> For the complete documentation index, see [llms.txt](https://ashrithsagar.gitbook.io/s_ip-lab/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://ashrithsagar.gitbook.io/s_ip-lab/experiment-7.md).

# Experiment-7

## Exercises

### Exercise-1

```matlab
%% Experiment - 7
% Exercise - 1
clc;
clear;

%% Read image
img_rgb = imread('lenna.jpg');  % Read image
img_gray = rgb2gray(img_rgb);  % Convert to grayscale
[M, N] = size(img_gray);

%% Histogram of an image without inbuilt function
img_histogram = zeros(256, 1);
for i = 1 : M
   for j = 1 : N
      intensity = img_gray(i, j) + 1;
      img_histogram(intensity) = img_histogram(intensity) + 1;
   end
end

%% Histogram of an image with inbuilt function
img_histogram_imhist = imhist(img_gray);

difference = img_histogram_imhist - img_histogram;
diff = any(difference)

%% Display image
figure;
imshow(img_gray)
title('Original Lenna (512\times 512)')

figure;
plot(img_histogram)
title('Histogram of Lenna')

figure;
plot(img_histogram_imhist)
title('Histogram of Lenna `imhist`')
```

### Exercise-2

```matlab
%% Experiment - 7
% Exercise - 2
clc;
clear;

%% Read image
img_rgb = imread('lenna.jpg');  % Read image
img_gray = rgb2gray(img_rgb);  % Convert to grayscale
[M, N] = size(img_gray);

%% Contrast stretching transformation
% Histogram
img_histogram = zeros(256, 1);
for i = 1 : M
    for j = 1 : N
        intensity = img_gray(i, j) + 1;
        img_histogram(intensity) = img_histogram(intensity) + 1;
    end
end

% Contrast stretching by Histogram Equalisation
contrast_stretch_table = uint8(cumsum(img_histogram) / sum(img_histogram) * 255);

img_contrast_stretched = zeros(M, N);
for i = 1 : M
    for j = 1 : N
        img_contrast_stretched(i, j) = contrast_stretch_table(1 + img_gray(i, j));
    end
end

% Min-Max Normalisation
img_max = max(img_gray, [], 'all');  % Maximum intensity 
img_min = min(img_gray, [], 'all');  % Minimum intensity
img_contrast_stretched_2 = uint8((img_gray - img_min) / (img_max - img_min) * 255);

%% Display image
figure;
imshow(img_gray)
title('Original Lenna (512\times 512)')

figure;
imshow(img_contrast_stretched_2)
title('Contrast Stretched Lenna (512\times 512)')
```

### Exercise-3

```matlab
%% Experiment - 7
% Exercise - 3
clc;
clear;

%% Read image
img_rgb = imread('lenna.jpg');  % Read image
img_gray = rgb2gray(img_rgb);  % Convert to grayscale
[M, N] = size(img_gray);

%% DFT of an image without inbuilt function
img_dft_real = zeros(M, N);  %% DFT results
img_dft_imag = zeros(M, N);  %% DFT results
m = 1 : M; n = 1 : N;
img_input = double(img_gray);

for k = 1 : M
    disp(k);
    for l = 1 : N
        twiddle_matrix_real = (cos(2 * pi * m / M) .^ k) .* (cos(2 * pi * n / N) .^ l);
        img_dft_real(k, l) = sum(img_input .* twiddle_matrix_real, 'all');
        twiddle_matrix_imag = (sin(2 * pi * m / M) .^ k) .* (sin(2 * pi * n / N) .^ l);
        img_dft_imag(k, l) = sum(img_input .* twiddle_matrix_imag, 'all');
    end
end
img_dft_real = 1/(M * N) * img_dft_real;
img_dft_imag = 1/(M * N) * img_dft_imag;
img_dft = img_dft_real - i * img_dft_imag;

%% Display image
figure;
imshow(img_gray)
title('Original Lenna (512\times 512)')

figure;
plot(img_dft)
title('DFT of Lenna')
```

### Exercise-4

```matlab
%% Experiment - 7
% Exercise - 4
clc;
clear;

%% Read image
img_rgb = imread('lenna.jpg');  % Read image
img_gray = rgb2gray(img_rgb);  % Convert to grayscale
[M, N] = size(img_gray);

%% Image reconstruction from DFT without inbuilt function
% DFT of an image without inbuilt function
img_dft_real = zeros(M, N);  %% DFT results
img_dft_imag = zeros(M, N);  %% DFT results
m = 1 : M; n = 1 : N;
img_input = double(img_gray);

for k = 1 : M
    disp(k);
    for l = 1 : N
        twiddle_matrix_real = (cos(2 * pi * m / M) .^ k) .* (cos(2 * pi * n / N) .^ l);
        img_dft_real(k, l) = sum(img_input .* twiddle_matrix_real, 'all');
        twiddle_matrix_imag = (sin(2 * pi * m / M) .^ k) .* (sin(2 * pi * n / N) .^ l);
        img_dft_imag(k, l) = sum(img_input .* twiddle_matrix_imag, 'all');
    end
end
img_dft_real = 1/(M * N) * img_dft_real;
img_dft_imag = 1/(M * N) * img_dft_imag;
img_dft = img_dft_real - i * img_dft_imag;

% Inverse DFT
img_idft = zeros(M, N);  %% IDFT results
m = 1 : M; n = 1 : N;

for k = 1 : M
    disp(k);
    for l = 1 : N
        twiddle_matrix_real = (cos(2 * pi * m / M) .^ k) .* (cos(2 * pi * n / N) .^ l);
        img_idft_real(k, l) = sum(img_dft .* twiddle_matrix_real, 'all');
        twiddle_matrix_imag = (sin(2 * pi * m / M) .^ k) .* (sin(2 * pi * n / N) .^ l);
        img_idft_imag(k, l) = sum(img_dft .* twiddle_matrix_imag, 'all');
    end
end
img_idft_real = 1/(M * N) * img_idft_real;
img_idft_imag = 1/(M * N) * img_idft_imag;
img_idft = img_idft_real + i * img_idft_imag;

%% Display image
figure;
imshow(img_gray)
title('Original Lenna (512\times 512)')

figure;
imshow(img_idft)
title('Reconstructed image from DFT of Lenna (512\times 512)')
```

### Exercise-5

```matlab
%% Experiment - 7
% Exercise - 5
clc;
clear;

%% Read image
img_rgb = imread('lenna.jpg');  % Read image
img_gray = rgb2gray(img_rgb);  % Convert to grayscale
[M, N] = size(img_gray);

%% DFT Transformation and Reconstruction
% DFT of an image with inbuilt function
img_dft = fft2(img_gray);

% Reconstruction of image from DFT with inbuilt function
img_reconstructed = uint8(ifft2(img_dft));

%% Display image
figure;
imshow(img_gray)
title('Original Lenna (512\times 512)')

figure;
plot(img_dft)
title('DFT of Lenna')

figure;
plot(abs(img_dft))
title('Magnitude spectrum of DFT of Lenna')

figure;
imshow(img_reconstructed);
title('Reconstructed image from DFT of Lenna (512\times 512)')
```

### Exercise-6

```matlab
%% Experiment - 7
% Exercise - 1
clc;
clear;

%% Read image
img_rgb = imread('lenna.jpg');  % Read image
img_gray = rgb2gray(img_rgb);  % Convert to grayscale
[M, N] = size(img_gray);

%% DFT of a rotated image
img_rotated = imrotate(img_gray, 90);
img_rotated_dft = fft2(img_rotated);

%% Display image
figure;
imshow(img_gray)
title('Original Lenna (512\times 512)')

figure;
plot(img_rotated_dft)
title('DFT of Rotated Lenna')

figure;
plot(abs(img_rotated_dft))
title('Magnitude spectrum of DFT of Rotated Lenna')
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://ashrithsagar.gitbook.io/s_ip-lab/experiment-7.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.