運動模型的建立：
在進入kalman跟蹤之前，首先要建立鼠標運動的模型，至少有兩個狀態變量：鼠標位置x,y，也可以是四個狀態變量：位置x,y和速度vx，vy。兩個測量變量：鼠標位置x,y。由於鼠標的運動是個隨機運動，並沒有一個精確復雜的數學模型。在粒子濾波博文中，也做過圖像跟蹤，跟那里程序類似的是，鼠標的位置主要通過上一時刻的位置再疊加一個隨機噪聲來預測。
opencv kalman代碼：
例程主要分為兩部分，第一部分是針對目標跟蹤而封裝好的的一個kalman濾波器類，方便以后擴展到其他程序中。第二部分是使用之前封裝好的kalman目標跟蹤類進行鼠標跟蹤。
第一部分：封裝好的用於目標跟蹤的濾波器類
# -*- coding: utf-8 -*-
'''
kalman2d - 2D Kalman filter using OpenCV
Based on http://jayrambhia.wordpress.com/2012/07/26/kalman-filter/
Copyright (C) 2014 Simon D. Levy
This code is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.
This code is distributed in the hope that it will be useful,
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this code. If not, see <http://www.gnu.org/licenses/>.
'''
from cv2 import cv
class Kalman2D(object):
'''
A class for 2D Kalman filtering
'''
def __init__(self, processNoiseCovariance=1e-4, measurementNoiseCovariance=1e-1, errorCovariancePost=0.1):
'''
Constructs a new Kalman2D object.
For explanation of the error covariances see
http://en.wikipedia.org/wiki/Kalman_filter
'''
# 狀態空間：位置--2d,速度--2d
self.kalman = cv.CreateKalman(4, 2, 0)
self.kalman_state = cv.CreateMat(4, 1, cv.CV_32FC1)
self.kalman_process_noise = cv.CreateMat(4, 1, cv.CV_32FC1)
self.kalman_measurement = cv.CreateMat(2, 1, cv.CV_32FC1)
for j in range(4):
for k in range(4):
self.kalman.transition_matrix[j,k] = 0
self.kalman.transition_matrix[j,j] = 1
#加入速度 x = x + vx, y = y + vy
# 1,0,1,0, 0,1,0,1, 0,0,1,0, 0,0,0,1
#如果把下面兩句注釋掉，那么位置跟蹤kalman濾波器的狀態模型就是沒有使用速度信息
# self.kalman.transition_matrix[0, 2]=1
# self.kalman.transition_matrix[1, 3]=1
cv.SetIdentity(self.kalman.measurement_matrix)
#初始化帶尺度的單位矩陣
cv.SetIdentity(self.kalman.process_noise_cov, cv.RealScalar(processNoiseCovariance))
cv.SetIdentity(self.kalman.measurement_noise_cov, cv.RealScalar(measurementNoiseCovariance))
cv.SetIdentity(self.kalman.error_cov_post, cv.RealScalar(errorCovariancePost))
self.predicted = None
self.esitmated = None
def update(self, x, y):
'''
Updates the filter with a new X,Y measurement
'''
self.kalman_measurement[0, 0] = x
self.kalman_measurement[1, 0] = y
self.predicted = cv.KalmanPredict(self.kalman)
self.corrected = cv.KalmanCorrect(self.kalman, self.kalman_measurement)
def getEstimate(self):
'''
Returns the current X,Y estimate.
'''
return self.corrected[0,0], self.corrected[1,0]
def getPrediction(self):
'''
Returns the current X,Y prediction.
'''
return self.predicted[0,0], self.predicted[1,0]
代碼詳細解讀：
這部分程序中，最主要的kalman濾波器的創建和使用。
self.kalman = cv.CreateKalman(4, 2, 0)該句命令為創建kalman濾波器，使用方法如下：
CreateKalman(dynam_params, measure_params, control_params=0)
它有3個輸入參數，dynam_params：狀態空間的維數；measure_param：測量值的維數；control_params：控制向量的維數，默認為0。由於這里該模型中並沒有控制變量，因此也為0。
cv.SetIdentity(self.kalman.process_noise_cov, cv.RealScalar(processNoiseCovariance)) cv.SetIdentity(self.kalman.measurement_noise_cov, cv.RealScalar(measurementNoiseCovariance)) cv.SetIdentity(self.kalman.error_cov_post, cv.RealScalar(errorCovariancePost))
代碼中這三句為設定過程噪聲協方差矩陣、測量噪聲協方差矩陣、以及初始化后驗誤差協方差矩陣。
創建完成以后，就只等待在主函數中調用，進行預測和更新了。
注意：在使用過程中，為達到好的跟蹤效果主要調節下示參數中的前兩個參數processNosieCovariance和measurementNoiseCovariance
__init__(self, processNoiseCovariance=1e-2, measurementNoiseCovariance=1e-1, errorCovariancePost=0.1)
第二部分：鼠標跟蹤主程序
#!/usr/bin/env python
'''
kalman_mousetracker.py - OpenCV mouse-tracking demo using 2D Kalman filter
Adapted from
http://www.morethantechnical.com/2011/06/17/simple-kalman-filter-for-tracking-using-opencv-2-2-w-code/
Copyright (C) 2014 Simon D. Levy
This code is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation, either version 3 of the
License, or (at your option) any later version.
This code is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this code. If not, see <http://www.gnu.org/licenses/>.
'''
# This delay will affect the Kalman update rate
DELAY_MSEC = 20
# Arbitrary display params
WINDOW_NAME = 'Kalman Mousetracker [ESC to quit]'
WINDOW_SIZE = 500
import cv2
import numpy as np
from sys import exit
from kalman2d import Kalman2D
class MouseInfo(object):
'''
A class to store X,Y points
'''
def __init__(self):
self.x, self.y = -1, -1
def __str__(self):
return '%4d %4d' % (self.x, self.y)
def mouseCallback(event, x, y, flags, mouse_info):
'''
Callback to update a MouseInfo object with new X,Y coordinates
'''
mouse_info.x = x
mouse_info.y = y
def drawCross(img, center, r, g, b):
'''
Draws a cross a the specified X,Y coordinates with color RGB
'''
d = 5
t = 2
color = (r, g, b)
ctrx = center[0]
ctry = center[1]
cv2.line(img, (ctrx - d, ctry - d), (ctrx + d, ctry + d), color, t, cv2.CV_AA)
cv2.line(img, (ctrx + d, ctry - d), (ctrx - d, ctry + d), color, t, cv2.CV_AA)
def drawLines(img, points, r, g, b):
'''
Draws lines
'''
cv2.polylines(img, [np.int32(points)], isClosed=False, color=(r, g, b))
def newImage():
'''
Returns a new image
'''
return np.zeros((500,500,3), np.uint8)
if __name__ == '__main__':
# Create a new image in a named window
img = newImage()
cv2.namedWindow(WINDOW_NAME)
# Create an X,Y mouse info object and set the window's mouse callback to modify it
mouse_info = MouseInfo()
cv2.setMouseCallback(WINDOW_NAME, mouseCallback, mouse_info)
# Loop until mouse inside window
while True:
if mouse_info.x > 0 and mouse_info.y > 0:
break
cv2.imshow(WINDOW_NAME, img)
if cv2.waitKey(1) == 27:
exit(0)
# These will get the trajectories for mouse location and Kalman estiamte
measured_points = []
kalman_points = []
# Create a new Kalman2D filter and initialize it with starting mouse location
kalman2d = Kalman2D()
# Loop till user hits escape
while True:
# Serve up a fresh image
img = newImage()
# Grab current mouse position and add it to the trajectory
measured = (mouse_info.x, mouse_info.y)
measured_points.append(measured)
# Update the Kalman filter with the mouse point
kalman2d.update(mouse_info.x, mouse_info.y)
# Get the current Kalman estimate and add it to the trajectory
estimated = [int (c) for c in kalman2d.getEstimate()]
kalman_points.append(estimated)
# Display the trajectories and current points
drawLines(img, kalman_points, 0, 255, 0)
drawCross(img, estimated, 255, 255, 255)
drawLines(img, measured_points, 255, 255, 0)
drawCross(img, measured, 0, 0, 255)
# Delay for specified interval, quitting on ESC
cv2.imshow(WINDOW_NAME, img)
if cv2.waitKey(DELAY_MSEC) == 27:
break
運行程序就能看到效果。
值得一提的是：狀態模型中使不使用速度變量，效果是不一樣的。
狀態模型中加入速度變量：
不加入速度變量：
調節之前提到的參數，得到最好的效果。
最后，讀者可以將本文中的程序稍作修改實現粒子濾波博文中視頻跟蹤穿紅衣女子，視頻可以在粒子濾波博文代碼材料中找到，祝好運。
（轉載請注明作者和出處：http://blog.csdn.net/heyijia0327 未經允許請勿用於商業用途）
reference：
2.Simon D. Levy將上述例程修改為python代碼
3.目標跟蹤模型
5.opencv官方資料2：該官方鏈接中有一個跟蹤旋轉點的c例程