Kursinhalt

Computer Vision Essentials

1. Introduction to Computer Vision

What is Computer Vision?Fundamentals of Image Processing Linear Algebra for Image Manipulation

2. Image Processing with OpenCV

Basic Transformations Fourier Transform Low-pass and High-pass Filters Noise Reduction and Smoothing Histogram Equalization Super-Resolution Techniques Edge Detection Corner and Blob Detection

3. Convolutional Neural Networks

Introduction to Convolutional Neural Networks Convolution Layers Pooling Layers Flattening Activation Functions Overview of Popular CNN Models Challenge: Building a CNN

4. Object Detection

Object Localization Object Detection Bounding Box Predictions Intersection Over Union (IoU) and Evaluation Metrics Non-Max Suppression (NMS)Anchor Boxes YOLO Model Overview Challenge: Object Detection with Custom Model and YOLO

5. Advanced Topics Overview

Transfer Learning in Computer Vision Overview of Face Recognition Overview of Image Generation

Intersection Over Union (IoU) and Evaluation Metrics

How It's Computed

Mathematically, IoU is given by:

Where:

Area of Overlap is the intersection of the predicted and actual bounding boxes;
Area of Union is the total area covered by both boxes.


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import numpy as np

def compute_iou(boxA, boxB):
    # Extract coordinates
    xA = max(boxA[0], boxB[0])
    yA = max(boxA[1], boxB[1])
    xB = min(boxA[2], boxB[2])
    yB = min(boxA[3], boxB[3])
    
    # Compute intersection area
    interArea = max(0, xB - xA) * max(0, yB - yA)
    
    # Compute areas of both boxes
    boxAArea = (boxA[2] - boxA[0]) * (boxA[3] - boxA[1])
    boxBArea = (boxB[2] - boxB[0]) * (boxB[3] - boxB[1])
    
    # Compute union area
    unionArea = boxAArea + boxBArea - interArea
    
    # Compute IoU
    iou = interArea / unionArea
    return iou

# Example usage
box1 = [50, 50, 150, 150]  # [x1, y1, x2, y2]
box2 = [100, 100, 200, 200]
iou_score = compute_iou(box1, box2)
print("IoU Score:", iou_score)

IoU as a Metric for Bounding Box Accuracy

IoU is commonly used to assess how well a predicted bounding box aligns with the ground truth. Higher IoU values indicate better alignment, with an IoU of 1.0 meaning perfect overlap and 0.0 meaning no overlap at all.

Thresholding IoU for True Positives and False Positives

To determine whether a detection is correct (true positive) or incorrect (false positive), a threshold for IoU is typically set. Commonly used thresholds include:

IoU > 0.5: considered a True Positive (TP);
IoU < 0.5: considered a False Positive (FP).

Setting higher IoU thresholds increases precision but may decrease recall since fewer detections meet the criteria.

Evaluation Metrics: Precision, Recall, and mAP

In addition to IoU, other evaluation metrics help assess object detection models:

Precision: measures the proportion of correctly predicted bounding boxes among all predictions;

\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}}

Recall: measures the proportion of correctly predicted bounding boxes among all ground truth objects;

\text{Recall}=\frac{\text{TP}}{\text{TP}+\text{FN}}

Mean Average Precision (mAP): computes the average precision across different IoU thresholds and object categories, providing a comprehensive evaluation of model performance.


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def precision_recall(tp, fp, fn):
    precision = tp / (tp + fp) if (tp + fp) > 0 else 0
    recall = tp / (tp + fn) if (tp + fn) > 0 else 0
    return precision, recall

# Example usage
tp, fp, fn = 50, 10, 20
precision, recall = precision_recall(tp, fp, fn)
print(f"Precision: {precision:.2f}, Recall: {recall:.2f}")

IoU serves as a fundamental metric in evaluating object detection models, helping assess the accuracy of predicted bounding boxes. By combining IoU with precision, recall, and mAP, researchers and engineers can fine-tune their models to achieve higher detection accuracy and reliability.

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Abschnitt 4. Kapitel 4

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Kursinhalt

Computer Vision Essentials

1. Introduction to Computer Vision

What is Computer Vision?Fundamentals of Image Processing Linear Algebra for Image Manipulation

2. Image Processing with OpenCV

Basic Transformations Fourier Transform Low-pass and High-pass Filters Noise Reduction and Smoothing Histogram Equalization Super-Resolution Techniques Edge Detection Corner and Blob Detection

3. Convolutional Neural Networks

Introduction to Convolutional Neural Networks Convolution Layers Pooling Layers Flattening Activation Functions Overview of Popular CNN Models Challenge: Building a CNN

4. Object Detection

5. Advanced Topics Overview

Transfer Learning in Computer Vision Overview of Face Recognition Overview of Image Generation

Intersection Over Union (IoU) and Evaluation Metrics

How It's Computed

Mathematically, IoU is given by:

Where:

Area of Overlap is the intersection of the predicted and actual bounding boxes;
Area of Union is the total area covered by both boxes.


              12345678910111213141516171819202122232425262728
            
import numpy as np

def compute_iou(boxA, boxB):
    # Extract coordinates
    xA = max(boxA[0], boxB[0])
    yA = max(boxA[1], boxB[1])
    xB = min(boxA[2], boxB[2])
    yB = min(boxA[3], boxB[3])
    
    # Compute intersection area
    interArea = max(0, xB - xA) * max(0, yB - yA)
    
    # Compute areas of both boxes
    boxAArea = (boxA[2] - boxA[0]) * (boxA[3] - boxA[1])
    boxBArea = (boxB[2] - boxB[0]) * (boxB[3] - boxB[1])
    
    # Compute union area
    unionArea = boxAArea + boxBArea - interArea
    
    # Compute IoU
    iou = interArea / unionArea
    return iou

# Example usage
box1 = [50, 50, 150, 150]  # [x1, y1, x2, y2]
box2 = [100, 100, 200, 200]
iou_score = compute_iou(box1, box2)
print("IoU Score:", iou_score)

IoU as a Metric for Bounding Box Accuracy

Thresholding IoU for True Positives and False Positives

To determine whether a detection is correct (true positive) or incorrect (false positive), a threshold for IoU is typically set. Commonly used thresholds include:

IoU > 0.5: considered a True Positive (TP);
IoU < 0.5: considered a False Positive (FP).

Setting higher IoU thresholds increases precision but may decrease recall since fewer detections meet the criteria.

Evaluation Metrics: Precision, Recall, and mAP

In addition to IoU, other evaluation metrics help assess object detection models:

Precision: measures the proportion of correctly predicted bounding boxes among all predictions;

\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}}

Recall: measures the proportion of correctly predicted bounding boxes among all ground truth objects;

\text{Recall}=\frac{\text{TP}}{\text{TP}+\text{FN}}

Mean Average Precision (mAP): computes the average precision across different IoU thresholds and object categories, providing a comprehensive evaluation of model performance.


              123456789
            
def precision_recall(tp, fp, fn):
    precision = tp / (tp + fp) if (tp + fp) > 0 else 0
    recall = tp / (tp + fn) if (tp + fn) > 0 else 0
    return precision, recall

# Example usage
tp, fp, fn = 50, 10, 20
precision, recall = precision_recall(tp, fp, fn)
print(f"Precision: {precision:.2f}, Recall: {recall:.2f}")

War alles klar?

Danke für Ihr Feedback!

Abschnitt 4. Kapitel 4

Computer Vision Essentials

Intersection Over Union (IoU) and Evaluation Metrics

How It's Computed

IoU as a Metric for Bounding Box Accuracy

Thresholding IoU for True Positives and False Positives

Evaluation Metrics: Precision, Recall, and mAP

1. What does Intersection over Union (IoU) measure in object detection?

2. Which of the following is considered a false negative in object detection?

3. How is Precision calculated in object detection?

Computer Vision Essentials

Intersection Over Union (IoU) and Evaluation Metrics

How It's Computed

IoU as a Metric for Bounding Box Accuracy

Thresholding IoU for True Positives and False Positives

Evaluation Metrics: Precision, Recall, and mAP

1. What does Intersection over Union (IoU) measure in object detection?

2. Which of the following is considered a false negative in object detection?

3. How is Precision calculated in object detection?