Omni-directional Multi-baseline Stereo
without Similarity Measures
Tomokazu Sato and Naokazu Yokoya
Graduate School of Information Science, Nara Institute of Science and Technology
8916-5 Takayama, Ikoma, Nara 630-0192, Japan
E-mail:{tomoka-s, yokoya}@is.naist.jp

Abstract
This paper proposes a novel method for estimating depth
from long-baseline image sequences captured by a precalibrated moving omni-directional multi-camera system(OMS). Our idea for estimating an omni-directional depth
map is very simple; only counting interest points in images is integrated with the framework of conventional multibaseline stereo. Even by a simple algorithm, depth can be
determined without computing similarity measures such as
SSD and NCC that have been used for traditional stereo
matching. The proposed method realizes robust depth estimation against image distortions and occlusions with lower
computational cost than traditional multi-baseline stereo
method. These advantages of our method are fit for characteristics of omni-directional cameras. In experiments, validity and feasibility of our algorithm are shown for both a
synthetic and real outdoor scene.

1. Introduction
Depth map estimation from omni-directional images is oneof very important problems in omni-directional computer
vision, because depth information is used in a number ofdifferent applications such as 3-D reconstruction, surveillance, and new view synthesize. In this paper, we focus on
the framework of multi-baseline stereo for moving camera
system that is one of standard for depth estimation for alarge number of image input.
The original multi-baseline stereo method was proposedby Okutomi and Kanade [1] for multiple image input. The
multi-baseline stereo has such a very good feature that anarbitrary number of images can be simultaneously used for
depth estimation. This increases the accuracy of depth estimation and decreases the ambiguity in stereo matching.
After their work, several researchers have utilized and also
extended the original multi-baseline stereo also for an omnidirectional camera system [2, 3, 4, 5, 6].
Recently, some researchers have employed the multibaseline stereo framework for a freely moving camera[3, 4, 5]. A freely moving video camera including a moving omni-directional camera is suitable for 3-D modelingof a large scale environment because it easily makes a long
distance baseline between cameras. However, there exist
some problems in multi-baseline stereo method for a moving video camera as follows:(1) Changing patterns in video images: Free motion ofvideo camera causes significant changes of looks forcorresponding points in video frames. Traditional similarity measure such as SSD (Sum of Squared Differences), which has been used for the multi-baseline
stereo, is weak for this effect.
(2) Occlusions: When a point on an object where depth
should be estimated is occluded by other objects ina part of input video, the occluder gives a negative score to the score function of the multi-baseline
stereo: SSSD (Sum of SSD). This negative score prevents the algorithm from obtaining correct estimationof depth map around occlusions.
(3) Computational cost: A large number of images consume the large amount of memory and computational
resources. That is especially hard problem for an
OMS that can take high-resolutional multiple images
for each position of the system. Some patches for the
problems (1) and (2) may also increase computationaltime.
To avoid these problems, we use interest points such as
corners and cross points of edges in video images as shownin Figure 1. The framework of our depth estimation is basically the same as the original multi-baseline stereo except
for a newly employed score function: TNIP (Total Numberof Interest Points). The idea is based on the assumption thatthe corners of objects and cross points of texture edges inthe 3-D space (3-D interest points) will appear in video images as 2-D interest points at the projected positions of the
3-D interest points. By searching a depth that maximizes
the total number of 2-D interest points under epipolar constraint, the depth can be determined as a position of a 3-D
interest point. A flow diagram of our algorithm is shown in( xz, yz, z )
W

W

W

W

k-th frame

j-th frame( x, y )f-th framei-th frame( xˆi , yˆ i )Figure 3: 3-D position of (x, y) with depth z and its projected line to each frame.
Figure 1: Examples of interest points.
(A) Detection of interest points(B) Depth estimation for interest points

depth map are detailed in Section 4. Experimental resultswith simulation and a real scene then show the validity andfeasibility of the proposed method in Section 5. Finally,
Section 6 describes conclusion and future work.

(C) Elimination of outliers(D) Depth map interpolation

Figure 2: Flow diagram of dense depth map estimation.
Figure 2. First, interest points are detected for all the video
images (A). Next, depths are estimated by multi-baseline
stereo using TNIP (B). Outliers of estimated depths are rejected based on their confidences (C). Finally, dense depth
maps are generated by interpolating sparse depth data (D).
By our method, the problems pointed out earlier can besolved; (1) interest points are strong for the effect of changing distortion, (2) the new score function TNIP is not significantly affected by occluders, (3) computational cost is drastically decreased because depth can be determined by only
counting interest points. However there exists one restriction that we cannot estimate depths for non-interest points
by using TNIP, that is not a critical problem for 3-D modeling and some other applications because usually 3-D interest points contain corners of the 3-D model. In most cases,
depth interpolation is sufficient.
Note that TNIP based multi-baseline stereo approach
may be felt similar to the feature based stereo methods forbinocular [7, 8] and trinocular [9, 10] stereo matching thatuse edge and corner features as candidates of corresponding
points. However, there is a notable difference that the feature based stereo methods need to use similarity measures
to determine depths. In these methods, feature points are
only used as candidates of corresponding points. Moreover,conventional feature based approaches are not designed totreat a large number of images simultaneously.
The rest of this paper is structured as follows. First, theoriginal multi-baseline stereo method for a moving video
camera is briefly described in Section 2. In Section 3, the
new score function TNIP for multi-baseline stereo is proposed. Stages (A) to (D) in Figure 2 for estimating a dense

2. Multi-baseline stereo by using SSSD
In this section, firstly, coordinate systems of a general moving camera are defined. The principle of the multi-baseline
stereo [1] using SSSD is then briefly summarized.

2.1. Definition of coordinate systems for moving camera
In the multi-baseline stereo, as shown in Figure 3, a depth
z of a pixel (x, y) in the f-th frame is estimated by using
images from the j-th to k-th frame (j ≤ f ≤ k). In thefollowing, for simplicity, we assume that the focal length is
1 and lens distortion effect has already been corrected by
known intrinsic parameters. In this case, a 3-D position of(x, y) with depth z is represented as (xz, yz, z) in the camera coordinate system of the f-th frame. The 3-D position(xz, yz, z) is projected to the position (x̂ i , yˆi ) in the imageof the i-th frame by the following expression.
⎞
⎛
⎞
⎛
ax̂i
xz
⎜ ayˆi ⎟⎜ yz ⎟⎟⎜⎟⎜(1)⎝ a ⎠ = Mf i ⎝ z ⎠ ,11
where a is a parameter, Mf i denotes a 4 × 4 transformation matrix from the camera coordinate system of the f-th
frame to the camera coordinate system of the i-th frame. In
the multi-baseline stereo, as shown in Figure 3, the point(x̂i , yˆi ) is constrained on the epipolar line, which is the projection of the 3-D line connecting the position (xz, yz, z)
and the center of projection in the f-th frame onto the i-thframe.

2.2. Depth estimation using SSSD
In the traditional multi-baseline stereo, depth z of pixel(x, y) is determined by using the similarity measure SSD.

The SSD is computed as the sum of squared differences between two image patterns that have a certain size W . The
SSD for (x, y) in the f-th frame and (xˆi , yˆi ) in the i-thframe is defined using image intensity I as follows.
SSDf ixy (z) = 
2
If (x + u, y + v) − Ii (x̂i + u, yˆi + v) . (2)(u,v)⊆W

To evaluate the error of the depth z for all the input images,
the SSD is summed up as follows:
SSSDf xy (z) =kSSDf ixy (z).

(3)

i=j

The depth z is determined for each frame so as to minimize
the SSSD function. Generally, to find a global minimumof the SSSD, depth z should be searched for all the depth
range along a 3-D line from a reference pixel (x, y).
If the pixel (x, y) in the f-th frame is occluded by otherobjects in the i-th frame, SSSDf xy (z) for the true depth
z is increased by the occluder because SSDf ixy (z) gives alarge error. Thus, to obtain a correct depth at such an occluded part, some other computationally expensive extensions should be added to the original multi-baseline stereo.
For example, a modified SSSD can be computed by summing up only lower halves of SSDs [5, 11]. However, there
still remains the computational cost problem and the image
distortion problem.

3. Multi-baseline stereo by counting
interest points
In this section, a new score function TNIP is defined to estimate depth z of pixel (x, y) using the multi-baseline stereo
framework. Generally, feature points in a 3-D space, suchas corners of objects and cross points of texture edges, appear as 2-D feature points in images at projected positionsof the 3-D feature points. Such a 2-D feature points can beeasily detected by interest operators such as Harris’s [12]and Moravec’s [13] operators.
In this study, depth z is determined so as to maximize theTNIP score function that is defined as follows.
T N IPf xy (z) =kHi (x̂i + u, ŷi + v).

(4)i=j (u,v)⊆W⎧⎨ 1 ; interest point exists at(u, v) in i-th frame .
Hi (u, v) =⎩0 ; otherwise(5)

The TNIP score represents the total number of interest
points that exist in (x̂ i , ŷi ) centered windows W for all theframes. Note that the size of W should be appropriately
small because interest points are not detected at positions
far from projected positions of (xz, yz, z) when there exists a feature point in 3-D space. It should be noted that the
new score function TNIP is originated assuming the use of alarge number of images. It shows its real ability when used
for a long image sequence.
By using the TNIP instead of the SSSD function in themulti-baseline stereo, computational time can be drasticallydecreased because the time consuming process of comparing intensity patterns can be removed from the depth estimation. Moreover, maximizing the TNIP can obtain a correct depth even if projected image patterns of 3-D objects
are much distorted by the motion of camera because positions of interest points are not affected by such a geometrictransformation. The TNIP has another good feature that theTNIP is not significantly influenced by occluders because it
counts only positive scores. These claims will be justified
by experiments later.

4. Dense depth map estimation froman image sequenceThis section details each stage of dense depth map estimation shown in Figure 2. In our method, first, interest
points in all the input images are detected by Harris interest operator (A). Next, depth of each detected interest point
is determined by the multi-baseline stereo framework with
the TNIP score function (B). Outliers of estimated depths
are then eliminated by using their confidences defined byconsidering the consistency among the results in multiple
frames (C). Finally, dense depth maps are generated by interpolating sparse depth data (D).

4.1. Detection of interest points
In the first stage (A), interest points such as corners andcross points of edges are detected in input images by Harris
interest operator [12]. Harris operator has been evaluatedby Schmid as one of the best operators with respect to therepeatability rate of detected position under different geometric transformation [14] 1 .
Input images are first smoothed by a Gaussian operator.
After that, deviations I x and Iy of pixel intensity are computed for all the pixels in x and y directions, respectively.
Feature quantity F (x) of the pixel x = (x, y) is then computed as a minimum eigenvalue of the matrix A that is defined below.
Ix (x)Iy (x)Ix (x)2A=.
(6)
Ix (x)Iy (x)Iy (x)2x∈W

1 Although SIFT(Scale Invariant Feature Transform)[15] is one of good
operator, detected positions by SIFT are usually far from edges. In thisresearch, SIFT does not fit for our purpose.

F (x) = min(λ1 , λ2 ),(7)where λ1 and λ2 are eigenvalues of the matrix A. Aftercomputing the feature quantity F (x) for all the pixels, local maxima of F (x) are detected as interest points. In thisstage, interest points are detected for all the frames in animage sequence.

In the second stage (B), depths of all the interest points detected in the stage (A) are computed by maximizing theTNIP score function defined in Section 3. The depth z issearched to find a maximum TNIP in a given range of depth
along a 3-D line from each reference pixel. By repeating theestimation of depth z for all the interest points in the input
image sequence, sparse depth data can be acquired.
Note that, in this stage, any intensity images are notneeded for depth estimation. Only 2-D positions of interest points and camera parameters should be stored to compute TNIP. It means that our method needs only 1/8 memory space to compute depth by compared with SSSD, if 8
bit grayscale images are assumed to be used for SSSD.

(a) plane 1(b) plane 2

Figure 4: Textures of planes.
10m

plane 15m
10m

plane 2first frame

last frame

2 5m

4.2. Depth estimation for interest points

middle frame
camera path

Figure 5: Layout of planes and camera path in simulation.

4.3. Elimination of outliers
In the third stage (C), unreliable depths are rejected by crossvalidation approach for multiple image input. As shownin Figure 3, the depth z estimated by using TNIP relatesinterest points at projected positions of the 3-D feature point(xz, yz, z) in neighboring frames with one another. In thispaper, the confidence Cp of an interest point p is defined byusing this relation as follows.
/ L i , 1; p ∈ L i }i∈Lp {0; p ∈
,
(8)
Cp =
|Lp |
where Lp denotes a set of interest points in neighboring
frames related by the depth z of the interest point p. C pmeans the consistency among depth data obtained in theneighboring frames, and is computed as a ratio that interest
points i(i ∈ L p ) are mutually related with the interest point
p. If all the depths are correctly estimated, Li (∀i ∈ Lp )should equal to L p . Only in this case, Cp becomes maximum value 1. In this stage, depth of the interest point p
whose confidence Cp is lower than a given threshold is regarded as an outlier, and is deleted.

4.4. Depth map interpolation
Depth interpolation is necessary to generate dense depth
maps because the TNIP-based multi-baseline stereo cannot
estimate a depth at non-interest points. In this paper, we
simply assume that the space among interest points is expected to be planar because interest points are corners of(a) first frame(b) middle frame(c) last frame

Figure 6: Sampled frames from 91 input images.
3-D objects. In the final stage (D), input images are divided
into triangle regions using interest points with Delaunay’s
triangulation method [16]. Depth data are then linearly interpolated for these triangles.

5. Experiments
We have carried out two kinds of experiments. One is concerned with the accuracy comparison between SSSD andTNIP in computer simulation. The other is conducted for
estimating a dense depth map for a real outdoor environment.

5.1. Comparison between SSSD and TNIP incomputer simulation
This experiment is carried out to show the validity of the useof the TNIP score function for feature based multi-baseline
stereo by comparing it with the traditional score function
SSSD.

SSSD (plane 1)
SSSD (plane 2)
TNIP (plane 1)
TNIP (plane 2)

8000
7000
6000
5000
4000
3000
2000
1000
0

10000
9000

average error of depth [mm]9000

average error of depth [mm]average error of depth [mm]10000

SSSD (plane 1)
SSSD (plane 2)
TNIP (plane 1)
TNIP (plane 2)

8000
7000
6000
5000
4000
3000
2000
1000
0

1x1

3x3

7x7

15x15

31x31

10000
9000

SSSD (plane 1)
SSSD (plane 2)
TNIP (plane 1)
TNIP (plane 2)

8000
7000
6000
5000
4000
3000
2000
1000
0

1x1

3x3

7x7

15x15

31x31

1x1

3x3

7x7

15x15

size of window W [pixel]

size of window W [pixel]

size of window W [pixel](a) σ=0.0 pixel(b) σ=1.0 pixel(c) σ=2.0 pixels

31x31

SSSD(plane 1)
SSSD(plane 2)
TNIP(plane 1)
TNIP(plane 2)

4000
3500
3000
2500
2000
1500
1000
500
0

5000
4500

SSSD(plane 1)
SSSD(plane 2)
TNIP(plane 1)
TNIP(plane 2)

4000
3500
3000
2500
2000
1500
1000
500
0

11

31

51

71

91

average error of depth [mm]

5000
4500

average error of depth [mm]average error of depth [mm]Figure 7: Average errors in depth estimation (varying window size and noise level).
5000
4500

SSSD(plane 1)
SSSD(plane 2)
TNIP(plane 1)
TNIP(plane 2)

4000
3500
3000
2500
2000
1500
1000
500
0

11

31

51

71

91

11

31

51

71

number of images N

number of images N

number of images N(a) σ=0.0 pixel(b) σ=1.0 pixel(c) σ=2.0 pixels

91

Figure 8: Average errors in depth estimation (varying number of input images and noise level).

(1) Setup of simulation: In the experiment, two textured
planes are located in a virtual environment, and a virtual
camera takes an image sequence by moving the camera
around these planes. To observe characteristics of TNIP
and SSSD, two kinds of texture patterns are used for theplanes, as shown in Figure 4. The layout of the planes andthe motion path of virtual camera are illustrated in Figure 5.
Totally 91 input images, some of which are shown in Figure
6, are taken by the moving camera whose motion draws aquarter circle as illustrated in Figure 5. By the motion of thecamera, the plane 1 is occluded by the plane 2 in after half of
the input images, and both textures are apparently distortedby the camera motion. This is one of very severe input fortraditional multi-baseline stereo. To observe raw characteristic of both score functions, outliers are not deleted anddepth data is not interpolated. To take into account camera
calibration errors about intrinsic and extrinsic camera parameters, the Gaussian noise with standard deviation σ isadded to projected positions of 3-D points. The searchingrange of depth for TNIP and SSSD is set as 3,000mm (near)to 35,000mm (far) in this simulation.
(2) Evaluation for varying window size and noise level:Firstly, depth of each interest point is estimated and evaluated for varying two parameters; the size of window W in
Eqs. (2) and (4), and the noise level σ for projected positionof 3-D point. In this experiment, all of the input images areused to compute TNIP and SSSD. Figure 7 denotes average
errors of estimated depth values with respect to varying window sizes and noise levels. This experiment has given us anconclusion that 3×3 window is the best for TNIP and larger
size windows have never give good scores because too large
size windows cannot distinguish interest points in an image.
On the other hand, in the case of SSSD, 15 × 15 window
gives totally better results than other window sizes. Notethat TNIP’s results for plane 1 and 2 have approximately
the same accuracy regardless of existence of occluded partin plane 1 in contrast with SSSD’s. This means that depths
by TNIP are not affected by occlusions and the differenceof texture patterns.
(3) Evaluation for varying number of input images andnoise level: Next, to observe the behavior of each scorefunction for the varying number of input images, 91 input images that are used to compute the score functions arethinned out to N images. According to the previous results,
in this case, window sizes for TNIP and SSSD are fixed to3 × 3 and 15 × 15, respectively. Figure 8 denotes average
errors of estimated depths with respect to varying noise levels and number of input images. In all the results, average
errors are monotonously decreased with respect to the number of input images. In this figure, we can confirm that TNIP
and SSSD’s behavior and accuracy for the varying numberof input images are almost the same except that the accu-

racy for the SSSD’s result on the occluded plane 1 is a little
worse than the other’s.
(4) Computational time: Table 1 indicates the average time to estimate a depth of a single pixel using all
the 91 input images with respect to different window
sizes. The computation time is measured by using a PC
(CPU: Pentium-4 Xeon 3.20GHz dual, Memory: 2GB).
Now, we can conclude that the computational cost of TNIP
(3 × 3 window) is about 40 times cheaper than SSSD’s(15 × 15 window) to achieve almost the same accuracy.
Table 1: Average computational time for estimating a depthof a single pixel [milli-seconds].
window size
SSSD
TNIP

1×1
10.4
7.2

3×3
23.1
8.2

(a) appearance

7×7
85.6
9.2

15 × 15356.4
10.8

31 × 311529
19.0(b) view volume

Figure 9: Omni-directional multi-camera system: Ladybug.

5.2. Dense depth map estimation in an outdoor
environment
In this experiment, an outdoor environment is captured byan Omni-directional Multi-camera System (OMS): Ladybug [17]. Figure 9 shows an appearance and view volumeof Ladybug. This camera system has six radially locatedcamera units and takes synchronized six image sequencesat 15fps (resolution of each camera: 768 × 1024 pixels).
First, the outdoor environment was captured by the OMS
as 3,000 images (500 frames). Figure 10 shows a sampled
frame of six input image sequences. Intrinsic camera parameters including geometric relations among fixed camera units are calibrated in advance by using a marker board
and a 3-D laser measure [18]. Extrinsic camera parameters of the input image sequences are estimated using bundle adjustment by tracking both a small number of featurelandmarks of known 3-D positions and a large number ofnatural features of unknown 3-D positions in input images
across adjacent camera units[19]. Figure 11 illustrates therecovered camera path that is used as an input for depth estimation. The curved line and pyramids denote the motion

Figure 10: Sampled frame of input image sequences.
path of a camera unit and its posture at every 20 frames, respectively. The length of the camera path is approximately
29m. The accuracy of estimated camera path is evaluated as
50mm about camera position and 0.07degree about camera
posture[19].
Next, omni-directional depth maps are actually estimated by the method described in Section 4. In the stage(A), interest points are detected in all the frames of six input image sequences by Harris operator. In this experiment,
1,750 interest points are detected on average in a single input image (10,500 points per frame).
In the stage (B), depths of all the interest points detectedin the stage (A) are estimated using the TNIP score function. In this stage, interest points in the (f − 100)-th tothe (f + 100)-th frames at every 2 frames (606 images,101
frames) are used to estimate depth data of the f-th frame.
The size of window W was set as 3 × 3 pixels according to
the result of the computer simulation described in the previous section. The searching range to find a maximum TNIP
in this stage is 1,000mm (near) to 80,000mm (far).
In the stage (C), low confidence depths are eliminated.
The threshold for C p defined in Eq. (8) was set as 0.5 in thisexperiment. Figure 12 shows the results of depth estimation
for the images in Figure 10. In this figure, depth values
are corded in intensity. Figure 13 indicates TNIP values ofrandomly selected six interest points in Figure 12. We canconfirm from Figure 13 that each TNIP plot has a single
apparent peak at a certain depth value and there are no othercomparable peaks. This clearly shows that depth estimation
can be easily achieved for these interest points.
Finally, omni-directional dense depth maps are generated in the stage (D). Figure 14 shows a panoramic image
that is generated from six input images shown in Figure 10.
Figure 15 shows the corresponding dense depth map. By

(a) top view

120

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TNIP

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TNIP

TNIP

Figure 12: Result of depth estimation for interest points in
Figure 10.

80000

0

In this paper, a novel multi-baseline stereo for a moving
camera has been proposed, where depth can be determinedby only counting the number of interest points. The proposed method shows its real ability when used for longtime and long-baseline image sequences and is congenialwith omni-directional images. Our method has be provento be robust against occlusions and image distortion problem that are caused by camera motion. Additionally, thecomputational cost for the proposed method is also cheaper
than the method based on the traditional SSSD function. In
experiments, these claims have been justified by using both

80000

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(c) point 3

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60

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depth [mm](b) point 2
TNIP

TNIP

60000

100

(d) point 4

6. Conclusion

40000

120

depth [mm]comparing these figures, we can confirm that a dense depth
map is correctly computed for most parts of the input image.
However, some incorrect depths are also observed aroundthe boundaries between the buildings and the sky. These
incorrect results are caused by depth interpolation over different objects. To improve the result, region information in
input images should be considered in the triangulation stage
(D).

20000

depth [mm](a) point 1

Figure 11: Camera path of OMS used for input (29m).

40
20

0

depth [mm](b) side view

60

60
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20
0

0

20000

40000

60000

depth [mm](e) point 5

80000

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depth [mm](f) point 6

Figure 13: TNIP scores for searching depth.
synthetic and real image sequences. In future work, estimated depth maps will be integrated to reconstruct a 3-D
model of a large outdoor environment.

References[1] M. Okutomi and T. Kanade: “A Multiple-baseline Stereo,”
IEEE Trans. Pattern Analysis and Machine Intelligence, Vol.
15, No. 4, pp. 353–363, 1993.
[2] S. B. Kang, J. A. Webb, C. Zitnick and T. Kanade: “A Multibaseline Stereo System with Active Illumination and Realtime Image Acquisition,” Proc. Int. Conf. on Computer Vision, pp. 88–93, 1995.
[3] S. B. Kang and R. Szeliski: “3-D Scene Data Recovery using
Omnidirectional Multibaseline Stereo,” Int. Journal of Computer Vision, Vol. 25, No. 2, pp. 167–183, 1997.
[4] W. Zheng, Y. Kanatsugu, Y. Shishikui and Y. Tanaka: “Robust Depth-map Estimation from Image Sequences with Pre-

Figure 14: Panoramic image generated from six images acquired by OMS.

Figure 15: Generated dense depth map.
cise Camera Operation Parameters,” Proc. Int. Conf. on Image Processing, Vol. II, pp. 764–767, 2000.

[12] C. Harris and M. Stephens: “A Combined Corner and Edge
Detector,” Proc. Alvey Vision Conf., pp. 147–151, 1988.

[5] T. Sato, M. Kanbara, N. Yokoya and H. Takemura: “Dense 3D Reconstruction of an Outdoor Scene by Hundreds-baseline
Stereo Using a Hand-held Video Camera,” Int. Journal ofComputer Vision, Vol. 47, No. 1-3, pp. 119–129, 2002.

[13] H. Moravec: “Towards Automatic Visual Obstacle Avoidance,” Proc. Int. Joint Conf. on Artificial Intelligence, p. 584,
1977.

[6] M. Okutomi, Y. Katayama and S. Oka: “A Simple Stereo Algorithm to Recover Precise Object Boundaries and SmoothSurface,” Int. Journal of Computer Vision, Vol. 47, No. 1-3,
pp. 261–273, 2002.
[7] H. H. Baker: “Edge Based Stereo Correlation,” Proc. Image
Understanding Workshop, pp. 168–175, 1980.
[8] W. E. L. Grimson: “Computational Experiments with a
Feature-based Stereo Algorithm,” IEEE Trans. on PatternAnalysis and Machine Intelligence, Vol. 7, No. 1, pp. 17–34,
1985.
[9] S. Pollard, M. Pilu, S. Hayes and A. Lorusso: “View Synthesis by Trinocular Edge Matching and Transfer,” Image andVision Computing, Vol. 18, No. 9, pp. 739–748, 2000.
[10] M. Agrawal and L. S. Davis: “Trinocular Stereo Using
Shortest Paths and the Ordering Constraint,” Int. Journal ofComputer Vision, Vol. 47, No. 1-3, pp. 43–50, 2002.
[11] S. B. Kang, R. Szeliski and J. Chai: “Handling Occlusions in
Dense Multi-view Stereo,” IEEE Conf. on Computer Vision
and Pattern Recognition, Vol.1, pp. 103–110, 2001.

[14] C. Schmid, R. Mohr and C. Bauckhage: “Evaluation of Interest Point Detectors,” Int. Journal of Computer Vision, Vol.
37, No. 2, pp. 151–172, 2000.
[15] D. G. Lowe: “Distinctive Image Features from Scale Invariant Keypoints,” Int. Journal of Computer Vision, Vol. 60, No.
2, pp. 91–110, 2004.
[16] P. Heckbert Ed.: Graphics Gems IV, pp. 47–59, Academic
Press, 1994.
[17] Point Grey Research Inc.: “Ladybug,”
http://www.ptgrey.com/.
[18] S. Ikeda, T. Sato and N. Yokoya: “High-resolution
Panoramic Movie Generation from Video Streams Acquiredby an Omnidirectional Multi-camera System,” Proc. IEEE
Int. Conf. on Multisensor Fusion and Integration for Intelligent System, pp. 155–160, 2003.
[19] T. Sato, S. Ikeda and N. Yokoya: “Extrinsic Camera Parameter Recovery from Multiple Image Sequences Captured byan Omni-directional Multi-camera System,” Proc. European
Conf. on Computer Vision, Vol. 2, pp. 326–340, 2004.