Image Scaling and Rotation in MATLAB: Implementing Geometric Transformations

# 2.1 Image Scaling and Resizing

## 2.1.1 Using the imresize Function

The `imresize` function is a commonly used tool in MATLAB for image scaling. It accepts an input image and a scale factor as parameters and returns a resized image. The scale factor is a number that represents the scaling ratio for each dimension of the image. For example, an image with a scale factor of 2 will be enlarged to twice its original size.

% Load an image
image = imread('image.jpg');

% Resize the image to twice its original size
resized_image = imresize(image, 2);

% Resize the image to half its original size
resized_image = imresize(image, 0.5);

# 2. MATLAB Image Scaling in Practice

## 2.1 Image Scaling and Resizing

### 2.1.1 Using the imresize Function

MATLAB provides the `imresize` function for image scaling. This function takes an image and a scale factor as input and returns the scaled image. The scale factor is a scalar or vector that specifies the scaling ratio for each dimension of the image.

% Read an image
image = imread('image.jpg');

% Scale the image to double its size
resized_image = imresize(image, 2);

% Scale the image down to half its size
resized_image = imresize(image, 0.5);

**Parameter Explanation:**

* `image`: The input image
* `scale`: The scale factor, which can be a scalar or vector
* `method`: The interpolation method, defaulting to `'bilinear'`, with other options including `'nearest'`, `'bicubic'`, `'lanczos3'`

**Code Logic:**

1. The `imresize` function resizes the image according to the specified scale factor.
2. If the scale factor is greater than 1, the image is enlarged; if less than 1, the image is reduced.
3. The interpolation method determines the pixel values of the resized image.

#### 2.1.2 Using Interpolation Methods

The `imresize` function supports various interpolation methods, including:

* `'nearest'`: Nearest neighbor interpolation, which selects the original pixel value closest to the scaled pixel's location
* `'bilinear'`: Bilinear interpolation, which uses the weighted average of original pixel values to calculate the scaled pixel value
* `'bicubic'`: Bicubic interpolation, which uses the weighted average and derivatives of original pixel values to calculate the scaled pixel value
* `'lanczos3'`: Lanczos interpolation, which uses a Lanczos filter to calculate the scaled pixel value

Different interpolation methods can produce different image qualities. The `'bilinear'` method is generally used for fast resizing, while `'bicubic'` and `'lanczos3'` provide higher image quality but at a higher computational cost.

## 2.2 Image Cropping and Mosaicking

### 2.2.1 Using the imcrop Function

The `imcrop` function is used to crop a rectangular area from an image. It takes an image and rectangle coordinates as inputs and returns the cropped image.

% Read an image
image = imread('image.jpg');

% Crop the top-left corner region of the image
cropped_image = imcrop(image, [0, 0, 100, 100]);

**Parameter Explanation:**

* `image`: The input image
* `rect`: Rectangle coordinates in the format `[x, y, width, height]`

**Code Logic:**

1. The `imcrop` function crops a region from the image based on the specified rectangle coordinates.
2. Rectangle coordinates specify the location and size of the top-left corner of the cropping area.
3. The cropped image contains only the pixels within the rectangular area.

### 2.2.2 Using the montage Function

The `montage` function is used to mosaic multiple images into a grid. It takes an array of images and the grid size as inputs and returns the mosaicked image.

% Read an array of images
images = {imread('image1.jpg'), imread('image2.jpg'), imread('image3.jpg')};

% Mosaic the images
mosaicked_image = montage(images);

**Parameter Explanation:**

* `images`: Array of images
* `layout`: Grid size, specified as `[rows, cols]`

**Code Logic:**

1. The `montage` function mosaics the array of images into a grid.
2. Grid size specifies the number of rows and columns of images in the mosaicked image.
3. The mosaicked image contains thumbnails of all the images, arranged in a grid.

# 3. MATLAB Image Rotating Practice

### 3.1 Clockwise and Counterclockwise Image Rotation

#### 3.1.1 Using the imrotate Function

The `imro