def find_edge_points(cluster_points, grid_shape):
    """
    Identify the edge points of a cluster on a grid.

    Parameters:
    cluster_points (list of tuples): List of (x, y) tuples representing points in the cluster.
    grid_shape (tuple): The shape of the grid (height, width).

    Returns:
    list: A list of (x, y) tuples representing the edge points of the cluster.
    """
    grid = np.zeros(grid_shape, dtype=bool)
    for x, y in cluster_points:
        grid[y, x] = True  # Mark the point as part of the cluster

    eroded_grid = binary_erosion(grid)

    # Edge points are original grid points minus eroded points
    edge_grid = grid & ~eroded_grid
    edge_points = np.argwhere(edge_grid)
    
    return np.array([(x, y) for y, x in edge_points])