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USC Computer Science Technical Reports, no. 874 (2006)

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USC Computer Science Technical Reports, no. 874 (2006)

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Content Automatic Pose Recovery for High-Quality Textures Generation

Jinhui Hu, Suya You, Ulrich Neumann
University of Southern California
{jinhuihu, suyay,uneumann}@graphics.usc.edu

Jinhui Hu
University of Southern California
jinhuihu@graphics.usc.edu

Abstract

This paper proposes new techniques to generate
high quality textures for urban building models by
automatic camera calibration and pose recovery. The
camera pose is decomposed into an orientation and a
translation, an edge error model and knowledge-based
filters are used to estimate correct vanishing points
with heavy trees occlusion, and the vanishing points
are used for the camera calibration and orientation
estimation. We propose new techniques to estimate the
camera orientation with infinite vanishing points and
translation with under-constraints. The final textures
are generated using color calibration and blending
with the recovered pose. A number of textures for
outdoor buildings are automatically generated, which
shows the effectiveness of our algorithms.

1. Introduction
High quality texture is a crucial element in today’s
vision and graphics applications. With the rapid
development of technologies for modeling, it becomes
more feasible to model a large-scale urban
environment [11]. These urban models are enhanced
by textures generated from ground view images, which
requires camera calibration and pose recovery.
Automatic camera calibration and pose recovery is
a challenging task for outdoor building images. The
camera orientation can be estimated using vanishing
points [2], however, heavy trees occlusion of outdoor
urban buildings (Figure 3(a)) causes vanishing points
extraction to be a difficult problem. Furthermore,
given a camera’s orientation, its translation (relative to
models) recovery is often an under-constraint problem
using a single image due to lack of features in rough
building models (Figure 3(g)) and the narrow field of
view of a camera (Figure 3 (c)). Lastly, it is very hard
to capture an image that covers a whole building due to
the small field of view a camera and the physical
barriers of narrow streets. Multiple images are often
necessary to generate textures for a whole building,
which causes other problems such as illumination
variation and parallax in different images. The goal of
this paper is to generate high quality textures for given
urban building models (especially rough models) by
automatic camera calibration and pose recovery.
Previous work [4] fix the image senor with the
range sensor to get the texture data, and the camera
pose is recovered by a simple calibration relative to the
range sensor. This technique has the advantage of
simple calibration, but lack of flexibility. Stamos and
Allen [13] use a freely moving camera to capture the
image data. The camera pose is computed by fitting
rectangular features from dense 3D range data, which
is not applicable for coarse urban models. Sunchun et
al. [6] propose a system to register ground images to
urban models using vanishing points to estimate the
orientation and 2D to 3D feature correspondences to
estimate the translation. The translation under-
constraint problem is solved by manually infer more
3D points from registered images, which is not
applicable when all images are of under-constraints.
This paper presents new techniques to solve the
challenges in generating textures for urban models.
Our algorithm uses an edge error model to group
image lines and knowledge-based filters to extract
correct vanishing points under heavy trees occlusion
for camera calibration and orientation estimation. We
derive equations for camera orientation estimation with
infinite vanishing points, and compute the translation
using multiple images when each single image does
not provide enough constraints. Our translation
estimation algorithm works for large base-line images,
which is a difficult case for stereo-based methods. The
final textures are generated using a color calibration
method and blending techniques to solve the
illumination and parallax problem in different images.

2. Pose Estimation
2.1. Camera model
The camera projection matrix is modeled using
Equation 1, where K is the internal parameter matrix,
and RT is the camera’s external parameter matrix. The
focal length and principle point can be estimated given
three orthogonal vanishing points [2]. When only two
vanishing points are available, the principle point is
assumed to be at the image center.
] [ T R K P =
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
1 0 0
0
0
0
0
v
u
K α
α
(1)
We decompose the camera’s external matrix into
orientation and translation. The orientation of the
camera is estimated using vanishing points extracted
by automatic line clustering, the translation is
computed using 3D to 2D corner correspondences, and
multiple images are used if one image does not provide
enough correspondences. A global registration
algorithm is used to refine the pose.
Figure 1. The edge error model and grouping method.

2.2. Orientation estimation
Vanishing points extraction
Vanishing points are used to estimate the camera’s
orientation due to lack of features in 3D urban models.
Many methods have been presented using vanishing
points for camera calibration and pose recovery
[1,8,12]. We opt to use an automatic line clustering
method in image space rather than Gaussian sphere
because of several reasons. Gaussian sphere method is
a global feature extraction method, which is sensitive
to spurious maxima. The accuracy of Gaussian sphere
method is limited to the discretizing accuracy, which is
hard to achieve the precision that an image can offer.
Edges are detected using Canny edge detector and
lines are extracted using Hough Transform as a
preprocess step for vanishing points extraction. The
intersections of all pairs of line segments are then
computed to find all possible vanishing points for line
grouping. We need a grouping criterion to assign lines
to different clusters (vanishing points). Many methods
[12] use a hard threshold of distance or angle, which is
sensitive to noise. We use a method that is based on an
edge error model without any hard thresholds.
The edge error model is as following. Consider the
representation of a line segment using two endpoints,
and assume the two end points have one pixel
precision, then two fan regions with a rectangular
region in the middle can be formed by moving the two
end points freely in the pixel squares (Figure 1(left)).
Since a true vanishing point cannot lie in the image
line segment, the rectangular region has no effect on
the intersection of edge regions. We take the middle
point of the edge, and form two fan regions with the
two end points. Furthermore, a true vanishing point
can only lie in one direction of the edge, so we just
take one of the fan region (Figure 1(middle)). Shufelt
[12] uses a constant value of one pixel as the noise
magnitude for the two end points, while we model the
noise magnitude as l c / = ε , where l is the length of
the edge, and c is set to 3.5 pixels. This model shows a
better result than setting the noise magnitude as a
constant value for all lines.
The grouping method is consistent with the edge
error model. For each cluster of two lines, we find the
intersection region A of the edges, and a test edge is
assigned to this cluster when its edge region overlaps
with region A. Furthermore, we use a strong clustering
constraint. A test edge is assigned to a cluster only if
its edge region covers the intersection point of the
cluster (Figure 1(right)). This guarantees the
intersection region of the edge regions in each cluster
is not empty, thus the vanishing point is not empty.
The normalized length of each edge is accumulated in
its assigned cluster, and the maximum clusters are
chosen to compute potential vanishing points.
Filtering spurious vanishing points
Most of our testing images are outdoor building
images with heavy occlusion by trees (Figure 3(a)),
which causes many spurious vanishing points.
Knowledge of the image and vanishing points are used
to filter spurious vanishing points. We first roughly
classify the extracted lines into x and y groups
according to the line orientation, then filter vanishing
points using the following three filters.
1) Line length. According to the edge error model,
longer lines are more reliable, however, we would like
also to keep shorter lines. So we first filter the lines
with a large length threshold, then estimate the
possible vanishing points, and these points are used to
find more line supporters according to the grouping
method.
2) Covering area. Another observation of the image
is that edges of trees only cover a small part of the
image region, so the ratio of the covering area against
the image area is also used to filter spurious vanishing
points.
3) Valid vanishing point. Vanishing points are the
intersection of image lines that correspond to parallel
lines in 3D, so a valid vanishing point will not lie on
the image segment in the image space. This filter is
very effective in reducing spurious clusters.
Finding clusters and grouping lines using all pairs
of line segments is computational expensive. Even
though we classify lines into two directions to reduce
the line number and use filters to reject spurious
clusters, the number of clusters may still be large. The
RANSAC algorithm is used to find the maximum
cluster of lines for x-y direction rather than testing each
pair of line segments. The vanishing point of z
direction is estimated using the orthogonal property of
the three directions, and supporting lines are found
using our grouping method to refine the position of the
vanishing point. The algorithm for vanishing points
extraction is summarized as following.
Rotation estimation
The rotation matrix and camera’s focal length and
principle point can be estimated given three orthogonal
vanishing points. Cipolla et al. [2] derive the following
equations:
R v
u
v v v
u u u
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
1 0 0
0
0
0
0
3 2 1
3 3 2 2 1 1
3 3 2 2 1 1
α
α
λ λ λ
λ λ λ
λ λ λ

⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
− − −
− − −
=
3 2 1
0 3 3 0 2 2 0 1 1
0 3 3 0 2 2 0 1 1
/ ) ( / ) ( / ) (
/ ) ( / ) ( / ) (
λ λ λ
α λ α λ α λ
α λ α λ α λ
v v v v v v
u u u u u u
R
Where
1
λ ,
2
λ and
3
λ are scale factors, is the
principle point, are the three orthogonal
vanishing points, and
) , (
0 0
v u
3 , 2 , 1 ) , ( = i v u
i i
α is the focal length. When only
two vanishing points are available, the third vanishing
point can be inferred by assuming that the principle
point is at the camera center [6].
Equation (3) gives the solution of the rotation
matrix for finite vanishing points, however, when the
vanishing points are at infinity (lines are parallel in the
image space), the solution becomes unclear.
We derive the equations to compute the rotation
matrix for infinite vanishing points using Euler angles.
A rotation matrix can be represented using three Euler
angles (We ignore singularity cases of 90 degrees,
which can be treated specifically).
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
+ + −
− + − +
−
=
cxcy sxcz sycxsz sxsz sycxcz
sxcy cxcz sxsysz cxsz sxsycz
sy cysz cycz
R
(4)
Where x, y, z are the three Euler angles, cx stands
for cosx, and sx stands for sinx. We classify the
situation into two cases according to the number of
infinite vanishing points, and derive the solutions
respectively.
1. One infinite vanishing point, two finite vanishing
points. Suppose the x direction vanishing point is at
infinite, thus the y direction rotation is zero, so:
Algorithm 1. Vanishing Points Extraction
1. Filtering lines use a large length threshold.
2. Random pick two lines and find the
intersection points.
3. Find the line supports using the grouping
method based on an edge error model.
4. Filtering the vanishing point with area ratio and
valid vanishing point filters. The vanishing
point with maximum supporters is stored to
find potential vanishing points
5. Repeat step 2 through 4 a number of times.
6. The estimated vanish points from step 5 are
used to find more line supporters, and the
positions of the vanishing points are refined.
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
=
cx sxcz sxsz
sx cxcz cxsz
sz cz
R
0

(5)
Substitute Equation (5) into Equation (2), we have:
R v
u
v v v
u u u
A
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
1 0 0
0
0
0
0
3 2 1
3 3 2 2 1 1
3 3 2 2 1 1
α
α
λ λ λ
λ λ λ
λ λ λ

(6)
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
+ − + +
+ − +
=
cx sxcz sxsz
cx v sx sxcz v cxcz sxsz v cxsz
cx u sxcz u sz sxsz u cz
0 0 0
0 0 0
α α α
α α

Assume 0 ≠ cz (the rotation around z axis is not 90
degrees, otherwise we have just two variables of x
and α, which is trivial to solve), from certain
operations on both sides, we have:
1 1 21 11
/ / v u A A = = ) /( ) (
0 0
sx v cx sx u ctgz + + α α
(7)
2 32 12
/ u A A = = sx sx u tgz / ) (
0
+ − α
2 32 22
/ v A A = =
0
v ctgx + α
(2) Without loss of generality, we assume the principle
points are at the image center, and 0 , 0
0 0
= = v u . Let
1 1 1
/ v u k = (although are at infinity, the slope of
the image lines is still finite since z rotation is not 90
degrees),
1 1
v u
2 2 2
/ v u k = , it is easy to find the solution of
Equation (7) as:
(3)
2 / 1
2 1
1
)] /( 1 [ cos k k x − =
−

(8)
tgx v v ) (
0 2
− = α
] / ) [(
2 0
1
α sx u sx u tg z − =
−

We can derive the solution in a similar way when
the y or z direction vanishing point is at infinite.
2. Two infinite vanishing points, one finite
vanishing points. Suppose x, y direction vanishing
points are at infinite, then the x, y direction rotation is
zero, so we have:
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡ −
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
1 0 0
0
0
3 2 1
3 3 2 2 1 1
3 3 2 2 1 1
cz sz
sz cz
v v v
u u u
α α
α α
λ λ λ
λ λ λ
λ λ λ

Thus, , where is the slope of
image lines that corresponds to the x direction
vanishing point. The focal length cannot be recovered
in this case. The other tow cases when the z-y or x-y
direction vanishing points are at infinite can be derived
in a similar way.
) / (
1 1
1
v u ctg z
−
=
1 1
/ v u

2.3. Translation estimation
Given the orientation of the camera, the translation
relative to the 3D models can be computed using two
2D to 3D point correspondences [6]. However, due to
the physical limitations (such as a camera’s small field
of view and narrow streets), sometimes only one 3D
corner or none corners are visible for a single image
(Figure 3(c)), which makes the translation estimation
problem an under-constraint problem.
Multiple images are used to compute the camera’s
translation when each single image does not provide
enough constraints. Let’s first consider two images,
each of which covers only one 3D model corner
(Figure 2). Given only one 2D to 3D point
correspondence, the position of the camera’s
projection center has ambiguity; it is along the line of
the 3D point and 2D image point (Figure 2 line ).
The ambiguity can be fixed for both images given one
extra 2D image point correspondence between the two
images. We give a geometrical explanation for this,
and the exact analytical solution is not shown due to
limited space.
1 1
i P
As shown in Figure 2, are the projection
centers of two images, are two 3D model
vertices, with as their image points respectively,
and is a given image correspondence pair. The
3D position of is along the line . Since the
orientation is fixed, the line forms a plane while
its end points moves along the line . The plane
intersects with the model plane at a line (or a
curve for a curved model surface). Similarly,
forms a plane while its end points moves
along the line , and the plane intersects
with the model plane at a line . So the 3D model
point is uniquely determined by the intersection of
line and . Hence the 3D position of is fixed by
the intersection of line and . Similarly, the 3D
position of is fixed by the intersection of
line and . Thus we can compute the 3D
translation for both images.
1
O
2
O
1
P
2
P
1
i
2
i
) , (
'
3 3
i i
1
O
1 1
i P
3 1
i O
1
O
1 1
i P
3 1 1
i O P
1
l
'
3 2
i O
2
O
2 2
i P
'
3 2 2
i O P
2
l
3
P
1
l
2
l
1
O
1 1
i P
3 3
i P
2
O
2 2
i P
'
3 3
i P
When there is an image that does not cover any 3D
model corners, we use two 2D image point
correspondences to fix its translation relative to a
chosen base image, and compute the translation in a
concatenate way. The translation ambiguity of the base
image is solved when two or more 3D model points are
visible from the image sequence.

2.4. Global registration
The pose computed for a single image using several
point correspondences is not robust, so a global
registration process is employed to refine the pose. 2D
image corners are extracted for each image, and they
are matched automatically using the estimated pose,
then the matched corners are used to find
corresponding 3D model points, and a bundle
adjustment process is used to refine poses by
minimizing the overall projection errors. The algorithm
to compute the pose with under-constraints is
summarized as following.

3. Texture generation
A base buffer [5] is allocated for each façade of the
building model to store the final textures. Each image
is warped to the base buffer, and multiple images are
blended.
Due to the illumination variation in different
images, the textures have different colors, which cause
visual inconsistence. A color rectification process is
used to solve the problem. We first chose an image as
(9)
Algorithm 2. Pose Recovery
1. Compute orientation using vanishing points.
2. Compute translation using multiple images.
3. Automatic find more 2D corner matches,
and compute their 3D model points
4. Refine the pose using bundle adjustment.
Figure 2. Translation estimation.
2
O 1
O
1
i
'
3
i
3
i
2
i
1
P
3
P
2
P
1
l
2
l

the base color image, then pixels with constant colors
in a window with user defined size (we use size 5 by 5
in our implementation) are extracted, and these pixels
are automatically matched with other images using the
estimated pose, finally each image is color rectified
with an affine color model [10].
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
+
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
b
g
r
O
O
O
b
g
r
a a a
a a a
a a a
b
g
r
33 33 33
23 23 23
13 12 11
'
'
'

Images taken at different viewpoints cause a
parallax problem. Blending all the overlapping area
will create ghost effects. We solve the problem by
automatically finding the best blending area based on
the histogram of the 2D matching corners between
images. The size of the area is a user-defined value,
which is set to a small value for strong parallax
images. This method helps to reduce visual defects
caused by parallax for highly structured textures such
as building bricks and windows. However, a more
complicated algorithm using dynamical programming
to find the best cut is necessary for unstructured
textures [3]. The algorithm is summarized as
following.

4. Results
Several different textures are generated using the
described method. The 3D models are generated using
LiDAR data with a semi-automatic modeling system
[15]. Pictures are taken with an un-calibrated camera at
different time, and the focal length and illumination
varies from image to image.
Figure 3(a) and (b) demonstrate the effectiveness of
the vanishing points extraction method using filters
described in algorithm 1. Many false vanishing points
(yellow points) are detected before the filtering due to
the heavy occlusion of trees and small-scale textures
(Figure 3(a)). These spurious vanishing points are
filtered using our algorithm, and only correct dominant
vanishing points are identified (Figure 3(b)). The x
direction vanishing point for the image in Figure 3(a)
is at infinite, and its orientation is recovered using
Equation 8. The final texture created from four
separated images is shown in Figure 3(i).
Two of the four original images used to create the
texture for another building are shown in Figure 3(c)
and (d). Each of the four images only covers one
corner of the building, so the translation is an under-
constraint problem. We first compute the orientation
for each of the image using automatically estimated
vanishing points, then combine the four images to
compute the translation, and the final pose are refined
using bundle adjustment. The four images are color
corrected, and warped to the base buffer using the
refined pose. The best blending area are automatically
detected (Figure 3(e)) to reduce parallax effects, and
the final texture is generated using blending techniques
(Figure 3(f)). More textures are generated using the
described technique (Figure 3 (h), (i)), and integrated
into a 3D environment (Figure 3 (g)).
(10)

Evaluation and discussion
We project model edges back to images with the
estimated pose, and use the projection error to evaluate
our method. The average projection error is above 10
pixels before the global registration, and within 3
pixels after the global registration.
Algorithm 3. Final Texture Generation
1. Find the constant color pixels in a base color
image, and match them over all images.
2. Rectify the color of all images.
3. Find the best blending area according to the
histogram of the 2D corner matches.
4. Warp each image to the base buffer, and blend
the images in the automatic detected best
blending area.
Our method uses multiple images to recover the
camera’s pose when each single image does not
provide enough constraints. The only requirement for
multiple images is that they provide at least one 2D
image point correspondence. So our method can be
applied to large base-line images, which is a difficult
case for stereo-based methods.
Since our algorithm does not require any constraints
on the viewpoint, we can also create textures when
there are 3D model occlusions, which is a difficult case
for mosaic-based method. However, we would like to
point out that images from different viewpoints cause a
parallax problem. Although this effect can be reduced
by blending or dynamical programming techniques, it
is better to take images at the same or close viewpoint
when there is no 3D occlusion.

5. Conclusion
This paper presents new techniques to address the
challenges in generating textures for urban models.
We decompose the camera pose into orientation and
translation, and use an edge error model and
knowledge-based filters to estimate correct vanishing
points. We derive equations to compute the orientation
with infinite vanishing points, estimate the translation
by combining information from multiple images when
each single image does not provide enough constraints,
and generate final textures with color calibration and
(a) (c) (e)
(b) (d) (f)
(h) (g) (i)
Figure 3. Results of generated textures.
blending. Future work includes using the registered
images to correct 3D models and model façade details.

6. References
[1] B. Caprile and V. Torre. Using vanishing points for
camera calibration. International Journal of Computer
Vision, pp.127–140, 1990.
[2] R. Cipolla, T. Drummond and D.P. Robertson. Camera
calibration from vanishing points in images of
architectural scenes. In Proceedings of British Machine
Vision Conference, pp.382–391, 1999.
[3] A. Efros, and W. T. Freeman. Image quilting for texture
synthesis and transfer. Proceedings of SIGGRAPH
2001, pp. 341–346, 2001.
[4] C. Fruh and a. Zakhor. Constructing 3D city models by
merging aerial and ground views. CGA, 23(6): 52-61,
2003.
[5] J. Hu, S. You, and U. Neumann. Texture painting from
video. Journal of WSCG, ISSN 1213–6972, Volume
13,pp. 119–125, 2005.
[6] S.C. Lee, S. K. Jung, and R. Nevatia. Integrating ground
and aerial views for urban site modeling. ICPR, 2002.
[7] D. Liebowitz, A. Criminisi and A. Zisserman. Creating
architectural models from images. Computer Graphics
Forum, 18(3): 39–50, 1999.
[8] D. Liebowitz and A. Zisserman. Metric rectification for
perspective images of planes. In CVPR, pp.482–488,
1998.
[9] L. Liu and I. Stamos. Automatic 3D to 2D registration
for the photorealistic rendering of urban scenes. CVPR
2005.
[10] F. Mindru, L. V. Gool and T. Moons. Model estimation
for photometric changes of outdoor planar color
surfaces cuased by changes in illumination and
viewpoint. ICPR, 2002.
[11] S. Noronha and R. nevatia, Detection and modeling of
buildings from multiple aerial images, PAMI, 23(5):
501-518,2001.
[12] J. Shufelt. Performance evaluation and analysis of
vanishing point detection techniques. PAMI, 21(3):282–
288, 1999.
[13] I. Stamos and P. Allen. Automatic registration of 2D
with 3D imagery in urban environments. ICCV, pp.731–
736, 2001.
[14] X. Wang et al. Recovering façade texture and
microstructure from real world images. In Proceedings
2nd International Workshop on Texture Analysis and
Synthesis at ECCV, pp. 145–149, 2002.
[15] S. You, J. Hu, U. Neumann, and P. Fox. Urban Site
Modeling From LiDAR, Second International
Workshop on Computer Graphics and Geometric
Modeling, 2003.

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Description

Jinhui Hu. "Automatic pose recovery for high-quality textures generation." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 874 (2006).

Asset Metadata

Creator Hu, Jinhui (author)

Core Title USC Computer Science Technical Reports, no. 874 (2006)

Alternative Title Automatic pose recovery for high-quality textures generation (title)

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)

Tag OAI-PMH Harvest

Format 6 pages (extent), technical reports (aat)

Language English

Unique identifier UC16269673

Identifier 06-874 Automatic Pose Recovery for High-Quality Textures Generation (filename)

Legacy Identifier usc-cstr-06-874

Format 6 pages (extent),technical reports (aat)

Rights Department of Computer Science (University of Southern California) and the author(s).

Internet Media Type application/pdf

Source 20180426-rozan-cstechreports-shoaf (batch), Computer Science Technical Report Archive (collection), University of Southern California. Department of Computer Science. Technical Reports (series)

Access Conditions The author(s) retain rights to their work according to U.S. copyright law. Electronic access is being provided by the USC Libraries, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Repository Email csdept@usc.edu

Inherited Values

Title Computer Science Technical Report Archive

Description Archive of computer science technical reports published by the USC Department of Computer Science from 1991 - 2017.

Coverage Temporal 1991/2017

Repository Email csdept@usc.edu

Repository Name USC Viterbi School of Engineering Department of Computer Science

Repository Location Department of Computer Science. USC Viterbi School of Engineering. Los Angeles\, CA\, 90089

Publisher Department of Computer Science,USC Viterbi School of Engineering, University of Southern California, 3650 McClintock Avenue, Los Angeles, California, 90089, USA (publisher)