From Pixels to Patterns: Mastering Harris Corner Detection in Computer Vision

In computer vision, corner detection is a critical technique used to extract meaningful information from images. One of the most popular algorithms for this task is Harris Corner Detection. In this article, we will dive deep into the mathematics behind Harris Corner Detection and implement it in Python using OpenCV. We will also display both the original image and the result of the Harris Corner Detection.

What is Harris Corner Detection?

Harris Corner Detection is an algorithm developed by Chris Harris and Mike Stephens in 1988 for corner detection. It is widely used due to its robustness and accuracy in detecting corners in an image.

Mathematics Behind Harris Corner Detection

The Harris Corner Detection algorithm works by examining the change in intensity in all directions in a local neighborhood of a pixel. The fundamental idea is that a corner exists where there is a significant change in intensity in multiple directions.

Step-by-Step Mathematical Explanation

1. Gradient Computation: Compute the gradient of the image intensity at each pixel. This is done using the Sobel operator to get the gradients in the x and y directions.

   $$I_x=\frac{\mathrm{\partial }I}{\mathrm{\partial }x},I_y=\frac{\mathrm{\partial }I}{\mathrm{\partial }\mathrm{y}}$$

2. Structure Tensor: Compute the structure tensor (also known as the second-moment matrix) for each pixel. The structure tensor is a 2x2 matrix that summarizes the gradient information in a local neighborhood around the pixel.

   $$M=\left[\begin{array}{cc}{I}_x^2& I_x{I}_y\\ I_x{I}_y& I_y^2\end{array}\right]$$

3. Corner Response Function: Compute the corner response function $R$ for each pixel using the determinant and trace of the structure tensor. The response function is given by:

   $$R=\det (M)-k\cdot (\text{trace}(M){)}^2$$

   Where:

   • $\det(M) = I_x^2 I_y^2 - (I_x I_y)^2$
     
   • $\text{trace}(M) = I_x^2 + I_y^2$
   • $k$ is a constant (usually $0.04$ to $0.06$)

4. Thresholding: Apply a threshold to the corner response function to identify significant corners. Typically, a pixel is considered a corner if $R$ is above a certain threshold.

Implementing Harris Corner Detection in Python

Let's implement the Harris Corner Detection algorithm in Python using OpenCV. We will also modify the code to display both the original image and the result of the Harris Corner Detection side by side.

For the complete source code and more insights, visit GitHub repository.

Explanation of the Code

1. Loading and Preprocessing the Image:

   • The image is loaded using cv2.imread.
   • It is converted to grayscale using cv2.cvtColor.

2. Applying Harris Corner Detection:

   • The grayscale image is converted to float32 type.
   • The cv2.cornerHarris function is used to detect corners.

3. Marking Corners on the Image:

   • The result of the corner detection is dilated for marking the corners.
   • A threshold is applied to identify significant corners, which are then marked in red.

4. Displaying the Results:

   • The original image and the Harris Corner Detection image are displayed side by side using Matplotlib.

Conclusion

Harris Corner Detection is a powerful technique for detecting corners in images. By understanding the mathematics behind the algorithm and implementing it in Python, you can effectively identify and visualize corners in various images. The source code provided here can be further extended to process multiple images and integrate with other computer vision tasks.

Feel free to experiment with different images and parameters to see how the algorithm performs. Happy coding!