OpenCV Integration

The einit library is designed to work seamlessly with OpenCV and other computer vision libraries. This section covers integration patterns and best practices.

Transformation Matrix Format

einit returns standard 4×4 homogeneous transformation matrices:

T = np.array([
    [R11, R12, R13, tx],
    [R21, R22, R23, ty],
    [R31, R32, R33, tz],
    [0,   0,   0,   1 ]
])

This format is directly compatible with: - OpenCV’s 3D functions - Open3D transformations - PCL (Point Cloud Library) - Standard robotics libraries

Common Integration Patterns

ICP Initialization

import cv2
from einit import register_ellipsoid

# 1. Get initial transformation with einit
T_init = register_ellipsoid(src_points, dst_points)

# 2. Apply initial transformation
src_aligned = apply_transform(src_points, T_init)

# 3. Refine with OpenCV ICP
retval, T_refine, inliers = cv2.estimateAffine3D(
    src_aligned.astype(np.float32),
    dst_points.astype(np.float32),
    confidence=0.99,
    ransacThreshold=0.01
)

# 4. Combine transformations
if retval:
    T_final = np.eye(4)
    T_final[:3, :4] = T_refine
    T_complete = T_final @ T_init
else:
    T_complete = T_init

RANSAC Integration

def robust_alignment(src, dst, max_iterations=1000):
    best_T = None
    best_inliers = 0

    for _ in range(max_iterations):
        # Sample subset of points
        indices = np.random.choice(len(src), min(100, len(src)), replace=False)
        src_sample = src[indices]
        dst_sample = dst[indices]

        # Get transformation
        T_candidate = register_ellipsoid(src_sample, dst_sample)

        # Evaluate on full dataset
        aligned = apply_transform(src, T_candidate)
        distances = np.linalg.norm(aligned - dst, axis=1)
        inliers = np.sum(distances < threshold)

        if inliers > best_inliers:
            best_inliers = inliers
            best_T = T_candidate

    return best_T

Multi-Scale Processing

def multiscale_alignment(src, dst, scales=[1.0, 0.5, 0.25]):
    T_cumulative = np.eye(4)

    for scale in scales:
        # Downsample point clouds
        n_points = int(len(src) * scale)
        indices = np.random.choice(len(src), n_points, replace=False)

        src_scale = src[indices]
        dst_scale = dst[indices]

        # Apply current transformation
        src_transformed = apply_transform(src_scale, T_cumulative)

        # Compute refinement
        T_delta = register_ellipsoid(src_transformed, dst_scale)
        T_cumulative = T_delta @ T_cumulative

    return T_cumulative

Performance Optimization

Preprocessing for Speed

def preprocess_for_alignment(points, target_size=1000):
    """Downsample and clean point cloud for faster processing."""
    if len(points) > target_size:
        # Uniform downsampling
        indices = np.linspace(0, len(points)-1, target_size, dtype=int)
        points = points[indices]

    # Remove outliers (optional)
    centroid = np.mean(points, axis=0)
    distances = np.linalg.norm(points - centroid, axis=1)
    threshold = np.percentile(distances, 95)  # Keep 95% of points
    mask = distances <= threshold

    return points[mask]

Batch Processing

def batch_align_clouds(src_clouds, dst_clouds):
    """Align multiple point cloud pairs efficiently."""
    transformations = []

    for src, dst in zip(src_clouds, dst_clouds):
        # Preprocess for consistency
        src_clean = preprocess_for_alignment(src)
        dst_clean = preprocess_for_alignment(dst)

        # Compute transformation
        T = register_ellipsoid(src_clean, dst_clean)
        transformations.append(T)

    return transformations

Error Handling

Robust Error Checking

def safe_alignment(src, dst, fallback='identity'):
    """Perform alignment with comprehensive error handling."""
    try:
        # Input validation
        if src.shape[0] < 4 or dst.shape[0] < 4:
            raise ValueError("Need at least 4 points for alignment")

        if src.shape != dst.shape:
            raise ValueError("Source and destination must have same shape")

        # Compute transformation
        T = register_ellipsoid(src, dst)

        # Validate result
        if not np.allclose(T[:3, :3] @ T[:3, :3].T, np.eye(3), atol=1e-6):
            raise ValueError("Computed rotation matrix is not orthogonal")

        return T, True

    except Exception as e:
        print(f"Alignment failed: {e}")

        if fallback == 'identity':
            return np.eye(4), False
        elif fallback == 'centroid':
            # Align centroids only
            t = np.mean(dst, axis=0) - np.mean(src, axis=0)
            T = np.eye(4)
            T[:3, 3] = t
            return T, False
        else:
            raise

Integration with Other Libraries

import open3d as o3d

def align_with_open3d(src_pcd, dst_pcd):
    # Convert to numpy arrays
    src_points = np.asarray(src_pcd.points)
    dst_points = np.asarray(dst_pcd.points)

    # Get initial transformation
    T_init = register_ellipsoid(src_points, dst_points)

    # Refine with Open3D ICP
    result = o3d.pipelines.registration.registration_icp(
        src_pcd, dst_pcd,
        max_correspondence_distance=0.1,
        init=T_init
    )

    return result.transformation

import pcl

def align_with_pcl(src_cloud, dst_cloud):
    # Extract points
    src_points = src_cloud.to_array()
    dst_points = dst_cloud.to_array()

    # Get initialization
    T_init = register_ellipsoid(src_points, dst_points)

    # Use PCL's ICP with initialization
    icp = src_cloud.make_IterativeClosestPoint()
    converged, transform, estimate, fitness = icp.icp(dst_cloud, T_init)

    return transform if converged else T_init