display different images on same figure
Display stack of images with same colormap
Display Stack of Images with different colormap

Display different images on same figure

Consider two different images. For instance, let us consider the picture of the cathedral in Milan and the logo of image processing blog.

The image processing logo will be placed on the cathedral image using matlab command ‘imagesc’

MATLAB CODE:

I = imread('duomo.jpg');

L = imread('logo.jpg');

display(size(I));

display(size(L));

figure,imagesc(1,1,I);hold on;

imagesc(3400,1150,imresize(L,[900 900]));

hold off; axis off;

Explanation:

The size of ‘duomo.jpg’ is 2053 x 4320 x 3

i.e 2053 rows and 4320 columns

The size of ‘logo.jpg’ is 328 rows and 328 columns

First the image of the cathedral is displayed using ‘imagesc’ command then on the same figure the logo is placed by mentioning the position.

imagesc(3400,1150,imresize(L,[900 900]));

Here 3920,1650 represents the position to place the logo.

And the logo is resized to 900x900

Since we want to display the images on the same figure, ‘hold on’ command is used.

Display stack of images with single colormap

MATLAB CODE:

I = imread('cameraman.tif');

T = I;

Numimg = 5;

rng = [1,1];

for in=1:numimg

hold on;

imagesc(rng(1),rng(2),T);colormap(gray);axis ij;

rng = round(size(I)/(numimg*2)*in);

fsz = size(I)-(rng*2);

if fsz==0

break;

else

T = imresize(T,fsz)+1;

end

hold off; axis off;

Explanation:

Same image with different size and different starting position is placed on the same figure.

The colormap gray is used for all the images.

Fig. Colormap(jet)

Display Stack of Images with different colormap

MATLAB CODE:

I1 = imread('peppers.png');

I1 = imresize(I1,[400,400]);

I = rgb2gray(I1);

T = I+1;

%Predefined colormaps

Cname = {'hsv(256)','jet(256)','hot(256)','spring(256)','summer(256)','cool(256)','summer(256)','lines(256)'};

RGB = zeros([size(I,1) size(I,2) 3]);

Numimg = 7; %Number of Images to display

rng = [1 1];

for in=1:numimg-1

%Define the colormap

map1 = im2uint8(colormap(cname{in}));

m = map1(:,1);

RGB(:,:,1) = m(T);

m = map1(:,2);

RGB(:,:,2) = m(T);

m = map1(:,3);

RGB(:,:,3) = m(T);

RGB = uint8(RGB);

hold on;

imagesc(rng(1),rng(2),RGB);axis ij;

rng = round(size(I)/(numimg*2)*in);

fsz = size(I)-(rng*2);

if fsz==0

break;

else

T = imresize(T,fsz)+1;

clear RGB

end

I2 = imresize(I1,size(T));

imagesc(rng(1),rng(2),I2); %Actual Image

hold off;axis off;

Explanation:

Here same image with different size and different colormap is displayed on the same figure.

To increase or decrease the number of images, first try to resize the image accordingly and then modify the number of images to display.

The above method can also be used for different images and different color maps can be applied to those images on a single figure.

STACK OF IMAGES:

For More Images and code:
Check : Create Stack of Images notes in Facebook

or
Create Stack of Images in Google Collections

Clustering can be defined as the grouping of data points based on some commonality or similarity between the points.

One of the simplest methods is K-means clustering. In this method, the number of clusters is initialized and the center of each of the cluster is randomly chosen. The Euclidean distance between each data point and all the center of the clusters is computed and based on the minimum distance each data point is assigned to certain cluster. The new center for the cluster is defined and the Euclidean distance is calculated. This procedure iterates till convergence is reached.

Let’s see how to generate some random data points and some random cluster points

MATLAB CODE:

%Generate sample data points and assign random centre for each cluster

%Number of data points

sz=100;

sz1=250;

X = random('unid',sz1,[sz 1]); %Value

Xp = random('unid',sz1,[sz 1]); %Position

%Number of clusters

c=6;

V=random('unid',sz1,[c 1]); %Value

Vp=random('unid',sz1,[c 1]); %Position

figure,plot(Xp,X,'*',Vp,V,'r+');title('Data points and the initial Cluster centers');

Explanation:

100 data points are generated and the number of clusters are assumed to be 6 and 6 random cluster points are generated.

Group the data points:

MATLAB CODE:

%Preallocate the vectors

V1=zeros(size(V));

Vp1=zeros(size(Vp));

flag=1;

while flag==1

%Find the euclidean distance between the data points and all the center of

%the clusters

J=sqrt(abs(repmat(Xp,[1 c])-repmat(Vp,[1 sz])').^2+abs(repmat(X,[1 c])-repmat(V,[1 sz])').^2);

%Find the minimum distance between the data point and the cluster

[mv,Gpos]=min(J,[],2);

CGroup=zeros([sz c]);

colr=colormap(jet(c));

figure(3),

for i = 1:c

Temp = find(Gpos==i);

CGroup(1:numel(Temp),i)=Temp;

V1(i,:)=mean(X(Temp));

Vp1(i,:)=mean(Xp(Temp));

Pos=ones(numel(Temp)*2,1)*Vp1(i);

Pos(2:2:end)=Xp(Temp);

Value=ones(numel(Temp)*2,1)*V1(i);

Value(2:2:end)=X(Temp);

%Define the new centre for each cluster

plot(Pos,Value,'Color',colr(i,:),'LineStyle','-','Marker','o');hold on;

plot(Vp1(i),V1(i),'k+');

end

hold off;

Diffv=abs(V-V1);

DiffVp=abs(Vp-Vp1);

%Iterate the process till there is no change in the cluster position

if(Diffv < 1)

flag=0;

else

V=V1;

Vp=Vp1;

end

figure,plot(Xp,X,'*',Vp,V,'g+');title('Data points and the Final Cluster centers');

Fig. The new position(red circle) of the clusters after the final iteration.

Explanation:

In the above figure, the data points are represented in blue color stars and the cluster centers are represented in red color cross shape.

Let’s consider one particular data point and all the cluster centers.

Data point position X = 13, Y = 20

Cluster 1 position X = 8, Y = 19

Cluster 2 position X = 13, Y = 15

Step 1: Find the Euclidean Distance:

Find the Euclidean distance(D1) between data point and the cluster 1 similarly, find the Euclidean distance(D2) between data point and the cluster 2

Distance D1 = sqrt((13-8).^2+(20-19).^2)) = 5.0990

Distance D2 = sqrt((13-13).^2+(20-15).^2))= 5.0000

Step 2: Find the minimum and assign the data point to a cluster

Now the minimum distance among the two results is for the cluster 2.

So the data point with (X,Y)=(13,20) is assigned to the cluster/group 2.

Step 3: Perform the step 1 and step 2 for all the data points and assign group accordingly.

Step 4: Assign a new position for the clusters based on the clustering done.

Find the average position of the newly assigned data points to a particular cluster and use that average as the new position for the cluster.

Step 5: Iterate this procedure till the position of the clusters are unchanged.

Number of clusters = 3

Number of clusters = 6

Number of clusters = 15

IMAGE PROCESSING

How to use different images and color maps on a same figure in MATLAB

K-means Clustering