如何将rgb视频转换为灰度并保存？

import cv2

def convert_rgb_to_gray_video(rgb_video_path, output_path):
    video = cv2.VideoCapture(rgb_video_path)
    
    width = int(video.get(cv2.CAP_PROP_FRAME_WIDTH))
    height = int(video.get(cv2.CAP_PROP_FRAME_HEIGHT))
    fps = video.get(cv2.CAP_PROP_FPS)
    fourcc = cv2.VideoWriter_fourcc(*'mp4v')
    output = cv2.VideoWriter(output_path, fourcc, fps, (width, height), 0)
    
    while True:
        ret, frame = video.read()
        if not ret:
            break
        gray_frame = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
        output.write(gray_frame)
    
    video.release()
    output.release()

# 使用示例
convert_rgb_to_gray_video('path/to/rgb/video.mp4', 'path/to/grayscale/video.mp4')