[Advanced] Pedestrian Detection in MATLAB Images: Using HOG+SVM for Pedestrian Detection

# 2.1 Histogram of Oriented Gradients (HOG) Features

The Histogram of Oriented Gradients (HOG) is a feature descriptor used to depict the distribution of gradient orientations in localized portions of an image. It involves the following steps:

1. **Image Tiling:** Dividing the image into equal-sized, overlapping tiles.
2. **Gradient Calculation:** Computing the gradient magnitude and direction for each pixel within each tile.
3. **Gradient Quantization:** Quantizing gradient directions into a finite number of bins (e.g., 9 bins).
4. **Histogram Statistics:** Counting the gradient magnitudes within each bin for every tile.
5. **Feature Vector Formation:** Concatenating histograms from each tile to form a feature vector.

# 2. Theoretical Foundations of Image Pedestrian Detection

### 2.1 Histogram of Oriented Gradients (HOG) Features

**2.1.1 The Process of Extracting HOG Features**

HOG features are descriptors based on image gradient information, and their extraction process mainly includes the following steps:

1. **Image Preprocessing:** Applying preprocessing operations such as grayscale conversion, normalization, and gamma correction to the input image to enhance robustness and reduce noise effects.
2. **Gradient Calculation:** Using a Sobel operator or other gradient operators to compute the horizontal and vertical gradients of the image.
3. **Cell Division:** Dividing the image into cells of equal size, typically 8x8 pixels.
4. **Gradient Histogram Calculation:** Calculating the histogram of gradient magnitudes and directions within each cell, usually using 9 bins.
5. **Block Normalization:** Grouping adjacent cells into blocks, typically 2x2 cells. Normalizing the histograms within each block to reduce the effects of lighting variations.
6. **Feature Vector Formation:** Concatenating the normalized histograms of all blocks into a long vector to form the HOG feature vector.

**2.1.2 Advantages and Limitations of HOG Features**

The advantages of HOG features include:

***Robustness:** Strong resilience to changes in lighting, noise, and cluttered backgrounds.
***High Computational Efficiency:** A relatively simple feature extraction process with high computational efficiency.
***Strong Feature Expression:** Effectively capturing the shape and texture information of pedestrians in images.

The limitations of HOG features are:

***Sensitivity to Deformation:** The recognition effect of HOG features may decrease for pedestrians with significant deformations.
***High Feature Dimensionality:** HOG feature vectors usually have high dimensions, which could increase the training and testing time for classifiers.

### 2.2 Support Vector Machine (SVM) Classifier

**2.2.1 Principles of SVM Classifier**

SVM is a binary classification algorithm. Its fundamental principle is to map data points to a high-dimensional feature space and find a hyperplane that separates points of different classes. The selection of the hyperplane satisfies the following conditions:

***Maximizing Margin:** The distance (margin) between the hyperplane and the nearest data points of different classes is maximized.
***Support Vectors:** Data points on the margin boundaries are called support vectors, which play a decisive role in the position of the hyperplane.

**2.2.2 Parameter Selection for SVM Classifier**

The performance of the SVM classifier is affected by the following parameters:

***Kernel Function:** The kernel function determines the mapping method of data points in the feature space, with common kernel functions including linear, polynomial, and Gaussian kernels.
***Penalty Parameter C:** The penalty parameter controls the classifier's tolerance for misclassification. A larger value of C leads to stricter classification but may cause overfitting.
***Kernel Parameter γ (gamma):** The kernel parameter γ controls the shape and range of influence of the kernel function. For the Gaussian kernel, a larger γ value results in a smaller range of influence.

Parameter selection is usually optimized through methods like cross-validation or grid search to achieve the best classification performance.

# 3. Image Pedestrian Detection in Practice with MATLAB

### 3.1 Image Preprocessing and HOG Feature Extraction