ICIP 2013 | 2013 IEEE International Conference on Image Processing | September 15 - 18, 2013 | Melbourne, Australia

1. SCALE RATIO ICP FOR 3D POINT CLOUDS WITH DIFFERENT SCALES
Baowei Lin1, Toru Tamaki1, Bisser Raytchev1, Kazufumi Kaneda1 and Koji Ichii1
1Hiroshima University, Japan
INTRODUCTION
FEATURES DESCRIPTORS
FINDING THE RATIO EXPERIMENTAL RESULTS
CONCLUSION
Point clouds of same scene generated by
structure from motion (SfM) usually have different sizes
Different size
It is challenge work to do 3D
registration of point clouds with
different sizes.
Related Work to Scale Alignment
Iterative closest point (ICP)
based alignment [Besl 1991].
-Need simple scenes
-Need initial pose and
scale
-Not robust to clutters
and occlusions and
missing part
spin images [Johnson 1998], NARF
[Steder 2010], shape context
[Belongie 2002], etc.
Feature based alignment
-Need appropriate
neighborhood size
3D SIFT [Scovanner 2007],
3D SURF [Knopp 2010], etc.
-Not robust to clutters
and occlusions and
missing part
Easy data
Different
data
Fixed scale
Adaptive scale
All non-scale-invariant features can be used.(spin images [Johnson 1998], NARF [steder 2010], etc.)
Here, we select spin images.
Spin Images
Point cloud
Spin images: Spin(w)
Image width w (only points close to 3D
point p are used to make a spin image)
p
Because spin images are not scale
invariant a certain range of local area
(neighborhood) should be specified.
Hence, to find the appropriate image
width, or scale, w becomes very
important.
Decide which set of spin images have minimum
of similarity by using Contribution rate.
Similar to each other
Different to each other
Similar to each other
Scale Estimation of a Single Point Cloud [Tamaki 2010]
• Define keyscale
similarity
w
Minimum (keyscale)
Sometimes, minimum is not unique.
Finding them is not stable.
We improve this method to estimate
the scale ratio directly.
similarity
w
• Limitation
Scale Ratio Estimation of Two Point Clouds
• Scale Ratio ICP
2
( ) .
d d
w w
d i
y y
E t
w tw
   
    
   

Objective function:
( , )d
ww y 
( ,y )d
wwScale ratio t is estimated by registering two plots
of point clouds (plot (a) and (b)).
We use the strategy of ICP to estimate t as follows:
1. Initialization
An exhaustive search is used to find an initial
rough estimate of t. First, overlapping curves are
extracted as plot (c) and (d). Then we find the
minimum in the range at discrete steps as the
initial estimate tinit:
argmin ( ).init
t
t E t
2. Find putative correspondences
For each point on curves (a), find the closest
point on the curves (d) with the current
estimate t.
3. Estimate t
The estimate of t based on the correspondences
can be obtained in a closed-form. By taking the
derivative of E(t) with respect to t and setting it to 0.
we have: '
2
.
ww
t
w



4. Iteration
Step 2 and 3 are iterated as t is updated until the
estimate converges.
Simulations
Original bunny 5 times larger bunny
• Dataset
For simulations demonstrating the concept, we
generated two synthetic 3D point clouds from stanford
bunny. One of them was scaled by the factor of 5.
For showing the robustness, we down-sampled or
added noise for the two synthetic bunnies.
• Results
simulations ground
truth
ours
method
keyscale
[Tamaki 2010]
mesh-resolution
[Johnson 1998]
noise-free, no random sampling 5 5.000 5.000 5.000
noise-free, both random sampling 5 5.052 5.053 5.053
noise-free, random sampling of one dataset 5 4.733 5.818 8.727
noise(0.1), no random sampling 10 10.000 10.000 1.000
noise(0.5), no random sampling 10 10.086 9.898 12.727
noise(1.0), no random sampling 10 10.842 10.909 16.363
Small and Real blocks
Our method always have the best performances
Small blocks
Real blocks
Point clouds Fail registration using ICP
without our method
Good registration using
ICP with our method
The proposed
method works
very efficiently
for both small
and real blocks.
We have proposed a method for matching scales of 3D point clouds. Experimental results
demonstrated that the proposed method works well for easy and different point cloud
datasets.
In future works, we will try to reduce the computational cost, which is still not so small due
to the repetition of PCA.