1. The document discusses methods for improving registration of RGB-D frames by generating accurate 3D point correspondences from 2D keypoints and weighting correspondences based on depth uncertainty. 2. It describes estimating the relative orientation of RGB and depth cameras, searching along epipolar lines to find corresponding 3D points, and assigning lower weights to points with higher random depth errors. 3. The results show that weighted registration outperforms non-weighted, producing more accurate trajectories with lower closing distances and angles between start and end frames.

1. Generation and Weighting of 3D Point Correspondences
for Improved Registration of RGB-D Data
Kourosh Khoshelham
Daniel Dos Santos
George Vosselman

2. MAPPING BY RGB-D DATA
 RGB-D cameras like Kinect have great potential for indoor
mapping;
 Kinect captures:
depth + color images @ ~30 fps
= sequence of colored point clouds
IR emitter RGB camera
+
IR camera

2

3. REGISTRATION OF RGB-D DATA
 Mapping requires registration of consecutive frames;
 Registration: transforming all point clouds into one coordinate
system (usually of the first frame).
Point i in frame j-1
Point i in frame j
𝑗−1
𝐗 𝑖,𝑗−1 = 𝐑 𝑗
𝑗−1
𝐗 𝑖,𝑗 + 𝐭 𝑗
Transformation from
frame j to frame j-1
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4. REGISTRATION BY VISUAL FEATURES
 Extraction and matching of keypoints is done more reliably in RGB
images;
 Two main components:
 Keypoint extraction and matching  SIFT, SURF, …
 Outlier detection  RANSAC, M-estimator, …
SURF
matches
Conversion to 3D
correspondences
(using depth data)
Removing
outliers
RANSAC
Least-squares
estimation of
registration
parameters
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5. CHALLENGES AND OBJECTIVES
 Challenge:
 Pairwise registration errors accumulate  deformed point cloud
 Objective:
 More accurate pairwise registration by:
i. Accurate generation of 3D correspondences from 2D points;
ii. Weighting 3D point pairs based on random error of depth.
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6. GENERATION OF 3D POINT CORRESPONDENCES
 2D keypoints  3D point correspondences ? (ill-posed)
 RGB image coordinates relate to depth image coordinates by a
shift?
 Note: the FOV of the RGB camera and IR camera are different!
 Our approach:
 Transform 2D keypoints from RGB to depth image using
relative orientation between the two cameras;
 Search along the epipolar line for the correct 3D coordinates.
 Note: relative orientation parameters are estimated during calibration.
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7. GENERATION OF 3D POINT CORRESPONDENCES
More formally:
 Given a keypoint in the RGB frame:
1. calculate the epipolar line in the depth frame using the relative
orientation parameters;
2. define a search band along the epipolar line using the minimum and
maximum of the range of depth values (0.5 m and 5 m respectively);
 For all pixels within the search band:
1. calculate 3D coordinates and re-project the resulting 3D point back
to the RGB frame;
2. calculate and store the distance between the reprojected point and
the original keypoint;
 Return the 3D point whose re-projection has the smallest distance
to the keypoint.
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8. GENERATION OF 3D POINT CORRESPONDENCES
Finding 3D points in the depth image (right) corresponding to 2D
keypoints in the RGB image (left) by searching along epipolar
lines (red bands).
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9. ESTIMATING RELATIVE ORIENTATION PARAMETERS
 Relative orientation between the RGB camera and IR camera:
 approximate by a shift;
 estimate by stereo calibration;
 estimate by space resection.
Manually measured markers in the disparity (left) and colour image (right)
used for the estimation of relative orientation parameters by space resection.
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10. WEIGHTING OF 3D POINT CORRESPONDENCES
 Observation equation in the estimation model:
vi  X i , j 1  R jj 1X i , j  t jj 1
 Approximate as:
vi  X i , j 1  X i , j
 Note: because of high frame rate transformation parameters between
consecutive frames are quite small.
 Define weights as:
wi 
k
2
v
i
k
 2
2
 Xi , j 1   Xi , j
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11. WEIGHTING OF 3D POINT CORRESPONDENCES
 We use random error of depth only:
 Relation between disparity (d) and depth (Z):
2
2
 Propagation of variance:  Z  c12 Z 4 d
 Weight:
Z 1  c0  c1 d
Calibration
parameters

kc12 d 2
wi  4
Z i , j 1  Z i4 j
,
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12. RESULTS: ACCURACY OF 3D POINT CORRESPONDENCES
 Relative orientation
 approximated by a shift
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13. RESULTS: ACCURACY OF 3D POINT CORRESPONDENCES
 Relative orientation
 estimated by stereo calibration
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14. RESULTS: ACCURACY OF 3D POINT CORRESPONDENCES
 Relative orientation
 estimated by space resection
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15. EFFECT OF WEIGHTS IN REGISTRATION
 Six RGB-D sequences of an office environment;
 Trajectories formed closed loops;
 Evaluation by closing error:
Closing
rotation
 R
 T
0
Closing
translation
v
n
 H1  H n1H1
2
n
1

Transformation from
last frame to first frame
Transformation from
first frame to last frame
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16. EFFECT OF WEIGHTS IN REGISTRATION
 Closing distance for the six sequences registered with and without
weights:
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17. EFFECT OF WEIGHTS IN REGISTRATION
 Closing angle for the six sequences registered with and without
weights:
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18. EFFECT OF WEIGHTS IN REGISTRATION
 Average closing errors for registrations with and without weight:
Average closing
distance [cm]
Average closing
angle [deg]
without weight
6.42
6.32
with weight
3.80
4.74
Registration
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19. EFFECT OF WEIGHTS IN REGISTRATION
 The trajectory obtained by weighted registration (in blue) is more
accurate than the one without weights (in red).
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20. EXAMPLE REGISTRATION RESULTS
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21. EXAMPLE REGISTRATION RESULTS
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22. CONCLUSIONS
 Accurate transformation of keypoints from the RGB space to the
3D space  more accurate registration of consecutive frames;
 Assigning weights based on random error of depth improves the
accuracy of pairwise registration and sensor pose estimates.
 Using weights  covariance matrices for pose vectors
 can be used to weight pose vectors in the global adjustment
 = more accurate loop closure
 Influence of synchronization errors (between RGB and IR cam)
 fine registration using point- and plane correspondences
extracted directly from the point cloud.
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23. 23

24. SUPPLEMENTARY SLIDES
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25. Measurement principle of Kinect
 Depth measurement by triangulation:
 The laser source emits a laser beam;
 A diffraction grating splits the beam to create a pattern of speckles
projected onto the scene;
 The speckles are captured by the infrared camera;
 The speckle image is correlated with a reference image obtained by
capturing a plane at a known distance from the sensor;
 The result of correlation is a disparity value for each pixel from which
depth can be calculated.
Resulting
disparity
image
IR image of pattern of
speckles projected to
the scene
25

26. Depth-disparity relation and calculation of point coordinates
From triangle similarities:
and:
Zk 
Zo
Z
1 o d
fb
Zk
( xk  xo  x)
f
Z
Yk   k ( yk  yo  y )
f
Xk  
where:
Zo
f
d
b
xk,yk
xo, yo
δx,δy
Distance of the reference plane
Focal lnegth of the IR camera
Measured disparity
Base length between emitter and IR camera
Image coordinates of point k
Principal point offsets
Lens distortion corrections
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27. Calibration
 Calibration procedure:
 focal length (f);
Standard calibration
of IR camera
 principal point offsets (xo, yo);
 lens distortion coefficients (in δx, δy);
 base length (b);
Depth calibration
 distance of the reference pattern (Zo).
Normalization:
d = md’+n
1
Zk  (
m
n
1
) d   (Z o  )
fb
fb
Depth calibration parameters
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28. Theoretical model of depth random error
Depth equation:
Zk
1
m
n
  ( Z o 1  )
 ( )d
fb
fb
Propagation
of variance
Depth random error:
Z  (
k
m
2
)Z k  d '
fb
Random error is a quadratic function of depth.
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29. Depth random error
 Standard deviation of
plane fitting residuals as
a measure of depth
random error;
 As expected, depth
random error increases
quadratically with
increasing distance from
the sensor.
1.0 m
2.0 m
3.0 m
4.0 m
5.0 m
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30. Depth resolution
 Distribution of plane fitting residuals on the
plane at 4 m distance
 Depth resolution is also proportional to the
squared distance from the sensor;
Side view of the points on the plane
at 4 m (effect of depth resolution)
At a maximum range of 5 m
depth resolution is 7 cm.
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