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import numpy as np

def monocular_depth_to_metric(depth_map, focal_length, baseline, image_width):
    """
    Convert a monocular depth map to metric depth.
    
    Args:
    depth_map (numpy.ndarray): Depth map from a monocular depth estimation model
    focal_length (float): Focal length of the camera in pixels
    baseline (float): An arbitrary baseline for scale (in meters)
    image_width (int): Width of the image in pixels
    
    Returns:
    numpy.ndarray: Estimated metric depth map
    """
    # Normalize depth map to 0-1 range if not already
    depth_norm = (depth_map - np.min(depth_map)) / (np.max(depth_map) - np.min(depth_map))
    
    # Convert normalized depth to a pseudo-disparity
    pseudo_disparity = 1 / (depth_norm + 1e-6)  # Adding epsilon to avoid division by zero
    
    # Scale factor to convert pseudo-disparity to pixel disparity
    # This is an approximation and may need adjustment
    scale = image_width / (2 * focal_length)
    
    # Estimate pixel disparity
    pixel_disparity = pseudo_disparity * scale
    
    # Convert to metric depth
    metric_depth = (focal_length * baseline) / pixel_disparity
    
    return metric_depth

# Example usage
depth_map = np.random.rand(480, 640)  # Example depth map from a monocular model
focal_length = 500  # Example focal length in pixels
baseline = 0.1  # Arbitrary baseline for scale (in meters)
image_width = 640

metric_depth = monocular_depth_to_metric(depth_map, focal_length, baseline, image_width)

print("Shape of metric depth map:", metric_depth.shape)
print("Min depth:", np.min(metric_depth), "meters")
print("Max depth:", np.max(metric_depth), "meters")