NAME : HÀ XUÂN CƯỜNGCLASS : 10ECCE

Exercise 1 & 2Fundamentals and Spatial Transformation

1. Read image with Matlaba. Load the image lena512.bmp, using imread(), and show it using imshow().

im = imread('lena512.bmp');imshow(im);

b. Get the type of the loaded image data (Use MATLAB function class()), and get the maximum and minimum data value for this image

class(im)ans =uint8

max(im(:))ans = 245

min(im(:))ans = 25

c. Convert the data to double type (use MATLAB function double()), show the double-typed image using imshow()

newim = double(im);imshow(newim);

d. Is the result from c correct? If not, how do you think you can correct it?The result from c is not correct. We can correct it in this way:

imshow(newim, [25 245]);

2. Color image and manipulationa. Load and show the image LightHouse_color.png

im = imread('LightHouse_color.png');imshow(im);

b. Show three plans R, G, B of this image

R=im;R(:,:,2:3)=0;imshow(R);title('Red plane')

G=im;G(:,:,1)=0;G(:,:,3)=0;imshow(G);title('Green plane');

imshow(im);B=im;B(:,:,1:2)=0;imshow(B);title('Blue plane');

c. Convert this color image to a grayscale image using rgb2gray. Display the result

gray=rgb2gray(im);imshow(gray);

d. Crop and show a patch (subimage) from this color image (Hint: get a submatrix using M(row1:row2, col1:col2))

subim=im(100:400,100:400,:);imshow(subim);

e. Divide this color image into 16 equal blocks. Place the blocks in the reverse order as below. Show the resulting color image

% Read the image.im = imread('LightHouse_color.png');% Get the dimensions of the image.[row, col, numberOfColorBands] = size(im);% Size of each block in rows.rowDist = [row/4 * ones(1, 4)];% Size of each block in columns.colDist = [col/4 * ones(1, 4)];% Divide the image into 16 blocks.divided = mat2cell(im, rowDist, colDist, numberOfColorBands);reversed = divided; %Prepare to reverse. % Reverse the order.for r = 1 : 4 for c = 1 : 4 reversed{r,c} = divided{5-r,5-c}; endend % Compare the original and resulting image.Re = cell2mat(reversed);subplot(121); imshow(im); title('Original Image');subplot(122);imshow(Re); title('Resulting Image');

The original image and the resulting color image:

3. Write an imagea. Reload the image LightHouse_color.png from exercise 2b. Exchange the plans R and G of this image, show the resulting image

im = imread('LightHouse_color.png');exchange=im;exchange(:,:,1) = im(:,:,3);exchange(:,:,3) = im(:,:,1);imshow(exchange);imwrite(exchange, 'exchangeImage.bmp');

c. Using imwrite to generate an image file for this new color image (for example bmp file). Check on your computer whether it is correct.

d.Here is the image from my computer, it is correct:

4. Read a video with Matlab

vid = VideoReader('snake.avi');n = vid.NumberOfFrames;frame = 1;set(gcf, 'units','normalized','outerposition',[0 0 1 1]);title('Video frames display');for i = 1:4; subplot(2, 2, i); index = randi(n); while (index < frame | index == frame) index = randi(n); end frame = index; imshow(read(vid,frame)); caption = sprintf('Frame #%d of %d Frames', ... frame,n); title(caption); drawnow;end

Here are some frames:

5. Image rotationa. Load a grayscale image b. Use imrotate to rotate this image with 45°, and then with 90°c. Show the original image and the rotated image in the same figure (using subplot)

im = imread('lena512.bmp');im1 = imrotate(im,45);im2 = imrotate(im,90);subplot(131);imshow(im);title('Original');subplot(132);imshow(im1);title('45 Degrees');subplot(133);imshow(im2);title('90 Degrees');

d. Write a program to carry out the rotation of an image, i.e. do not use the function imrotate. Compare with the results from question b.

Here is the function carrying out the rotating:

function ImRotated = RotateFunction(im, degree); switch mod(degree, 360) % Special cases case 0 ImRotated = im; case 90 ImRotated = rot90(im); case 180 ImRotated = im(end:-1:1, end:-1:1); case 270 ImRotated = rot90(im(end:-1:1, end:-1:1)); % General rotations otherwise % Convert to radians and create transformation matrix a = degree*pi/180; R = [+cos(a) +sin(a); -sin(a) +cos(a)]; % Figure out the size of the transformed image [m,n,p] = size(im); dest = round( [1 1; 1 n; m 1; m n]*R ); dest = bsxfun(@minus, dest, min(dest)) + 1; ImRotated = zeros([max(dest) p],class(im));

% Map all pixels of the transformed image to the original image for i = 1:size(ImRotated,1) for j = 1:size(ImRotated,2) source = ([i j]-dest(1,:))*R.'; if all(source >= 1) && all(source <= [m n]) % Get all 4 surrounding pixels C = ceil(source); F = floor(source); % Compute the relative areas A = [... ((C(2)-source(2))*(C(1)-source(1))),... ((source(2)-F(2))*(source(1)-F(1))); ((C(2)-source(2))*(source(1)-F(1))),... ((source(2)-F(2))*(C(1)-source(1)))]; % Extract colors and re-scale them relative to area cols = bsxfun(@times, A, double(im(F(1):C(1),F(2):C(2),:))); % Assign ImRotated(i,j,:) = sum(sum(cols),2); end end end end

And use it to rotate image:

im = imread('lena512.bmp');im1 = RotateFunction(im,45);im2 = RotateFunction(im,90);subplot(131);imshow(im);title('Original');subplot(132);imshow(im1);title('45 Degrees');subplot(133);imshow(im2);title('90 Degrees');

The figure below is the result of RotateFunction. As we see, this result is the same as the result from question b.

6. Image downsamplinga. Load the grayscale image Lenab. Use imresize to downsample this image by factor of 2 (in each dimension).

Compare the options nearest and bilinear.

im = imread('lena512.bmp');N = imresize(im,0.5,'nearest');B = imresize(im,0.5,'bilinear');subplot(121);imshow(N);title('Nearest');subplot(122);imshow(B);title('Bilinear');

With Nearest-neighbor interpolation, the output pixel is assigned the value of the pixel that the point falls within. No other pixels are considered. Meanwhile with Bilinear interpolation, the output pixel value is a weighted average of pixels in the nearest 2-by-2 neighborhood. This explains why the image with Bilinear interpolation seem to be smoother

c. Write a simple program to downsample the Lena image by factor of 2, i.e. do not use imresize. Generalize for factor of k. (Hint: in this question we omit a lowpass filtering step before downsampling)

. A simple program to downsample the Lena image by factor of 2:

im = imread('lena512.bmp');oldsize=size(im);newsize=ceil(oldsize./2);rowindex =(((1:newsize(1))-1).*2)+1;colindex =(((1:newsize(2))-1).*2)+1;newim = im(rowindex, colindex, :);subplot(121);imshow(im);title('Original');subplot(122);imshow(newim);title('Downsampling');

Generalize for factor of k:

function newim = downsampling(im, k);oldsize=size(im);newsize=ceil(oldsize./k);rowindex =(((1:newsize(1))-1).*k)+1;colindex =(((1:newsize(2))-1).*k)+1;newim = im(rowindex, colindex, :);subplot(121);imshow(im);title('Original');subplot(122);imshow(newim);title('Downsampling');

7. Quantizationa. Load an grayscale imageb. Quantize this image if 6 bits are used to represent an intensity value. Show the

result

im=imread('lena512.bmp');quantizedIm=im;quantizedIm= floor(quantizedIm/2^3)*2^3;

subplot(121);imshow(im);title('Original');subplot(122);imshow(quantizedIm);title('Quantized Image if 6bits are used');

c. Repeat question b with 4 bits and 1 bit. Show the original image and all the obtained results (from questions b and c) in the same figure.

im=imread('lena512.bmp');quantizedIm6=im;quantizedIm4=im;quantizedIm1=im;quantizedIm6= floor(quantizedIm6/2^3)*2^3;quantizedIm4= floor(quantizedIm4/2^5)*2^5;quantizedIm1= floor(quantizedIm1/2^8)*2^8;subplot(221);imshow(im);title('Original');subplot(222);imshow(quantizedIm6);title('Quantized Image if 6bits are used');subplot(223);imshow(quantizedIm4);title('Quantized Image if 4bits are used');subplot(224);imshow(quantizedIm1);title('Quantized Image if 1bits are used');

8. Statisticsa. Load the grayscale image Lenab. Find the maximum and minimum intensity values of the image

lena = imread('lena512.bmp');im = lena;max = max(im(:))min = min(im(:))

max = 245

min = 25

c. Find the mean, standard deviation and variance of the intensity values

lena = imread('lena512.bmp'); im_double = double(lena); % get number of rows and columns value [r,c] = size(lena); % mean of gray scale image mean = sum(im_double(:))/(r*c) % variance of gray scale image % Compute E{x^2}SquareValue = im_double.^2;meanOfSquare = sum(SquareValue(:))/(r*c);% Compute [E{x}]^2SquareOfMean = mean^2;% Var{x} = E{x^2} - [E{x}]^2variance = meanOfSquare - SquareOfMean

mean = 124.0505variance = 2.2900e+003

d. Divide the image into non-overlapping blocks of 8 x 8 pixels. The mean of the intensity values of each block is then used to represent this block, i.e. each block becomes one pixel. Show this resulting image (with smaller size) and the original one in the same figure

% Read the image.im = imread('lena512.bmp');[rows, cols] = size(im);numBlocksR = rows/8;numBlocksC = cols/8;% Size of each block in rows.blockVectorR = [8 * ones(1, numBlocksR)];% Size of each block in columns.blockVectorC = [8 * ones(1, numBlocksC)];% Divide the image into 16 blocks.divided = mat2cell(im, blockVectorR, blockVectorC);newim = ones(64); %Prepare to create new image.for r = 1 : numBlocksR for c = 1 : numBlocksC newim(r,c) = mean(mean(divided{r,c})); endendsubplot(1,2,1);imshow(im);title('Original Image');subplot(1,2,2);imshow(uint8(newim));title('Resulting Image');