Checkerboard Corner Detection

Implement simplified checkerboard corner detection for camera calibration, a crucial step in Structure from Motion and SLAM. This task involves identifying the corners of a checkerboard pattern in an image, which is essential for estimating camera parameters.

Checkerboard corners are used in camera calibration because they provide high precision, known 3D geometry, and are easy to detect. The corners of a checkerboard can be represented by a grid of points in 3D space, with each point having a known position $x_i, y_i, z_i$ . When projected onto a 2D image, these points form a grid of corners, which can be detected using corner detection algorithms.

To detect these corners, the following steps are involved:

Apply a corner detector to the image, which calculates the Harris response $R = \det(\mathbf{M}) - k \cdot \trace^2(\mathbf{M})$ , where $\mathbf{M}$ is the structure tensor.
Filter the detected corners by their pattern, ensuring they form a grid.
Refine the corner locations to sub-pixel accuracy.

R = \det\begin{bmatrix} I_{xx} & I_{xy} \\ I_{xy} & I_{yy} \end{bmatrix} - k \cdot (I_{xx} + I_{yy})^2

This technique is widely used in robotics and computer vision applications, such as autonomous vehicles and augmented reality systems.

Example:

Input:

image = checkerboard image
board_size = (6, 9)  # 6×9 internal corners

Output:

List of 54 corner coordinates

Reasoning:

Harris corners gives many candidates. Filter to keep only those forming 6×9 grid. Refine positions for sub-pixel accuracy.

Constraints:

image: Grayscale image with checkerboard
board_size: (rows, cols) of internal corners
Return: List of corner coordinates

Example:

Constraints:

Test Results