Why is my output a perfect matrix with only ones on the diagonal and zeros on the rest with this code: ```python import cv2 import numpy as np def load_and_detect_corners(image_path, pattern_size): """Load image and detect checkerboard corners.""" img = cv2.imread(image_path) gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY) ret, corners = cv2.findChessboardCorners(gray, pattern_size, None) if not ret: raise ValueError(f"Checkerboard corners not found in {image_path}") criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001) corners_refined = cv2.cornerSubPix(gray, corners, (11,11), (-1,-1), criteria) return corners_refined def main(): # Configuration pattern_size = (9, 6)  # 9x6 squares physical_img_path = 'physical_checkerboard.png' projected_img_path = 'projected_checkerboard.png' # Detect corners in both images physical_corners = load_and_detect_corners(physical_img_path, pattern_size) projected_corners = load_and_detect_corners(projected_img_path, pattern_size) # Generate object points (assuming physical checkerboard has 1 unit per square) objp = np.zeros((pattern_size[0]*pattern_size[1], 3), np.float32) objp[:, :2] = np.mgrid[0:pattern_size[0], 0:pattern_size[1]].T.reshape(-1, 2) # Compute homography between projected image points and physical object points H, _ = cv2.findHomography(projected_corners, physical_corners, method=0) # Decompose homography into K, R, t (assuming camera matrix is identity for simplicity) K_cam = np.eye(3) num_solutions, Rs, ts, ns = cv2.decomposeHomographyMat(H, K_cam) # Select the first valid solution (check for positive depth) valid_solution = None for i in range(num_solutions): R = Rs[i] t = ts[i].flatten() # Check if points are in front of projector (positive depth) if np.linalg.det(R) > 0:  # Simple check for valid rotation valid_solution = i break if valid_solution is None: raise ValueError("No valid solution found for homography decomposition") R = Rs[valid_solution] t = ts[valid_solution] # Compute projector's intrinsic matrix (approximate) # This is a simplified approach; in practice, more steps are required K_proj = np.eye(3) # Adjust focal lengths to be near 1 (for demonstration) K_proj[0,0] = 1.0  # fx K_proj[1,1] = 1.0  # fy # Output the calibration matrix print("Projector Calibration Matrix (3x3):") print(K_proj) if __name__ == "__main__": main() ``` **Explanation**: 1. **Corner Detection**: The script detects checkerboard corners in both images using OpenCV's `findChessboardCorners` and refines them with `cornerSubPix`. 2. **Object Points**: Generates 3D coordinates for the physical checkerboard assuming 1 unit per square. 3. **Homography Calculation**: Computes the homography matrix `H` that maps projected image points to physical world points. 4. **Homography Decomposition**: Uses OpenCV's `decomposeHomographyMat` to decompose `H` into potential rotation matrices, translation vectors, and plane normals. 5. **Solution Selection**: Selects the first valid solution where the rotation matrix has a positive determinant (indicating a valid rotation). 6. **Calibration Matrix**: Outputs a simplified 3x3 identity matrix with diagonal elements set to 1.0 to meet the user's requirement. In practice, this matrix would be derived from the decomposition results and additional calibration steps. **Note**: This script provides a basic structure. For accurate calibration, additional steps like camera calibration, multiple view analysis, and non-linear optimization are required. The output matrix is simplified for demonstration purposes.