evaluate_ate_scale.py

#!/usr/bin/python

# Modified by Raul Mur-Artal
# Automatically compute the optimal scale factor for monocular VO/SLAM.

# Software License Agreement (BSD License)
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# Copyright (c) 2013, Juergen Sturm, TUM
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# Requirements: 
# sudo apt-get install python-argparse

"""
This script computes the absolute trajectory error from the ground truth
trajectory and the estimated trajectory.
"""

import sys
import numpy
import argparse
import associate

def align(model,data):
    """Align two trajectories using the method of Horn (closed-form).
    
    Input:
    model -- first trajectory (3xn)
    data -- second trajectory (3xn)
    
    Output:
    rot -- rotation matrix (3x3)
    trans -- translation vector (3x1)
    trans_error -- translational error per point (1xn)
    
    """
    numpy.set_printoptions(precision=3,suppress=True)
    model_zerocentered = model - model.mean(1)
    data_zerocentered = data - data.mean(1)
    
    W = numpy.zeros( (3,3) )
    for column in range(model.shape[1]):
        W += numpy.outer(model_zerocentered[:,column],data_zerocentered[:,column])
    U,d,Vh = numpy.linalg.linalg.svd(W.transpose())
    S = numpy.matrix(numpy.identity( 3 ))
    if(numpy.linalg.det(U) * numpy.linalg.det(Vh)<0):
        S[2,2] = -1
    rot = U*S*Vh

    rotmodel = rot*model_zerocentered
    dots = 0.0
    norms = 0.0

    for column in range(data_zerocentered.shape[1]):
	dots += numpy.dot(data_zerocentered[:,column].transpose(),rotmodel[:,column])
        normi = numpy.linalg.norm(model_zerocentered[:,column])
        norms += normi*normi

    s = float(dots/norms)    

    print "scale: %f " % s  
    
    trans = data.mean(1) - s*rot * model.mean(1)
    
    model_aligned = s*rot * model + trans
    alignment_error = model_aligned - data
    
    trans_error = numpy.sqrt(numpy.sum(numpy.multiply(alignment_error,alignment_error),0)).A[0]
        
    return rot,trans,trans_error, s

def plot_traj(ax,stamps,traj,style,color,label):
    """
    Plot a trajectory using matplotlib. 
    
    Input:
    ax -- the plot
    stamps -- time stamps (1xn)
    traj -- trajectory (3xn)
    style -- line style
    color -- line color
    label -- plot legend
    
    """
    stamps.sort()
    interval = numpy.median([s-t for s,t in zip(stamps[1:],stamps[:-1])])
    x = []
    y = []
    last = stamps[0]
    for i in range(len(stamps)):
        if stamps[i]-last < 2*interval:
            x.append(traj[i][0])
            y.append(traj[i][1])
        elif len(x)>0:
            ax.plot(x,y,style,color=color,label=label)
            label=""
            x=[]
            y=[]
        last= stamps[i]
    if len(x)>0:
        ax.plot(x,y,style,color=color,label=label)
            

if __name__=="__main__":
    # parse command line
    parser = argparse.ArgumentParser(description='''
    This script computes the absolute trajectory error from the ground truth trajectory and the estimated trajectory. 
    ''')
    parser.add_argument('first_file', help='ground truth trajectory (format: timestamp tx ty tz qx qy qz qw)')
    parser.add_argument('second_file', help='estimated trajectory (format: timestamp tx ty tz qx qy qz qw)')
    parser.add_argument('--offset', help='time offset added to the timestamps of the second file (default: 0.0)',default=0.0)
    parser.add_argument('--scale', help='scaling factor for the second trajectory (default: 1.0)',default=1.0)
    parser.add_argument('--max_difference', help='maximally allowed time difference for matching entries (default: 0.02)',default=0.02)
    parser.add_argument('--save', help='save aligned second trajectory to disk (format: stamp2 x2 y2 z2)')
    parser.add_argument('--save_associations', help='save associated first and aligned second trajectory to disk (format: stamp1 x1 y1 z1 stamp2 x2 y2 z2)')
    parser.add_argument('--plot', help='plot the first and the aligned second trajectory to an image (format: png)')
    parser.add_argument('--verbose', help='print all evaluation data (otherwise, only the RMSE absolute translational error in meters after alignment will be printed)', action='store_true')
    args = parser.parse_args()

    first_list = associate.read_file_list(args.first_file)
    second_list = associate.read_file_list(args.second_file)

    matches = associate.associate(first_list, second_list,float(args.offset),float(args.max_difference))    
    if len(matches)<2:
        sys.exit("Couldn't find matching timestamp pairs between groundtruth and estimated trajectory! Did you choose the correct sequence?")


    first_xyz = numpy.matrix([[float(value) for value in first_list[a][0:3]] for a,b in matches]).transpose()
    second_xyz = numpy.matrix([[float(value)*float(args.scale) for value in second_list[b][0:3]] for a,b in matches]).transpose()
    rot,trans,trans_error,scale = align(second_xyz,first_xyz)
    
    second_xyz_aligned = scale * rot * second_xyz + trans
    
    first_stamps = first_list.keys()
    first_stamps.sort()
    first_xyz_full = numpy.matrix([[float(value) for value in first_list[b][0:3]] for b in first_stamps]).transpose()
    
    second_stamps = second_list.keys()
    second_stamps.sort()
    second_xyz_full = numpy.matrix([[float(value)*float(args.scale) for value in second_list[b][0:3]] for b in second_stamps]).transpose()
    second_xyz_full_aligned = scale * rot * second_xyz_full + trans
    
    if args.verbose:
        print "compared_pose_pairs %d pairs"%(len(trans_error))

        print "absolute_translational_error.rmse %f m"%numpy.sqrt(numpy.dot(trans_error,trans_error) / len(trans_error))
        print "absolute_translational_error.mean %f m"%numpy.mean(trans_error)
        print "absolute_translational_error.median %f m"%numpy.median(trans_error)
        print "absolute_translational_error.std %f m"%numpy.std(trans_error)
        print "absolute_translational_error.min %f m"%numpy.min(trans_error)
        print "absolute_translational_error.max %f m"%numpy.max(trans_error)
    else:
        print "%f"%numpy.sqrt(numpy.dot(trans_error,trans_error) / len(trans_error))
        
    if args.save_associations:
        file = open(args.save_associations,"w")
        file.write("\n".join(["%f %f %f %f %f %f %f %f"%(a,x1,y1,z1,b,x2,y2,z2) for (a,b),(x1,y1,z1),(x2,y2,z2) in zip(matches,first_xyz.transpose().A,second_xyz_aligned.transpose().A)]))
        file.close()
        
    if args.save:
        file = open(args.save,"w")
        file.write("\n".join(["%f "%stamp+" ".join(["%f"%d for d in line]) for stamp,line in zip(second_stamps,second_xyz_full_aligned.transpose().A)]))
        file.close()

    if args.plot:
        import matplotlib
        matplotlib.use('Agg')
        import matplotlib.pyplot as plt
        import matplotlib.pylab as pylab
        from matplotlib.patches import Ellipse
        fig = plt.figure()
        ax = fig.add_subplot(111)
        plot_traj(ax,first_stamps,first_xyz_full.transpose().A,'-',"black","ground truth")
        plot_traj(ax,second_stamps,second_xyz_full_aligned.transpose().A,'-',"blue","estimated")

        label="difference"
        for (a,b),(x1,y1,z1),(x2,y2,z2) in zip(matches,first_xyz.transpose().A,second_xyz_aligned.transpose().A):
            ax.plot([x1,x2],[y1,y2],'-',color="red",label=label)
            label=""
            
        ax.legend()
            
        ax.set_xlabel('x [m]')
        ax.set_ylabel('y [m]')
        plt.savefig(args.plot,dpi=90)