Summary  
This chapter covers geometric image transformations—resizing via scaling factors or explicit dimensions, rotating with affine matrices, and cropping through array slicing.  

General domain of usage  
Image processing

**OpenCV (Open Source Computer Vision Library)** is a powerful open-source library designed for real-time computer vision and image processing. It provides tools for manipulating images, detecting objects, and even working with deep learning models.

Definition

## Reading and Displaying an Image
Before performing transformations, let's first load and display an image using OpenCV. We have already imported the photo. But in your local computer for simple reading and displaying the photo you should use:

```
import cv2

image = cv2.imread('path/to/image.jpg')
cv2.imshow('Image title', image)
```

## Resizing an Image

Resizing is useful for scaling images up or down while maintaining aspect **ratio** (`fx` and `fy` parameters),
where `fx` and `fy` define the scaling factor for width and height.

```
resized_image = cv2.resize(image, fx=0.7, fy=0.5)
```

You can also specify **exact pixel dimensions** (`dsize` parameter),
where `dsize` is `(new_y, new_x)` output shape.

```
resized = cv2.resize(image, (100, 100))
```

## Rotating an Image
To rotate an image by a specific angle, we use `cv2.getRotationMatrix2D()` and `cv2.warpAffine()`.

- `cv2.getRotationMatrix2D(center, angle, scale)` defines the rotation matrix;
- `cv2.warpAffine(image, matrix, output_size)` applies the transformation.

```
height, width = image.shape[:2]
centre = (width // 2, height // 2)

rotation_matrix = cv2.getRotationMatrix2D(centre, 180, 1)
rotated = cv2.warpAffine(image, rotation_matrix, (width, height))
```


## Cropping an Image
Cropping extracts a specific region from an image. It's done using NumPy slicing.
The syntax `image[start_y:end_y, start_x:end_x]` selects a region of interest.

```
cropped = image[450:500, 250:350]
```

import unittest
import importlib
import numpy as np
import cv2

def _dynamic_test(test_case, condition, success_message, failure_message):
    if condition:
        test_case._testMethodName = success_message
        test_case.assertTrue(True, success_message)
    else:
        test_case._testMethodName = failure_message
        test_case.fail(failure_message)

class TestImageProcessing(unittest.TestCase):

    @classmethod
    def setUpClass(cls):
        global user_code
        user_code = importlib.import_module("user_code")

    def test_variables_existence_and_types(self):
        """Check all necessary variables are declared and have correct types."""

        variables_to_check = {
            'image': np.ndarray,
            'resized': np.ndarray,
            'rotation_matrix': np.ndarray,
            'rotated': np.ndarray,
            'cropped': np.ndarray,
        }

        for var_name, expected_type in variables_to_check.items():
            with self.subTest(variable=var_name):
                var = getattr(user_code, var_name, None)
                condition = var is not None and isinstance(var, expected_type)
                if var is None:
                    failure_message = f"The variable `{var_name}` is not declared."
                elif not isinstance(var, expected_type):
                    failure_message = f"The variable `{var_name}` should be of type `{expected_type.__name__}`, but got `{type(var).__name__}`."
                else:
                    failure_message = ""
                _dynamic_test(
                    self,
                    condition,
                    f"The variable `{var_name}` exists and has the correct type `{expected_type.__name__}`.",
                    failure_message
                )

    def test_resized_image_shape(self):
        """Check that the resized image has the correct shape (100, 100)."""
        expected_shape = (100, 100)
        actual_shape = user_code.resized.shape[:2]

        _dynamic_test(
            self,
            actual_shape == expected_shape,
            f"The resized image has the correct shape {expected_shape}.",
            f"Expected resized image shape {expected_shape}, but got {actual_shape}."
        )

    def test_rotation_matrix_correctness(self):
        """Check that the rotation matrix is correctly computed."""
        height, width = user_code.image.shape[:2]
        expected_matrix = cv2.getRotationMatrix2D((width // 2, height // 2), 90, 1)

        try:
            np.testing.assert_array_almost_equal(user_code.rotation_matrix, expected_matrix, decimal=5)
            condition = True
            success_message = "The rotation matrix matches the expected values."
            failure_message = "Rotation matrix mismatch (values differ)."
        except AssertionError:
            condition = False
            success_message = "Rotation matrix check unexpectedly passed."  # needed to avoid UnboundLocalError
            failure_message = "Rotation matrix mismatch (values differ)."

        _dynamic_test(
            self,
            condition,
            success_message,
            failure_message
        )

    def test_rotated_image_shape_matches_original(self):
        """Check that the rotated image shape matches the original image shape."""
        original_shape = user_code.image.shape
        rotated_shape = user_code.rotated.shape

        _dynamic_test(
            self,
            original_shape == rotated_shape,
            "The rotated image shape matches the original image shape.",
            f"Expected rotated image shape {original_shape}, but got {rotated_shape}."
        )

    def test_cropped_image_shape_correctness(self):
        """Check that the cropped image has the correct dimensions."""
        cropped_height, cropped_width = user_code.cropped.shape[:2]
        expected_shape = (450 - 100, 600 - 250)

        _dynamic_test(
            self,
            (cropped_height, cropped_width) == expected_shape,
            f"The cropped image has the correct dimensions {expected_shape}.",
            f"Expected cropped image dimensions {expected_shape}, but got {(cropped_height, cropped_width)}."
        )

    def test_cropped_image_pixel_values(self):
        """Check that the cropped image matches the expected pixel values."""
        expected_cropped = user_code.image[100:450, 250:600]

        try:
            np.testing.assert_array_equal(user_code.cropped, expected_cropped)
            condition = True
            success_message = "The cropped image contains the correct pixel values."
            failure_message = "Cropped pixel values mismatch (values differ)."
        except AssertionError:
            condition = False
            success_message = "Cropped pixel values check unexpectedly passed."
            failure_message = "Cropped pixel values mismatch (values differ)."

        _dynamic_test(
            self,
            condition,
            success_message,
            failure_message
        )

if __name__ == "__main__":
    unittest.main()


test_code.py

Comprehensive introduction to Computer Vision, focusing on machine perception and interpretation of visual data. Covers image preprocessing, feature extraction, object detection, and deep learning techniques used in modern vision systems.

Computer vision enables machines to interpret and analyze visual data, mimicking human perception. This section covers the basics of image representation, color models, and mathematical foundations essential for understanding how computers process images. You'll explore real-world applications, from autonomous vehicles to medical imaging, and learn how Computer vision integrates with AI and machine learning. 

OpenCV is a powerful library for image manipulation and computer vision tasks. This section covers essential techniques like image filtering, transformations, edge detection, and segmentation. You'll learn how to perform blurring, thresholding, contour detection, and feature extraction to enhance and analyze images efficiently.

CNNs process visual data using convolution, pooling, and activation layers to extract features for tasks like image classification and object detection. Key components include padding, convolution for feature extraction, pooling for complexity reduction, and activation for non-linearity. Popular architectures like AlexNet, VGG, and ResNet power AI in healthcare, autonomy, and security.

Object detection is a fundamental task in computer vision that involves identifying and localizing objects within an image. Unlike image classification, which assigns a single label to an entire image, object detection not only classifies objects but also determines their positions using bounding boxes. This section covers key techniques and algorithms used in object detection, ranging from traditional methods to deep learning-based approaches like YOLO and U-Net.

Computer vision has significantly advanced over the years, shifting from basic image processing methods to complex deep learning techniques. This section delves into the latest innovations in computer vision, focusing on transfer learning, facial recognition, and image generation. We will explore the benefits of pre-trained models on performance, the principles of facial recognition technology, and the way AI creates images through deep learning.

Basic Transformations

Reading and Displaying an Image

Resizing an Image

Rotating an Image

Cropping an Image

解答