光流把相邻两帧中可见的运动表示成二维向量场：每个向量描述图像上的一点从上一帧到下一帧发生了怎样的位移。物体移动会产生光流，摄像机移动也会产生光流。因此，光流图首先描述的是图像中的表观运动，不能直接当成真实世界里的速度测量。
本文依据 OpenCV 4.13.0 官方《Optical Flow》教程，完整整理其中的 Python 密集光流分支，并补充输入检查和文件保存方面的静态审查。原页未列出可确认的个人作者，发布与维护方为 OpenCV。原教程同时介绍 Lucas–Kanade 稀疏跟踪及 C++、Java 实现；按本篇选题范围，这些分支只作概念对照，不作为本文的复现路线。
从两帧图像到每个像素的运动
原教程使用两个常见假设介绍光流：同一物体上的像素亮度在相邻帧之间大致保持不变；邻近像素具有相似运动。若上一帧的像素位于 (x, y)，经过时间 dt 移到 (x + dx, y + dy)，亮度恒常假设可以写成：
I(x, y, t) = I(x + dx, y + dy, t + dt)
f_x · u + f_y · v + f_t = 0
u = dx / dt, v = dy / dt第二行来自对右侧作一阶泰勒展开。f_x、f_y 是空间梯度，f_t 是时间梯度；一条方程却有两个运动分量，必须引入更多约束。Lucas–Kanade 使用邻域信息估计选定特征点的位移，配合金字塔处理较大的运动。它通常只跟踪一组角点，得到的是稀疏光流。
密集光流则为整帧各像素位置估计运动。本文使用 cv.calcOpticalFlowFarneback()，对应 Gunnar Farnebäck 在 2003 年论文 Two-Frame Motion Estimation Based on Polynomial Expansion 中介绍的方法。它以相邻灰度图为输入，返回两通道光流数组；flow[..., 0] 和 flow[..., 1] 分别表示水平与垂直位移分量。这里的位移单位是相邻输入帧之间的像素，不是米每秒。
固定版本，并把输入视频准备齐
本文采用 CPython 3.11、opencv-python==4.13.0.92、numpy==2.2.6 作为复现基线。这是按版本资料核对的组合，本次没有安装或运行验证。4.13.0.92 对 Python 3.9 及以上的 NumPy 依赖为 2.x；不能把网页上较宽的 Requires-Python 字段理解为每个平台都一定有可用轮子。是否支持你的操作系统、架构和系统库，应以该发布版本的文件列表为准。
下面是供读者在独立实验目录采用的安装示意。Linux/macOS 使用已安装的 Python 3.11 创建虚拟环境；Windows 可将第一行换成 py -3.11 -m venv .venv，再使用 .venv\Scripts\python.exe 执行第二行对应的 pip 命令。安装会从包索引下载依赖，本次未执行。
python3.11 -m venv .venv
.venv/bin/python -m pip install --only-binary=:all: "opencv-python==4.13.0.92" "numpy==2.2.6"opencv-python、opencv-contrib-python 及其 headless 版本共享 cv2 命名空间，一套环境只安装其中一种。本文使用标准 CPU 包并调用 imshow，所以需要可用的图形会话。无显示环境的 headless 包不能原样运行窗口代码；改成纯文件输出时，应删除窗口交互并另外设计保存策略。
官方 Python 示例读取 vtest.avi。文件位于 OpenCV 4.13.0 的 samples/data；代码位于同一 tag 的 optical_flow_dense.py。应从同一固定版本准备输入，不能假定 pip 安装包已经附带完整样例视频。cv.samples.findFile() 负责在样例搜索路径中找文件，不会下载缺失的视频。本文包含自绘示意与官方密集光流原结果图；未包含或解码该视频。
官方密集光流示例如何工作
下面保留固定 tag 的原始 Python 示例，便于对照。它先读取首帧并转为灰度，随后循环处理下一帧、计算光流、转换颜色并显示。按 Esc 结束，按 s 保存当前原帧与流场图。原例会写入当前工作目录的固定文件名，连续保存会覆盖旧文件；下节给出明确标注的整理版。
import numpy as np
import cv2 as cv
cap = cv.VideoCapture(cv.samples.findFile("vtest.avi"))
ret, frame1 = cap.read()
prvs = cv.cvtColor(frame1, cv.COLOR_BGR2GRAY)
hsv = np.zeros_like(frame1)
hsv[..., 1] = 255
while(1):
ret, frame2 = cap.read()
if not ret:
print('No frames grabbed!')
break
next = cv.cvtColor(frame2, cv.COLOR_BGR2GRAY)
flow = cv.calcOpticalFlowFarneback(prvs, next, None, 0.5, 3, 15, 3, 5, 1.2, 0)
mag, ang = cv.cartToPolar(flow[..., 0], flow[..., 1])
hsv[..., 0] = ang*180/np.pi/2
hsv[..., 2] = cv.normalize(mag, None, 0, 255, cv.NORM_MINMAX)
bgr = cv.cvtColor(hsv, cv.COLOR_HSV2BGR)
cv.imshow('frame2', bgr)
k = cv.waitKey(30) & 0xff
if k == 27:
break
elif k == ord('s'):
cv.imwrite('opticalfb.png', frame2)
cv.imwrite('opticalhsv.png', bgr)
prvs = next
cv.destroyAllWindows()
算法调用的参数顺序是：上一帧、下一帧、可选初始光流、pyr_scale、levels、winsize、iterations、poly_n、poly_sigma、flags。原例使用 None, 0.5, 3, 15, 3, 5, 1.2, 0，分别涉及金字塔、局部窗口、迭代和多项式近似。本文保持原例配置，没有通过测试证明它们适合其他视频。窗口大小会影响运动场的平滑程度与细节表现，调参应结合具体场景和计算成本验证。
cv.cartToPolar() 把水平、垂直分量转换成幅度与角度，默认以弧度表示角度。8 位 OpenCV HSV 图的色相使用半角度标度，因此原例以 ang * 180 / np.pi / 2 写入 H 通道；S 通道固定为 255；V 通道保存幅度的 0～255 归一化结果。最后通过 cv.COLOR_HSV2BGR 转成窗口显示使用的 BGR 图像。
读懂颜色，也读懂它的限制
同一种色相表示同一个运动方向，越亮通常表示本帧内越大的位移幅度。但 cv.NORM_MINMAX 对每一对相邻帧独立计算最小值、最大值并缩放。某一帧的亮黄色与另一帧的亮黄色不能据此认定为相同速度：色相只表示方向，亮度也没有使用跨帧固定标尺。
比较跨帧位移时，应保存原始 flow 或幅度，或者采用明确的固定幅度到亮度映射并说明饱和阈值。报告实际物理速度还需要真实时间间隔、空间标定和相机运动处理。waitKey(30) 是窗口事件等待，不等于精确的采样时间，也不能代替视频时间戳。曝光变化、遮挡、反光、纹理不足和大幅度运动，都可能使光流与真实物体运动偏离。
整理版：检查输入，避免反复覆盖快照
静态检查发现，原例第一次 cap.read() 后没有检查 ret；视频缺失或解码失败时，cvtColor 可能直接报错。它也没有检查 imwrite 的结果，没有显式释放视频句柄。以下是基于原例的修订稿，不是官方逐字代码，也未经过执行测试：保留光流参数与 HSV 映射；只接收实际存在的本地文件；检查首帧与帧尺寸；在新建的独立输出目录中用帧编号保存；检查写入结果，并用 finally 释放资源。
# Based on OpenCV 4.13.0 optical_flow_dense.py (Apache-2.0).
# Changed for WWJ: local input validation, first-frame checks,
# unique output directory, checked writes, and resource cleanup.
# Static review only: this adapted example has not been executed.
import argparse
from pathlib import Path
import tempfile
import cv2 as cv
import numpy as np
parser = argparse.ArgumentParser()
parser.add_argument("video", type=Path, help="trusted local video file")
args = parser.parse_args()
video = args.video.expanduser().resolve(strict=True)
if not video.is_file():
raise ValueError("Input must be a local regular file")
output_dir = Path(tempfile.mkdtemp(prefix="optical-flow-", dir="."))
print("Snapshots will be saved under:", output_dir.resolve())
cap = cv.VideoCapture(str(video))
try:
if not cap.isOpened():
raise RuntimeError("Cannot open video")
ok, first = cap.read()
if not ok or first is None:
raise RuntimeError("Cannot decode the first frame")
previous_gray = cv.cvtColor(first, cv.COLOR_BGR2GRAY)
hsv = np.zeros_like(first)
hsv[..., 1] = 255
frame_number = 0
while True:
ok, frame = cap.read()
if not ok or frame is None:
print("End of input or decode failure")
break
frame_number += 1
if frame.shape != first.shape:
raise RuntimeError("Frame dimensions changed")
current_gray = cv.cvtColor(frame, cv.COLOR_BGR2GRAY)
flow = cv.calcOpticalFlowFarneback(
previous_gray, current_gray, None, 0.5, 3, 15, 3, 5, 1.2, 0
)
magnitude, angle = cv.cartToPolar(flow[..., 0], flow[..., 1])
hsv[..., 0] = angle * 180 / np.pi / 2
hsv[..., 2] = cv.normalize(magnitude, None, 0, 255, cv.NORM_MINMAX)
flow_bgr = cv.cvtColor(hsv, cv.COLOR_HSV2BGR)
cv.imshow("Input frame", frame)
cv.imshow("Dense optical flow", flow_bgr)
key = cv.waitKey(30) & 0xff
if key == 27:
break
if key == ord("s"):
for suffix, picture in (("frame", frame), ("flow", flow_bgr)):
target = output_dir / f"{frame_number:06d}-{suffix}.png"
if not cv.imwrite(str(target), picture):
raise OSError(f"Could not write {target}")
previous_gray = current_gray
finally:
cap.release()
cv.destroyAllWindows()
将整理版保存为 dense_flow_reviewed.py 后，可在上述实验环境中以本地视频路径为参数运行，例如 .venv/bin/python dense_flow_reviewed.py ./vtest.avi。程序创建新的 optical-flow-* 目录，按 s 时才保存图片。读取失败可能是正常到达结尾，也可能是中途解码错误，示例不会武断地将两者等同。对不可信视频，仍须考虑媒体解码器及资源消耗风险；这里的路径检查不构成完整安全沙箱。
来源与审查说明
本文为授权中文整理，来源：OpenCV 4.13.0 — Optical Flow，并对照该 tag 的教程 Markdown、Python 示例和 Object Tracking API 文档。环境信息参见 opencv-python 4.13.0.92 与 NumPy 2.2.6。资料核对日期：2026-10-05。
OpenCV 4.13.0 仓库采用 Apache License 2.0，完整许可证文本公开可读。本文明确标注翻译整理及代码修改，保留 OpenCV 和 Farnebäck 的归属；没有把仓库许可证扩大解释为所有第三方照片、视频的独立许可。
仅作源文与代码静态审查，没有运行安装命令、视频解码、图形窗口或保存测试，也没有生成运行截图。未发现硬编码秘密或命令注入路径，不代表不存在其他漏洞。
官方密集光流结果图
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