ortion 
0 use 
lition, 
stereo 
kable 
pixel 
ated a 
of the 
of the 
ed to 
tion 
ndow 
'ctive 
rping 
24) is 
lock- 
o the 
has 
yrtion 
3). In 
le of 
Xt of 
ages. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
  
Points n,,and m> represent matching end point between r, and 
[,, on the other hand m; and ;n, are matching end point between 
F2 and I. 
  
  
  
1. I 
(a) (b) 
I 
* A 
; m, 
A 
E = m, : : 
v elec Rte ° : : : 
A m, ; : : 
SEHE M E ET TT . : 
i Si on 
i 5i Lui 
f Hy > 
0 te 7 LP EE I 
Figure 3. The original stereo images of ‘man’ and 
corresponding projective distortion result. (a) Line profile on 
left image. (b) Line profile on right image. (c) Correspondence 
of line profiles. 
The length of /; is not equal to that of r;. but /; corresponds to r, 
in real world coordination. Inevitably, other window-based 
stereo matching method is not fit to projective stereo image (T. 
Kanade, 1994). Since conventional window-based stereo 
matching methods use the same size in reference local window 
and searching local window, those methods cannot found 
correct matching point. In conclusion, analyses above show that 
wndow warping technique is necessary needed in matching 
process. 
2.2 Window Warping using Fant's algoritm 
  
  
  
window warping 
  
0 “ooogd- 
n n-2 nf n amd Qul 
WU d W pix.) Wace Wig) Wi) War) J 
Figure 4. The window warping using Fant's algorithm. 
769 
We use the Fant's algorithm so as to warp local windows in 
hierarchical BMA process. First, local window in low reliability 
region is warped to candidate windows. Second, we evaluate 
matching possibility between reference window and warped 
window. 
The main benefit of this separable algorithm is the lower 
complexity in 1-D resampling. The fittest window among the 
candidate window can be represented as Equation (1) 
n+k 
FER : n 2: 
WW, = AGMINW, 7 mor]? 
(1) 
where © is window warping size, and w is a local window in a 
block matching. We warp a local mask to the horizontal 
direction under the assumption of epipolar geometry on an input 
image. 
3. PROPOSED STEREO MATCHING WITH AN 
ADAPTIVE WINDOW WARPING ALGORITHM 
Figure 5 shows a stereo matching method we proposed. The 
proposed matching algorithm consists of four steps. The first 
step is an object extraction. In the second step, hierarchical 
block matching is performed to avoid local minima. The multi- 
resolution images are used in hierarchical block matching 
because the upper disparity result has the disambiguate 
characteristic. In the third step, the reliability-map with two 
disparity-maps (left-to-right and right-to-left) is obtained. 
Reliability includes bi-directional consistency checking and 
local disparity variance. The last step is the block matching 
process such that the warping window is used in a low reliable 
region and the normal window is used in a high reliable region.. 
  
Stereo Images 
  
  
  
Object Extraction 
Bidirectional BMA 
Depth Map Reliability 
  
  
  
  
  
  
  
  
  
  
  
Bidirectional Depth Map 
Check Correlation 
N 
Y 
Mask 
Resampling 
(UP & DOWN ) 
3 
  
Fixed Mask 
  
  
  
  
  
  
Bidirectional HBMA 
Modified Hierarchical BMA 
  
  
LR RL 
BMA BMA NK 
  
  
  
  
  
  
  
  
  
  
  
  
v 
Final 
Disparity Map 
  
  
  
  
  
Figure 5. The block diagram of the proposed algorithm.