前言

• 先放效果图。目标框内左上角，显示的是目标距离相机的纵向距离。目标横向距离、速度已求出，没在图片展示。
• 这里不仅仅实现对目标检测框的跟踪，且可以实现单相机进行对目标进行测距跟踪。
• 想了解详细原理可以参考往期博客：【目标跟踪】多目标跟踪sort （python 代码） 。这里不过多赘述，直接上代码，如有疑问，欢迎私信交流。

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python代码（带注释）

• 代码输入：1、连续帧图片，2、每帧图片的检测结果。(需要数据的可以私信我)
• 代码参考:git地址
• 输出结果以视频形式保存

main.py

检测结果为 det.txt ，图片格式为 000001.jpg 。用的是跟踪挑战开源数据。
这部分代码主要是加载检测数据，读取图片。调用跟踪与测距接口进行计算
可以设置 dispaly 与 video_save 是否 show 图片 与保存视频
x_p 里面包含目标离相机纵向与横向距离，还有速度、加速度。可以自行更改 putText 图片展示信息

import os
import cv2
from sort import *

if __name__ == '__main__':
    display, video_save = False, True  # 是否show,结果是否存视频
    max_age, min_hits, iou_threshold = 3, 3, 0.3  # sort算法参数
    colours = 255 * np.random.rand(32, 3)  # 随机生产颜色
    video = cv2.VideoWriter("video.mp4", cv2.VideoWriter_fourcc('m', 'p', '4', 'v'), 10,
                            (1920, 1080)) if video_save else None
    mot_tracker = Sort(max_age=max_age, min_hits=min_hits, iou_threshold=iou_threshold)  # 创建sort跟踪器
    seq_dets = np.loadtxt("det.txt", delimiter=',')  # 加载检测txt结果
    for frame in range(int(seq_dets[:, 0].max())):
        frame += 1  # 从1帧开始
        dets = seq_dets[seq_dets[:, 0] == frame, 2:7]
        dets[:, 2:4] += dets[:, 0:2]  # [x1,y1,w,h] to [x1,y1,x2,y2] 左上角x1,y1，w，h ——>左上角x1,y1，右下角x2,y2
        mot_tracker.update(dets)  # kalman 预测与更新
        trackers = mot_tracker.trackers
        image_path = os.path.join(".\\img", '%06d.jpg' % (frame))  # 图片路径
        image = cv2.imread(image_path)
        # x_p 目标横向、纵向距离。速度以及加速度
        for d, x_p in trackers:
            x1, y1, w, h = d.get_state()[0]  # 获取 当前目标框状态
            id = d.id
            color = colours[int(id) % 32, :]
            color = (int(color[0]), int(color[1]), int(color[2]))
            cv2.rectangle(image, (int(x1), int(y1)), (int(w), int(h)), color, 3)  # 画框
            cv2.putText(image, str(int(id)), (int(x1), int(y1) - 10), cv2.FONT_HERSHEY_SIMPLEX, 1,
                        color, 3)  # 画id
            cv2.putText(image, str(np.round(x_p[0][0], 2)), (int(x1), int(y1) + 30),
                        cv2.FONT_HERSHEY_SIMPLEX, 1,
                        color, 3)  # 画距离
        if display:
            cv2.namedWindow("show")
            cv2.imshow("show", image)
            cv2.waitKey(0)
        if video_save:
            video.write(image)

sort.py

这部分代码为核心计算代码，主要调用 kalman 预测 predict 与 更新 update
在跟踪航迹 self.trackers 里面添加距离信息，也进行一个预测与更新，不参与匹配权重的运算。
主要对测距起到一个平滑的作用。

from __future__ import print_function
from kalman import *
from distance import *


def linear_assignment(cost_matrix):
    try:
        import lap
        _, x, y = lap.lapjv(cost_matrix, extend_cost=True)
        return np.array([[y[i], i] for i in x if i >= 0])  #
    except ImportError:
        from scipy.optimize import linear_sum_assignment
        x, y = linear_sum_assignment(cost_matrix)
        return np.array(list(zip(x, y)))


def iou_batch(bb_test, bb_gt):
    bb_gt = np.expand_dims(bb_gt, 0)
    bb_test = np.expand_dims(bb_test, 1)

    xx1 = np.maximum(bb_test[..., 0], bb_gt[..., 0])
    yy1 = np.maximum(bb_test[..., 1], bb_gt[..., 1])
    xx2 = np.minimum(bb_test[..., 2], bb_gt[..., 2])
    yy2 = np.minimum(bb_test[..., 3], bb_gt[..., 3])
    w = np.maximum(0., xx2 - xx1)
    h = np.maximum(0., yy2 - yy1)
    wh = w * h
    o = wh / ((bb_test[..., 2] - bb_test[..., 0]) * (bb_test[..., 3] - bb_test[..., 1])
              + (bb_gt[..., 2] - bb_gt[..., 0]) * (bb_gt[..., 3] - bb_gt[..., 1]) - wh)
    return (o)


def associate_detections_to_trackers(detections, trackers, iou_threshold=0.3):
    if (len(trackers) == 0):
        return np.empty((0, 2), dtype=int), np.arange(len(detections)), np.empty((0, 5), dtype=int)

    iou_matrix = iou_batch(detections, trackers)

    if min(iou_matrix.shape) > 0:
        a = (iou_matrix > iou_threshold).astype(np.int32)
        if a.sum(1).max() == 1 and a.sum(0).max() == 1:
            matched_indices = np.stack(np.where(a), axis=1)
        else:
            matched_indices = linear_assignment(-iou_matrix)
    else:
        matched_indices = np.empty(shape=(0, 2))

    unmatched_detections = []
    for d, det in enumerate(detections):
        if (d not in matched_indices[:, 0]):
            unmatched_detections.append(d)
    unmatched_trackers = []
    for t, trk in enumerate(trackers):
        if (t not in matched_indices[:, 1]):
            unmatched_trackers.append(t)

    matches = []
    for m in matched_indices:
        if (iou_matrix[m[0], m[1]] < iou_threshold):
            unmatched_detections.append(m[0])
            unmatched_trackers.append(m[1])
        else:
            matches.append(m.reshape(1, 2))
    if (len(matches) == 0):
        matches = np.empty((0, 2), dtype=int)
    else:
        matches = np.concatenate(matches, axis=0)

    return matches, np.array(unmatched_detections), np.array(unmatched_trackers)


class Sort(object):
    def __init__(self, max_age=1, min_hits=3, iou_threshold=0.3):
        self.max_age = max_age
        self.min_hits = min_hits
        self.iou_threshold = iou_threshold
        self.trackers = []
        self.frame_count = 0
        self.distance_kalman = Distance(0.1)  # 0.1s 1s 十帧
        self.p = np.eye(6)  # 初始化协方差
        self.r_t = np.array(
            [0, 0, 1, 0,
             1, 0, 0, 0,
             0, 1, 0, 1.2,
             0., 0., 0., 1.]).reshape(4, 4)  # 相机外参
        self.k = np.array([1000, 0.0, 960, 0.0, 1000, 540, 0.0, 0.0, 1.0]).reshape(3, 3)  # 相机内参
        self.h = 1.2  # 相机离地面高度 1.2 m
        self.pitch = 0  # 相机 pitch （俯仰角）

    def update(self, dets=np.empty((0, 5))):
        self.frame_count += 1
        # 根据上一帧航迹的框 预测当前帧的框.
        trks = np.zeros((len(self.trackers), 5))
        to_del, ret = [], []
        for t, trk in enumerate(trks):
            pos = self.trackers[t][0].predict()[0]  # 预测框的状态
            self.trackers[t][1] = self.distance_kalman.predict_kalman(self.trackers[t][1])  # 预测距离的状态
            trk[:] = [pos[0], pos[1], pos[2], pos[3], 0]
            if np.any(np.isnan(pos)):
                to_del.append(t)
        trks = np.ma.compress_rows(np.ma.masked_invalid(trks))
        for t in reversed(to_del):
            self.trackers.pop(t)
        # 匈牙利匹配 上一帧预测框与当前帧检测框进行 iou 匹配
        matched, unmatched_dets, unmatched_trks = associate_detections_to_trackers(dets, trks, self.iou_threshold)
        # 如果匹配上 则更新修正当前检测框
        for m in matched:
            det = dets[m[0], :]
            distance = get_distance((det[0] + det[2]) / 2, det[3], self.h, self.pitch, self.k, self.r_t[:3, :3],
                                    self.r_t[:3, 3])
            self.trackers[m[1]][1] = self.distance_kalman.updata_kalman([distance[0], distance[1]],
                                                                        self.trackers[m[1]][1])
            self.trackers[m[1]][0].update(det)
        # 如果检测框未匹配上，则当作新目标，新起航迹
        for i in unmatched_dets:
            det = dets[i, :]
            distance = get_distance((det[0] + det[2]) / 2, det[3], self.h, self.pitch, self.k, self.r_t[:3, :3],
                                    self.r_t[:3, 3])  # 目标测距
            # 目标状态 （x,y,vx,vy,ax,ay） kalman协方差
            x_p = (np.array([[distance[0], 0, 0, distance[1], 0, 0]]).T, self.p)
            trk = [KalmanBoxTracker(det), x_p]
            self.trackers.append(trk)
        i = len(self.trackers)
        for trk in reversed(self.trackers):
            d = trk[0].get_state()[0]
            if (trk[0].time_since_update < 1) and (
                    trk[0].hit_streak >= self.min_hits or self.frame_count <= self.min_hits):
                ret.append(np.concatenate((d, [trk[0].id + 1])).reshape(1, -1))  # +1 as MOT benchmark requires positive
            i -= 1
            # 如果超过self.max_age（3）帧都没有匹配上，则应该去除这个航迹
            if (trk[0].time_since_update > self.max_age):
                self.trackers.pop(i)
        if (len(ret) > 0):
            return np.concatenate(ret)
        return np.empty((0, 5))

kalman.py

这部分代码是 kalman 算法核心代码
主要对目标框 bbox 进行预测与更新。bbox 状态为 [center_x, center_y, s, r, center_x’, center_y’, s’]
s = w * h r = w / h bbox 宽高比保持不变

import numpy as np
from filterpy.kalman import KalmanFilter


def convert_bbox_to_z(bbox):
    w = bbox[2] - bbox[0]
    h = bbox[3] - bbox[1]
    x = bbox[0] + w / 2.
    y = bbox[1] + h / 2.
    s = w * h
    r = w / float(h)
    return np.array([x, y, s, r]).reshape((4, 1))


def convert_x_to_bbox(x, score=None):
    w = np.sqrt(x[2] * x[3])
    h = x[2] / w
    if (score == None):
        return np.array([x[0] - w / 2., x[1] - h / 2., x[0] + w / 2., x[1] + h / 2.]).reshape((1, 4))
    else:
        return np.array([x[0] - w / 2., x[1] - h / 2., x[0] + w / 2., x[1] + h / 2., score]).reshape((1, 5))


class KalmanBoxTracker(object):
    count = 0

    def __init__(self, bbox):
        self.kf = KalmanFilter(dim_x=7, dim_z=4)
        self.kf.F = np.array(
            [[1, 0, 0, 0, 1, 0, 0],
             [0, 1, 0, 0, 0, 1, 0],
             [0, 0, 1, 0, 0, 0, 1],
             [0, 0, 0, 1, 0, 0, 0],
             [0, 0, 0, 0, 1, 0, 0],
             [0, 0, 0, 0, 0, 1, 0],
             [0, 0, 0, 0, 0, 0, 1]])
        self.kf.H = np.array(
            [[1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0]])

        self.kf.R[2:, 2:] *= 10.
        self.kf.P[4:, 4:] *= 1000.
        self.kf.P *= 10.
        self.kf.Q[-1, -1] *= 0.01
        self.kf.Q[4:, 4:] *= 0.01

        self.kf.x[:4] = convert_bbox_to_z(bbox)
        self.time_since_update = 0
        self.id = KalmanBoxTracker.count
        KalmanBoxTracker.count += 1
        self.history = []
        self.hits = 0
        self.hit_streak = 0
        self.age = 0

    def update(self, bbox):
        self.time_since_update = 0
        self.history = []
        self.hits += 1
        self.hit_streak += 1
        self.kf.update(convert_bbox_to_z(bbox))

    def predict(self):
        if ((self.kf.x[6] + self.kf.x[2]) <= 0):
            self.kf.x[6] *= 0.0
        self.kf.predict()
        self.age += 1
        if (self.time_since_update > 0):
            self.hit_streak = 0
        self.time_since_update += 1
        self.history.append(convert_x_to_bbox(self.kf.x))
        return self.history[-1]

    def get_state(self):
        return convert_x_to_bbox(self.kf.x)

distance.py

这部分代码是测距核心代码，以及对目标测距的预测与更新
目标状态为 （x,y,vx,vy,ax,ay） 目标横向距离，纵向距离，横向速度，纵向速度，横向加速度，纵向加速度。
关于目标前后帧匹配，是利用 iou 匹配进行的，所以要基于目标检测框的匹配跟踪。

import numpy as np


def get_distance(pixe_x, pixe_y, h, pitch, K, R, T):
    sigma = np.arctan((pixe_y - K[1][2]) / K[1][1])
    z = h * np.cos(sigma) / np.sin(sigma + pitch)  # 深度
    x_pixe, y_pixe = 2 * K[0][2] - pixe_x, 2 * K[1][2] - pixe_y
    camera_x = z * (x_pixe / K[0][0] - K[0][2] / K[0][0])
    camera_y = z * (y_pixe / K[1][1] - K[1][2] / K[1][1])
    camera_z = z
    x = R[0][0] * camera_x + R[0][1] * camera_y + R[0][2] * camera_z + T[0]
    y = R[1][0] * camera_x + R[1][1] * camera_y + R[1][2] * camera_z + T[1]
    # z = R[2][0] * camera_x + R[2][1] * camera_y + R[2][2] * camera_z + T[2]
    return x, y


class Distance():
    def __init__(self, t):
        self.t = t  # 时间间隔0.1s
        self.F = np.array([[1, t, t * t / 2, 0, 0, 0],
                           [0, 1, t, 0, 0, 0],
                           [0, 0, 1, 0, 0, 0],
                           [0, 0, 0, 1, t, t * t / 2],
                           [0, 0, 0, 0, 1, t],
                           [0, 0, 0, 0, 0, 1]])
        self.sigma_a = 0.02  # 加速度误差0.2m/s2
        self.sigma_x, self.sigma_y = 0.3, 0.2  # x、y测量距离误差
        self.Q = np.array([[np.power(t, 4) / 4, np.power(t, 3) / 3, np.power(t, 2) / 2, 0, 0, 0],
                           [np.power(t, 3) / 3, np.power(t, 2) / 2, t, 0, 0, 0],
                           [np.power(t, 2) / 2, t, 1, 0, 0, 0],
                           [0, 0, 0, np.power(t, 4) / 4, np.power(t, 3) / 3, np.power(t, 2) / 2],
                           [0, 0, 0, np.power(t, 3) / 3, np.power(t, 2) / 2, t],
                           [0, 0, 0, np.power(t, 2) / 2, t, 1]]) * self.sigma_a * self.sigma_a  # 过程噪声矩阵
        self.R_n = np.array([[self.sigma_x ** 2, 0], [0, self.sigma_y ** 2]])  # 测量噪声协方差
        self.H = np.array([[1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0]])

    def updata_kalman(self, Z, X_P):
        """
        :param Z:测量值
        :param X:状态矩阵   [x,vx,ax,y,vy,ay]
        :param P:状态协方差矩阵
        :return:更新后的X,P
        """
        X, P = X_P
        # print(H @ P @ H.T)
        Z_1 = np.array([Z]).T
        # print(Z_1)
        K = P @ np.transpose(self.H) @ np.linalg.inv(np.dot(np.dot(self.H, P), np.transpose(self.H)) + self.R_n)
        # print(H @ K)
        X = X + K @ (Z_1 - self.H @ X)
        P = (np.identity(6) - K @ self.H) @ P @ np.transpose(np.identity(6) - K @ self.H) + K @ self.R_n @ np.transpose(
            K)
        return X, P

    def predict_kalman(self, X_P):
        X, P = X_P
        X = self.F @ X
        P = self.F @ P @ np.transpose(self.F) + self.Q
        return X, P

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结语

• 运行 main.py ，结果会保存视频。博主在本地是跑通的，如果有什么疑问，可以私信交流。
• 关于数据，我是在网上找的开源数据跑的。相机的参数是模拟的。