cted in the LIDAR 
AR point cloud, 
“points falling in a 
erate the LiDAR 
R intensity image 
the following 2D 
(1) 
and (E, N) is the 
ing Easting and 
ite system origin, 
ft corner, (Eo, No) 
ipping Easting and 
. LIDAR intensity 
| the LiDAR data 
int cloud used to 
should be filtered 
ased on elevation 
ilar height as the 
used for filtering. 
icles on the bridge 
s, and thus, those 
e void areas in the 
also exist; see the 
eure 3 (a). In order 
al outlier removal 
n each point’s 
bridge points. For 
its closest » points 
| distances obey a 
n distances outside 
mean and standard 
removed from the 
3 (a) and (b). 
  
(b) 
> surface (a) and 
b) 
\ 
lane estimation is 
ind the robust 3D 
nts is recomputed 
stimated 3D plane 
1ld be perfectly on 
ane. Subsequently, 
ned on the refined 
Is à concave shape. 
€ also determined 
based on checking elevation value with respect to their 
neighbourhood in a circular searching area, since the elevation 
difference should be large for boundary points and small for 
non-boundary points. The concave hull polygon (white) 
connecting those concave hull boundary points (yellow) and the 
bridge boundary points (blue) are illustrated in the Figure 4. 
3.2 Co-registration 
In our earlier research on multiple-domain imagery co- 
registration, a new approach based on LPFFT (Reddy and 
Chatterji, 1996; Wolberg and Zokai, 2000), Harris Corners, 
PDF mean-shift matching (Comaniciu et al, 2003) and 
RANSAC (Fischler and Bolles, 1981) affine transformation 
estimation was proposed (Toth, et al, 2011). With a limited 
dataset, the proposed method achieved promising results, and 
thus, it is applied to estimate the geometric transformation 
which is assumed an affine transformation, between the LiDAR 
intensity and aerial images. Figure 5 shows the workflow of the 
proposed co-registration approach. 
— P. Ud 
n 
i 
3 
* 
M 
; 
{ 
1 
Bon Big E Nl Tp. ee So P E 
    
Figure 4. Concave hull boundary points (yellow) and bridge 
boundary points (blue) 
  
  
  
  
  
  
  
  
  
/ / 
/ / Simitarit i 
/ / AM y validation 
/ / PF l 
e image A, 8 See e 1 eT Sunt ay P4 based on Monte 
f / estimation 
/ / Carlo 
/ 
Affine 
transformation © Regional feature |, Regional feature 
estimation i matching PY generation 
(RANSAC) 
  
  
  
  
  
  
  
  
  
Figure 5. Workflow of the affine transformation estimation 
First, the similarity transformation regarded as the coarse 
geometric transformation is estimated via a standard LPFFT 
registration method. Next is the similarity validation step where 
the scale and rotation parameter are validated based on a Monte 
Carlo process; more precisely, a Monte Carlo test is performed 
for a set of scale and rotation values computed from the 
originally estimated parameters (sg,$o) via following 
equations: 
s = {s|s; = so Hi + 65} 
2 
¢ = {loi = pot i-5¢} e 
The second image is transformed using each scale and rotation 
combination in the set. If the estimated scale and rotation 
parameters are correct, the images should have comparable 
orientation and scale. Then, FFT-accelerated NCC (Normalized 
Cross Correlation), an efficient NCC computation method, can 
be used to estimate the translation parameters for each image 
pair by searching the maximum NCC values. Those maximum 
NCC values of all image pairs should be kept at a significantly 
31 
  
high level, which means small scale and rotation changes 
around the correct scale and rotation still lead to a high NCC 
value. If the estimated scale and rotation are wrong, the 
maximum NCC values of all image pairs should be small. 
Figure 6 (a) shows the typical NCC surface based on the wrong 
(So, $9) and (b) based on the correct (so, $9) paramters. If the 
EOPs (Exterior Orientation Parameters) of aerial image are 
available, it is also possible to introduce a rotation angle 
constraint to improve the performance of similarity 
transformation estimation. According to our experiences, the 
scale and rotation parameters can be reliably estimated based on 
orientation angle constraint and the Monte Carlo validation. The 
translation parameters, however, may not be easily estimated by 
LPFFT. Therefore, translation parameters are estimated through 
the edge NCC matching method. 
m 
T ME 
sui 
$4. 
Uus 
    
  
   
e : SE 5 = 2 ii : eS 
(a) (b) 
Figure 6. NCC value surface; wrong scale and rotation 
parameter (a) and correct scale and rotation parameter (b) 
The second image is transformed using the estimated scale and 
rotation angle, so the image pair should have similar orientation 
and scale. A number of rectangle reference patches are 
generated in the first image, and subsequently, those reference 
patches are matched in the second image. Thus, the translation 
parameters can be computed as the center point image 
coordinate differences between the reference patch and matched 
patch. The correct translation is determined by a statistical 
analysis of all computed translations. The translations with 
highest frequency are accepted as correct translations, see 
Figure 7. 
  
eost Nis i 
= SE 3 me d DE Sx $ me x se 
ae 4m x 3 + xe $ 
WEHEN DEREN HR PRR EEE 
(a) (b) 
Figure 7. NCC value surface; wrong scale and rotation 
parameter (a) and correct scale and rotation parameter (b) 
The Harris Corners detector is used to extract feature points, 
and circular regions cantered on strong HC features are created 
in both images, including the imported locations from the other 
image. Next the scale- and rotation-invariant PDF descriptor is 
used to describe the circular feature region. The PDF function is 
represented in a 256-dimensional feature descriptor. The 
similarity between two feature descriptors is computed via the 
Bhattacharyya Coefficient, which is the cosine of angle 
correlation between the two feature descriptors, defined as: 
m 
p p(p.q) => JPu- Au = cosd > 0 (3) 
u=1