Stefano Mattoccia
Stereo Vision:
Algorithms and Applications
Stefano Mattoccia
Department of Computer Science (DISI)
University of Bologna
stefano.mattoccia@unibo.it
www.vision.deis.unibo.it/smatt
January 12, 2013
Stefano Mattoccia
Updates
•
Jan 2015: added new 3D applications
•
Added details about our stereo camera with FPGA processing
•
November 21, 2011: added experimental results for ��Linear
stereo matching�� (ICCV2011), Min et al��s algorithm (ICCV2011),
description of ��Fast Segmentation driven (FSD)�� (IC3D)
algorithm and description of SGM
•
May 19, 2011: added experimental results of FBS on the GPU
[71] and the VisionSt stereo camera
•
July 25, 2010: Linux and Windows implementations of the
Fast Bilateral Stereo algorithm available at:
www.vision.deis.unibo.it/smatt/fast_bilateral_stereo.htm
•
April 20th, 2010: included descriptions and experimental
results for papers [67], [68], [69]
The latest version of this document is available here:
http://www.vision.deis.unibo.it/smatt/Seminars/StereoVision.pdf
Stefano Mattoccia
Outline
•
Introduction to stereo vision
•
Overview of a stereo vision system
•
Algorithms for visual correspondence
•
Computational optimizations
•
Hardware implementation
•
Applications
Stefano Mattoccia
What is stereo vision ?
•
Is a technique aimed at inferring depth
from two or more cameras
•
Wide research topic in computer vision
•
This seminar is concerned with
•
binocular stereo vision systems
•
dense stereo algorithms
•
stereo vision applications
•
Emphasis is on approaches that are (or
might be hopefully soon) feasible for
realtime/hardware implementation
Stefano Mattoccia
Applications
www.nasa.gov
www.nasa.gov
www.vision.deis.unibo.it/smatt/stereo
Stefano Mattoccia
O
P
Q
p��q
��
Single camera
•
Both (real) points (P and Q)
project into the same image
point (p �� q)
•
This occurs for each point
along the same line of sight
•
Useful for optical illusions��
��
: image plane
O: optical center
Courtesy of http://www.coolopticalillusions.com/
Stefano Mattoccia
P
Q
p��q
p
q
OR
OT
��
T
��
T
Stereo camera
With two (or more) cameras we can infer depth, by means of
triangulation, if we are able to find corresponding
(homologous) points in the two images
��
��
Reference R
Target T
Stefano Mattoccia
How to solve the correspondence problem ?
2D search domain ?
No!! Thanks to the
epipolar constraint
Reference (R)
Target (T)
Reference (R)
Target (T)
?
Stefano Mattoccia
P
Q
p��q
p
q
OR
OT
��
R
��
T
Epipolar constraint
•
Consider two points P and Q on the same line of sight of
the reference image R (both points project into the same
image point p��q on image plane ��
R
of the reference image)
•
The epipolar constraint states that the correspondence for
a point belonging to the (red) line of sight lies on the
green line on image plane ��
T
of target image
��
��
Reference R
Target T
Stefano Mattoccia
P
Q
p��q
p
q
OT
OR
��
R
��
T
Stereo camera in standard form
Once we know that the search space for corresponding points
can be narrowed from 2D to 1D, we can put (virtually) the
stereo rig in a more convenient configuration (standard
form)  corresponding points are constrained on the same
image scanline
��
��
Reference R
Target T
y
y
Stefano Mattoccia
Original stereo pair
Stereo pair in standard form
Cameras are ��perfectly�� aligned
and with the same focal length
Stefano Mattoccia
Disparity and depth
B (Baseline)
O
R
O
T
x
R
x
T
Z
P
p
p��
With the stereo rig in standard form and by considering
similar triangles (PO
R
O
T
and Ppp��):
( )
fZ
xxb
Z
b
R
T
−
−
+
=
d
fb
xx
fb
Z
T
R
⋅
=
−
⋅
=
T
R
xx−
is the disparity
f
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Disparity and depth
Stefano Mattoccia
Disparity map
x
R
x
T
Reference
Target
The disparity is the difference between the x coordinate of
two corresponding points; it is typically encoded with
greyscale image (closer points are brighter).
B
(Baseline)
O
R
O
T
x
R
x
T
Z
P
p
p��
B
(Baseline)
O
R
O
T
x
R
x
T
Z
P
p
p��
Disparity is higher for points closer to the camera
Stefano Mattoccia
Range field (Horopter)
Given a stereo rig with baseline b and focal length f, the
range field of the system is constrained by the disparity
range [d
min
, d
max
].
min
d
fb⋅
max
d
fb⋅
Horopter
Stefano Mattoccia
•
Depth measured by a stereo vision system is discretized
into parallel planes (one for each disparity value)
•
A better (virtual) discretization can be achieved with
subpixel techniques (see Disparity Refinements)
min
d
fb⋅
max
d
fb⋅
Stefano Mattoccia
•
The range field (horopter) using 5 disparity values
[d
min
, d
min
+4]
min
d
fb⋅
4
min +
⋅
d
fb
Stefano Mattoccia
•
Using 5 disparity values [��
+d
min
,��
+d
min
+4]
•
With ��
>0, horopter gets closer and shrinks (depth
and obviously area/volume)
min
d
fb
+
��
⋅
4
min +
+
��
⋅
d
fb
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Accuracy vs Resolution: quantitative analysis
Add here !
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Color or greyscale sensors ?
Insert here
Key module in stereo vision?
The algorithm is crucial in this technology
State of the art
(e.g. ICCV 2011)
Traditional
algorithm
Stefano Mattoccia
Overview of a stereo vision system
Rectification
Stereo
Correspondence
Triangulation
Calibration
(offline)
PC, FPGA
Stereo pair
Rectified stereo pair
Disparity map
Depth map
Intrinsic
and extrinsic
parameters
Stefano Mattoccia
Calibration (offline)
Rectification
Stereo
Correspondence
Triangulation
Calibration
(offline)
Calibration is carried out acquiring and
processing 10+ stereo pairs of a known
pattern (typically a checkerboard)
Offline procedure aimed at finding:
•
Intrinsic parameters of the two cameras
(focal length, image center, parameters
of lenses distortion, etc)
•
Extrinsic parameters
(R and T that aligns the two cameras)
Stefano Mattoccia
Rectification
Stereo
Correspondence
Triangulation
Calibration
(offline)
•
Calibration is available in OpenCV [39] and
Matlab [40]
•
A detailed description of calibration can be
found in [20,21,22]
•
Next slides show 20 stereo pairs used for
calibrating a stereo camera
Stefano Mattoccia
R
T
R
T
Stefano Mattoccia
R
T
R
T
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Rectification
Rectification
Stereo
Correspondence
Triangulation
Calibration
(offline)
Stereo camera in
standard form
Using the information from the calibration step:
a) removes lens distortions
b) turns the stereo pair in standard form
Stefano Mattoccia
Stereo correspondence
Aims at finding homologous points in the
stereo pair.
Rectification
Stereo
Correspondence
Triangulation
Calibration
(offline)
disparity map
This topic will be extensively analyzed in
the next slides...
Stefano Mattoccia
Triangulation
Rectification
Stereo
Correspondence
Triangulation
Calibration
(offline)
Given the disparity map, the baseline and the
Focal length (calibration): triangulation
computes
the position of the correspondence in the 3D
space
d
fb
Z
⋅
=
f
x
ZX R
=
f
y
ZY R
=
d(x,y)
(X,Y,Z)
disparity map
depth map
Stefano Mattoccia
Datasets: stereo sequences
Sequences acquired with stereo cameras are available at:
http://www.vision.deis.unibo.it/smatt/stereo.htm
The datasets include:
•
calibration parameters
•
original sequences
•
rectified sequences
•
disparity maps
Stefano Mattoccia
Architectures
•
Microprocessors
 Floating Point (FP) units + SIMD
 C/C++ (+ assembly)
 power,cost and size are the main drawbacks
•
Low power & low cost processor
 C/c++
 no FP
 no SIMD (often)
•
GPUs (Graphic Processing Units)
– raw power
 high power dissipation and cost
 programming is difficult (CUDA and OpenCL help)
•
FPGA (Field Programmable Gate Array)
 efficient, low power (<1 W), low cost
 programming language: VHDL
 coding is difficult and tailored for specific devices
Our custom FPGAbased stereo camera 1/3
•
We have designed a realtime stereo camera with
depth maps computed according to state of the art
algorithms
•
Details: www.vision.deis.unibo.it/smatt
•
Youtube channel:
www.youtube.com/channel/UChkayQwiHJuf3nqMikhxAlw
Our custom FPGAbased stereo camera 2/3
•
Processing at 30+ fps (640x480)
•
Power consumption: < 2.5 Watt
•
Self powered via USB cable
•
Weight: < 80 g with lenses and holders
Our custom FPGAbased stereo camera 3/3
www.youtube.com/watch?v=KXFWIvrcAYo
Stefano Mattoccia
Some available stereo cameras
www.videredesign.com
www.ptgrey.com
www.nvela.com
www.valdesystems.com
www.focusrobotics.com
www.tyzx.com
www.minoru3dwebcam.com
*
FPGA/ASIC
DSP
www.visionst.com
Stefano Mattoccia
Why is stereo correspondence so challenging ?
Next slides show
common pitfalls��
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Photometric distortions and noise
Specular surfaces
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Foreshortening
Uniqueness constraint ? :(
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? ? ?
? ?
Perspective distortions
Uniform/ambiguous regions
?
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Repetitive/ambiguous patterns
How to reduce ambiguity... ?
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Transparent objects
Occlusions and discontinuities 1/2
?
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Occlusions and discontinuities 2/2
Reference
Target
Target
Reference
?
?
Stefano Mattoccia
Middlebury stereo evaluation
[11] D. Scharstein and R. Szeliski, ��A taxonomy and evaluation of dense twoframe stereo correspondence algorithms��
Int. Jour. Computer Vision, 47(1/2/3):7–42, 2002
[15] D. Scharstein and R. Szeliski,
http://vision.middlebury.edu/stereo/eval/
Scharstein and Szeliski provide:
•
a methodology for the evaluation of (binocular)
stereo vision algorithms [11]
•
datasets with groundtruth [11,15,17,18,19]
•
online evaluation procedure and ranking [15]
Datasets (with groundtruth) of stereo pairs affected by
photometric distortions are also available in [15].
The Middlebury stereo evaluation site [15] provides a framework
and a dataset (showed in the next slide) for benchmarking
novel algorithms.
Stefano Mattoccia
Middlebury dataset (2003) [15]
D. Scharstein and R. Szeliski,
http://vision.middlebury.edu/stereo/eval/
Tsukuba, Venus, Teddy and Cones stereo pairs
Right
Left
DISC
ALL
NON_OCC
Groundtruth
Stefano Mattoccia
The correspondence problem
According to the taxonomy proposed in [11] most stereo
algorithms perform (subset of) these steps:
1) Matching cost computation
2) Cost aggregation
3) Disparity computation/optimization
4) Disparity refinement
Local algorithms perform:
1 ⇒
2 ⇒
3 (with a simple Winner Takes All (WTA) strategy)
Global Algorithms perform:
1 (⇒
2) ⇒
3 (with global or semiglobal reasoning)
Stefano Mattoccia
Preprocessing (0)
•
Laplacian of Gaussian (LoG) filtering [41]
•
Subtraction of mean values computed in nearby pixels [42]
•
Bilateral filtering [16]
•
Census transform
Sometime is deployed a preprocessing stage mainly to
compensate for photometric distortions.
Typical operations include:
[41] T. Kanade, H. Kato, S. Kimura, A. Yoshida, and K. Oda, Development of a VideoRate Stereo Machine
International Robotics and Systems Conference (IROS '95), Human Robot Interaction and Cooperative Robots, 1995
[42] O. Faugeras, B. Hotz, H. Mathieu, T. Viville, Z. Zhang, P. Fua, E. Thron, L. Moll, G. Berry,
Realtime correlationbased stereo: Algorithm. Implementation and Applications, INRIA TR n. 2013, 1993
[16] A. Ansar, A. Castano, L. Matthies, Enhanced realtime stereo using bilateral filtering
IEEE Conference on Computer Vision and Pattern Recognition 2004
Stefano Mattoccia
The simplest (naive and unused) local approach:
W
W
H
H
x
y
x
x+dmax
Reference (R)
Target (T)
Reference (R)
Target (T)
epipolar
line
Stefano Mattoccia
Result
(disappointing)
Groundtruth
•
matching cost (1): pixelbased absolute difference
between pixel intensities
•
disparity computation (3): Winner Takes All (WTA)
Reference
0
dmax
d
Winner d*
),
(
),(
ydxIyxI
T
R
+
−
Stefano Mattoccia
Basically exist two different (not mutually exclusive)
strategies:
•
Local algorithms use the simple WTA disparity selection
strategy but reduce ambiguity (increasing the signal to
noise ratio (SNR)) by aggregating matching costs over a
support window (aka kernel or correlation window).
Sometime a smoothness term is adopted. Steps 1+2 (+ WTA)
•
Global (and semiglobal*) algorithms search for disparity
assignments that minimize an energy function over the whole
stereo pair using a pixelbased matching cost (sometime the
matching cost is aggregated over a support). Steps 1+3
How to improve the results of the naive approach ?
This hypothesis is implicitly assumed by local
approaches while it is explicitly modelled by
global approaches
Both approaches assume that the scene is piecewise
smooth. Sometime this assumption is violated...
* subset of the stereo pair
Stefano Mattoccia
Local approaches:
In order to increase the SNR (reduce ambiguity) the
matching costs are aggregated over a support window
Reference (R)
Target (T)
Global (and semiglobal*) approaches:
( )
( )
d
Ed
EdE
smooth
data
+
=
)(
* subset of the stereo pair
Many algorithms search for the disparity assignment that
minimize a certain cost function over the whole* stereo
pair
Stefano Mattoccia
Matching cost computation (1)
Pixelbased matching costs
),
(
),(
),,(
ydxIyxI
dyxe
T
R
+
−
=
•
Absolute differences
(
)2
),
(
),(
),,(
ydxIyxI
dyxe
T
R
+
−
=
•
Squared differences
•
Robust matching measures (Mestimators)
•
Limit influence of outliers
•
Example: truncated absolute differences (TAD)
{
}
TydxI
yxI
dyxe
T
R
,),
(
),(
min
),,(
+
−
=
R
T
I
R
(x,y)
I
T
(x,y)
Stefano Mattoccia
R
x
1+
R
x
1−
R
x
dx
R +
1
++
dx
R
1−
+
dx
R
),(
yxI
R
R
),
(
ydxI
R
T
+
),(
~
yxI
R
R
),
(
~
ydxI
R
T
+
•
Dissimilarity measure insensitive to image sampling
(Birchfield and Tomasi [27])
( )
!"
!
#
$
!%
!
&
'
−
+
+
−
=
+
�ܡ�−
+
�ܡ�−
),(
~
),
(
min
,),
(
~
,
min
min
),,(
2
1
2
1
2
1
2
1
yxIydxI
ydxIyxI
dyxe
R
R
T
xx
x
T
R
R
xx
x
R
R
R
R
R
Reference (R)
Target (T)
BT helps at depth and color
discontinuities
Stefano Mattoccia
C(x,y,d)
likelihood/confidence
of each correspondence
The Disparity Space Image (DSI) is a 3D matrix (WxHx(d
max

d
min
)
Each element C(x,y,d) of the DSI represents the cost of
the correspondence between I
R
(x
R
,y) and I
T
(x
R
+d,y)
Stefano Mattoccia
Areabased matching costs:
��
��
+
−
=
Sx
T
R
ydxIyxI
dyxC
),
(),(
),,(
•
Sum of Absolute differences (SAD)
(
)
��
��
+
−
=
Sx
T
R
ydxIyxI
dyxC
2
),
(
),(
),,(
•
Sum of Squared differences (SSD)
•
Sum of truncated absolute differences (STAD)
{
}
��
��
+
−
=
Sx
T
R
TydxIyxI
dyxC
,),
(),(
min
),,(
S
Stefano Mattoccia
•
Normalized Cross Correlation [57]
•
Zero mean Normalized Cross Correlation [58]
•
Gradient based MF [59]
•
Non parametric [60,61]
•
Mutual Information [30]
•
. . .
•
Combination of matching costs
Stefano Mattoccia
Add content here
Areabased matching costs
Stefano Mattoccia
Cost aggregation (2)
Let��s start by examining the simplest Fixed Window (FW)
cost aggregation strategy (TAD, disparity selection WTA)
Reference (R)
Target (T)
Groundtruth
Fixed Window (FW)
What��s wrong with FW ?
Stefano Mattoccia
FW (with WTA reasoning) fails in most points for the
following reasons:
a)
b)
c)
d)
Reference (R)
Target (T)
a) implicitly assumes frontalparallel surfaces
b) ignores depth discontinuities
c) does not deal explicitly with uniform areas
d) does not deal explicitly with repetitive patterns
Stefano Mattoccia
S
S
a) FW implicitly assumes frontalparallel surfaces
Often violated in practice: top figure, slanted surfaces (down), etc.
FW
Ideal
FW
Nevertheless, almost all stateoftheart cost aggregation
strategies rely on the assumption that all the points
belonging to the support share the same disparity (only few
exceptions).
FW
Ideal
front view
front view
front view
front view
S
S
x
z
x
z
z
z
x
x
Stefano Mattoccia
b) FW ignores depth discontinuities
FW
Implicitly assuming frontalparallel surface in the real
scene is violated near depth discontinuities.
S
Aggregating the matching costs of two populations at
different depth (aligned foreground and misaligned
background (outliers)) results in the typical inaccurate
localization of depth borders.
Background is
misaligned !
Robust matching measures (TAD) can partially reduce the
influence of outliers
Stefano Mattoccia
S
Ideal
Stateoftheart cost aggregation strategies aim at shaping
the support in order to include only points with the same
(unknown) disparity.
FW
S
For what concerns FW: decreasing the size of the support
helps in reducing the border localization problem.
However, this choice renders the correspondence problem more
ambiguous (especially when dealing with uniform regions and
repetitive patterns, see the next slide).
In practice, for the FW approach the choice of the optimal
size of the support is done empirically.
Stefano Mattoccia
S
S
S
S
FW does not deal explicitly with ambiguous regions 
uniform areas c) and repetitive patterns d)
FW
Ideal
FW
Ideal
In both cases an ideal cost aggregation strategy should
extend its support in order to include as much points at
the same (unknown) depth as possible.
Stefano Mattoccia
Quite surprisingly, in spite of its limitations, FW is widely
adopted in practice (probably it is the most frequently used
algorithm for real applications).
•
Easy/fast implementation
•
Fast, thanks to incremental calculation schemes
•
Runs in realtime on standard processors (SIMD)
•
Has limited memory requirements
•
Hardware implementations (FPGA) run in realtime
with limited power consumption (<1W)
Before analyzing more sophisticated approaches let��
s consider
two optimization techniques used by FW and other algorithms:
•
Integral Images (II)
•
BoxFiltering (BF)
Stefano Mattoccia
Optimization: Integral Images
(aka Summmed Area Table)
y
x
( )
( ) ��
��
<
<
<
<
=
=
yjxi
yjxi
jiI
yxS
jiI
yxS
,
2
2
,
),(
,
),(
,
W
•
Straightforward extension to stereo
(2 images)
I(x,y)
H
F. Crow, Summedarea tables for texture mapping, Computer Graphics, 18(3):207–212, 1984
Stefano Mattoccia
Left
x
y
2n+1
2n+1
��
−
=
+
++
−
+
+
=
n
n
ji
iyj
dxRiyjxL
dyx
SAD
,
)
,
(
)
,
(
),,(
Right
x+d
y
2n+1
2n+1
y+1
y+1
),1,(
),,(
),1,(
d
yxUdyx
SAD
d
yx
SAD
+
+
=
+
��
−
=
++
++
−
++
+
n
nj
nyjdxR
nyjxL
)1
,
()1
,(
=
+
),1,(
dyxU
��
−
=
−
++
−−
+
n
nj
nyjdxRnyjxL)
,
()
,(
−
Optimization: BoxFiltering 1/2
M. Mc Donnel. Boxfiltering techniques. Computer Graphics and Image Processing, 17:65–70, 1981
Stefano Mattoccia
Left
x
y
2n+1
2n+1
Y+1
Right
x+d
y
2n+1
2n+1
Y+1
��
−
=
++
++
−
++
+
n
nj
nyjdxR
nyjxL
)1
,
()1
,(
=
+
),1,(
dyxU
��
−
=
−
++
−−
+
n
nj
nyjdxRnyjxL)
,
()
,(
−
),1,(
),,(
),1,(
d
yxUdyx
SAD
d
yx
SAD
+
+
=
+
[
]
max
..0
d
d ��
xn1
y+n+1
D
x+dn1
y+n+1
D'
x+n
C
x+d+n
C'
yn
A
yn
A'
B
B'
(
)
'
'
'
'
),1,1(
,1,
DD
CCBBAA
d
y
xUd
yxU
−−−
+
−−−
+
+
−
=
+
(
)
'
'
'
'
),1,1(
),,(
,1,
DD
CCBBAA
d
y
xUdyx
SAD
d
yx
SAD
−−−
+
−−−
+
+
−
+
=
+
Optimization: BoxFiltering 2/2
Stefano Mattoccia

Both require 4 operations per point

Integral images can handle supports of different size

Integral Images has overflow issues
(for example, with int32 and S2 ⇒
WxH<256x256)

Integral images is more demanding in terms of memory
requirements. For single images:
WxHxsizeof(data_type) Vs �� Wxsizeof(int32) for S2
BoxFiltering Vs Integral Images
In practice, integral images may be convenient when
supports of different size are required.
Extension of boxfiltering to more complex shapes was
proposed in [47].
Stefano Mattoccia
Optimizations:
Single Instruction Multiple Data (SIMD)
a
b
Op
A
B
Op
It��
s a computation paradigm that that allow for processing
with the same operation multiple data in parallel.
•
Several computer vision algorithms are suited for SIMD
•
SIMD features are available in most current processors
•
Intel processors SIMD available since Pentium (MMX)
•
SIMD mapping is difficult (assembly)
SIMD
16 Ops in
parallel !
Scalar computation 1 Op
Stefano Mattoccia
Single Matching Phase Algorithm [48,49]
•
Image type: grayscale
•
Preprocessing: subtraction of mean values
•
Matching cost (Step 1): Absolute Differences
•
Aggregation strategy (Step 2): FW
•
Disparity selection (Step 3): WTA
•
Outlier detection: efficient strategy (later, Step 4)
•
Discards uniform areas: yes, analyzing image variance
•
Optimizations: boxfiltering + SIMD instructions (SSE)
•
Subpixel interpolation up to 1/16 of pixel (later)
•
Runs in realtime on a standard PC
L. Di Stefano, M. Marchionni, S. Mattoccia, A fast areabased stereo matching algorithm
Image and Vision Computing, 22(12), pp 9831005, October 2004
L. Di Stefano, M. Marchionni, S. Mattoccia, A PCbased realtime stereo vision system
Machine Graphics & Vision, 13(3), pp. 197220, January 2004
Stefano Mattoccia
How far can we go with more effective
(frontal parallel) cost aggregation strategies ?
We made an experiment computing ideal frontal parallel
supports using the ground truth.
With 43x43 max support, TAD and a WTA strategy:
Results (errors in red)
There is room for improvements...
Stefano Mattoccia
•
Compared to pixelbased approaches the support aggregation
(potentially) allows for improving robustness
•
An ideal (frontal parallel) cost aggregation strategies
should include in the support only points with similar
disparity:
•
expanding in regions at similar depth (left)
•
shrinking near depth discontinuities (right)
Stefano Mattoccia
What about symmetric/asymmetric support,
discontinuities and occlusions ?
•
(Unknown) Occlusions and discontinuities play a central
role for support aggregation strategies. The next slides
depict relevant cases using a simple object laying on a
planar background
•
Occlusions and discontinuities are strictly related
Stefano Mattoccia
Case 1: no half occlusion, no discontinuity
Stefano Mattoccia
Case 2: near half occlusion vs inside
discontinuity
Stefano Mattoccia
Case 3: inside half occlusion vs any > depth = occlusion !!
?
Stefano Mattoccia
Case 4: near half occlusion vs near discontinuity
Stefano Mattoccia
Case 5: no half occlusion, no discontinuity
Stefano Mattoccia
Case 6: near discontinuity, near occlusion
Stefano Mattoccia
Case 7: inside discontinuity, near occlusion
Stefano Mattoccia
Case 8: near discontinuity, no occlusion no discontinuity
Stefano Mattoccia
Case 9: inside occlusion vs any > depth = occlusion !!
?
Stefano Mattoccia
Case 10: near occlusion and discontinuity vs near discontinuity
Stefano Mattoccia
Case 11: near discontinuity vs near discontinuity
Stefano Mattoccia
Case 12: near discontinuity vs near discontinuity and occlusion
Stefano Mattoccia
Classification and evaluation of cost
aggregation strategies for stereo correspondence
F. Tombari, S. Mattoccia, L. Di Stefano, E. Addimanda, Classification and evaluation of cost aggregation methods for stereo
correspondence, IEEE International Conference on Computer Vision and Pattern Recognition (CVPR 2008)
Accompanying web site and software:
www.vision.deis.unibo.it/spe/SPEHome.asp
•
In [1] we classified, implemented and evaluated (accuracy
and execution time) 10+ stateoftheart cost aggregation
strategies
•
Since the focus is on the cost aggregation strategy the
evaluation methodology includes only DISC and NON_OCC
Stefano Mattoccia
•
Analyzed a subset of relevant stateoftheart cost
aggregation strategies
•
position
•
shape
•
position and shape
•
weights
•
Most of these techniques compute the support using a
symmetric strategy
•
Benchmarking platform: Intel Core Duo 2.14 GHz CPU
•
Execution time: Teddy stereo pair (size 450x373) with
and a disparity search range of 60.
•
Optimizations: the same proposed by authors*, no SIMD,
no multicores, etc
•
The next slides describe most of these methods and some
novel approaches not included in the paper (i.e. Fast
Aggregation [64], Fast Bilateral Stereo (FBS) [65] and
the Locally Consistent (LC) methodology [66])
Stefano Mattoccia
Fixed Window: results
Stefano Mattoccia
Shiftable Windows [11]
D. Scharstein and R. Szeliski, A taxonomy and evaluation of dense twoframe stereo correspondence algorithms
Int. Jour. Computer Vision, 47(1/2/3):7–42, 2002
R
T
•
This approach aims at reducing the border localization
problem of FW not constraining the support to be centered
on the central position
•
Support is symmetric
•
Execution time: 12 sec
S
The position with the best score
is selected
Stefano Mattoccia
Shiftable Windows: results
Stefano Mattoccia
Multiple Windows [7]
H. Hirschmuller, P. Innocent, and J. Garibaldi, Realtime correlationbased stereo vision with reduced border errors
Int. Journ. of Computer Vision, 47:1–3, 2002
•
The number of elements in the support is constant
•
The shape of the support is not constrained to be rectangular
•
Support is symmetric
•
Proposed for 5, 9 and 25 subwindows (5W, 9W and 25W)
•
Execution time (9W): 11 sec (*)
+ 4 out of
according to the matching cost computed
over the single subwindows
With 9 subwindows (9W):
S
Stefano Mattoccia
Support: some shapes (with 9 subwindows)
R
T
S
Stefano Mattoccia
Multiple (9) Windows: results
Stefano Mattoccia
Variable Windows [12]
O. Veksler, Fast variable window for stereo correspondence using integral images
In Proc. Conf. on Computer Vision and Pattern Recognition (CVPR 2003), pages 556–561, 2003
•
Pixelbased cost function: Birchfield and Tomasi
•
Size of the support varies while shape is constrained (square)
•
Position of the support changes (shiftable windows)
•
Support is symmetric
•
Efficient search based on a DP technique
•
Execution time: 16 sec (good tradeoff speed/accuracy)
R
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Stefano Mattoccia
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Stefano Mattoccia
Variable Windows: results
Stefano Mattoccia
Segmentation
D. Comaniciu and P. Meer, Mean shift: A robust approach toward feature space analysis!
IEEE Transactions on Pattern Analysis and Machine Intelligence, 24:603–619, 2002
•
Partitioning of the image in regions made of connected
pixels with similar colors intensity
•
Useful in stereo for cost aggregation, disparity refinement,
outliers detection, etc
Original
Segmented [50]
Stefano Mattoccia
Segmentation based [5]
•
Assumption: depth within each segment varies smoothly
•
Segmentation of reference image (Not Symmetrical)
•
Shape and size unconstrained (within max support)
•
Pixelbased cost function: Mestimator
•
Requires explicit segmentation
•
Each cost is weighted 1 (same segment) or
��<<1
(different segment)
•
Execution time: 2 sec (fast)
M. Gerrits and P. Bekaert, Local Stereo Matching with Segmentationbased Outlier Rejection
Proc. Canadian Conf. on Computer and Robot Vision, 2006
Stefano Mattoccia
R
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For each point within the maximum allowed support:
•
points within the same segment of the central point
(reference image) assume weight 1
•
points outside are weighted ��<<
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Stefano Mattoccia
Segmentation based: results
Stefano Mattoccia
Bilateral Filtering [51]
Weight function
•
Edge preserving smoothing technique
•
In the sum each element is weighted
according to its spatial and color
proximity (wrt the central point)
•
Implicitly deploys segmentation
Conventional
smoothing
Bilateral
Filtering
C. Tomasi and R. Manduchi. Bilateral filtering for gray and color images. In
ICCV98, pages 839–846, 1998
Original
image
Stefano Mattoccia
•
Costs are symmetrically weighted
by spatial and color proximity
•
Implicitly deploys segmentation
•
Pixelbased cost function: TAD
•
Symmetric support
•
Execution time: 17 minutes (very slow)
K. Yoon and I. Kweon. Adaptive supportweight approach for correspondence search IEEE PAMI, 28(4):650–656, 2006
Adaptive Weights [14]
R
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Stefano Mattoccia
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Stefano Mattoccia
Adaptive Weights: results
Stefano Mattoccia
Stefano Mattoccia
•
Segments both images
•
Discard the spatial proximity assumption: weights
rely only on segmentation and color proximity
•
Cost function: TAD
•
Symmetric support
•
Execution time: 30 minutes (very slow)
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Segment Support [10]
F. Tombari, S. Mattoccia, L. Di Stefano, Segmentationbased adaptive support for accurate stereo correspondence
IEEE PacificRim Symposium on Image and Video Technology (PSIVT 2007)
and then combined (symmetric support)
pi
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Stefano Mattoccia
Adaptive weights
Adaptive weights
Ideal vs Segment Support
Ideal vs Segment Support
Depth borders
Planar regions
Stefano Mattoccia
Repetitive patterns
R
T
Adaptive weights
T
Ideal vs Segment Support
Stefano Mattoccia
Segment Supports: results
Stefano Mattoccia
Fast Aggregation [64]
F. Tombari, S. Mattoccia, L. Di Stefano, E. Addimanda, Near realtime stereo based on effective cost aggregation
International Conference on Pattern Recognition (ICPR 2008)
R
T
•
Assumption: depth within each segment varies smoothly
•
Cost function: TAD
•
Segments only the reference image R
•
Asymmetric support (reference image)
•
Support extends to the entire segment (R)
•
Fast: 0.6 sec (segmentation accounts for 40%80%)
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r
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p
q
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WP
Stefano Mattoccia
•
Cw tries to avoid ��
segment locking��
•
Cw may help in highly textured regions (small
segments)
•
However, Cw may introduce artifacts (discontinuities)
since aggregation is performed on a fixed window
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Stefano Mattoccia
Fast Aggregation: results
Stefano Mattoccia
Fast Bilateral Stereo framework (FBS) [65]
S. Mattoccia, S. Giardino,A. Gambini, Accurate and efficient cost aggregation strategy for stereo correspondence based on
approximated joint bilateral filtering, Asian Conference on Computer Vision (ACCV2009)
•
Symmetric support
•
Combines accuracy of adaptive weights approaches with
efficiency of traditional (correlative) approach
•
Deploys a regularized range filter computed on a block
basis of size wxw
•
Increase noise robustness
•
Efficient pixelwise cost computation by means of
integralimage/boxfiltering schemes
•
Results comparable to top performing approaches
Segment Support and Adaptive Weights
•
Fast: 32 sec on Teddy (w=3)
•
Moreover, several tradeoff speed vs accuracy are
feasible: 14 sec (w=5) , 9 sec (w=7), 5 sec (w=9)
www.vision.deis.unibo.it/smatt/fast_bilateral_stereo.htm
Stefano Mattoccia
•
The range filter is computed on a blockbasis deploying
the average value within the block
•
To avoid inaccurate localization of the discontinuities
the central point is kept as reference
•
Spatial filter computed on block basis
Three supports computed
by Fast Bilateral Stereo
w
w
W
W
y
x
x+d
Stefano Mattoccia
FBS (w=3) vs Adaptive Weights (AW)
FBS
AW
Stefano Mattoccia
Fast Bilateral Stereo: results (w=3, w=5)
w=3
w=5
Stefano Mattoccia
Fast Bilateral Stereo: results (w=7, w=9)
w=7
w=9
Fast Bilateral Stereo on the GPU [71]
•
The local nature of the FBS algorithm allows to
exploit parallel capabilities available in GPUs
•
Compared to a single core CPU, on the Middlebury
dataset, the implementation of FBS with CUDA enables
to obtain:
•
70X speedup on an NVIDIA GEForce 460 GTX GPU
•
100X speedup on an NVIDIA Tesla C2070 GPU(*)
The measured execution time, with parameters w=3 and
W=19, is (Teddy stereo pair): 300 ms for the GEForce 460
GTX and 200 ms on the Tesla C2070
Detailed results available in:www.vision.deis.unibo.it/smatt/FBS_GPU.html
(*) We acknowledge with thanks NVIDIA for the donation of the Tesla C2070
S. Mattoccia, M. Viti, F. Ries,. Near realtime Fast Bilateral Stereo on the GPU, 7th IEEE Workshop on Embedded Computer
Vision (ECVW20011), CVPR Workshop, June 20, 2011, Colorado Springs (CO), USA
Fast Segmentationdriven (FSD)
S. Mattoccia, L. DeMaeztu, A fast segmentationdriven algorithm for fast and accurate stereo correspondence, IC3D 2011
•
Applies the SS strategy on a block basis
•
Results equivalent to SS much more quickly (comparable
to FBS)
•
Compared to AW and FBS is effective also with greyscale
images
0
5
10
15
20
25
30
35
3
5
7
Block size (b pixels)
E
x
e
c
ution
tim
e
(s
e
c
on
ds
)
Teddy 1 core
Teddy 4 cores
Tsukuba 1 core
Tsukuba 4 cores
b=3
b=7
b=5
Stefano Mattoccia
Locally Consistent (LC) stereo [66]
S. Mattoccia, A locally global approach to stereo correspondence, 3D Digital Imaging and Modeling (3DIM2009)
•
Exploits the mutual relationships among neighboring
pixels by explicitly modeling the continuity
constraints
•
Very accurate (significant improvements near depth
discontinuities and low textured regions)
•
Notable improvements compared to stateoftheart
approaches
•
Fast 37 sec* on Teddy (unoptimized code) deploying the
disparity hypotheses provided by Fast Bilateral Stereo
•
Fast: 15 sec* on Teddy (unoptimized code) deploying the
disparity hypotheses provided by Fixed Window
* significantly reduced (see next slides/ECVW 2010 paper [68])
www.vision.deis.unibo.it/smatt/lc stereo.htm
Measurements performed on a 2.49GHz Intel Core Duo processor
Stefano Mattoccia
Before (FBS
19(3)
)
LC
19
Locally Consistent stereo: results with FBS
After LC
19
(+ FBS
19
)
LC
Stefano Mattoccia
Before (FW
4
)
After LC
19
(+ FW
4
)
LC
19
Locally Consistent stereo: results with FW
LC
Stefano Mattoccia
Locally consistent (LC) stereo vs FW: details
FW
4
After
LC
19
(+ FW
4
)
LC
Stefano Mattoccia
•
The next slide provides an updated quantitative
evaluation of the approaches described so far
(yellow) according to the methodology described
in [1]
•
The updated evaluation is available online at:
http://www.vision.deis.unibo.it/spe/SPEresults.aspx
•
According to this evaluation the Locally Consistent
approach combined with the disparity hypotheses
provided by the Fast Bilateral Stereo (FBS) algorithm
outperforms the other approaches
•
The FBS ranks second and provides a good tradeoff
between accuracy and execution time (see the results
in the table with different parameters of the FBS
algorithm)
•
In the successive slides will be described novel
approaches that rely on the LC technique (see papers
[67],[68],[69])
Stefano Mattoccia
(Updated)Quantitative evaluation [1] (TAD)
Algorithm
Rank
Tsukuba
Tsukuba
Venus
Venus
Teddy
Teddy
Cones
Cones
Time Teddy
Acc.
nonocc
disc
nonocc
disc
nonocc
disc
nonocc
disc
hh:mm:ss
LocallyConsist(FBS 39(3))
1
1.77
5.92
0.27
1.77
9.3
17.9
4.75
10.5
00:00:37
FBS 39(3)
3.13
2.95
8.69
1.15
6.64
10.7
20.8
5.23
11.4
00:00:28
Segment support
3.25
2.15
7.22
1.38
6.27
10.5
21.2
5.83
11.8
00:39:30
LocallyConsist(FW)
3.5
3.07
9.63
0.66
5.11
10.6
21.8
5.3
11.6
00:00:15
FBS 45(5)
5.75
3.34
9.99
2.11
6.72
11.5
21.8
6.81
13.8
00:00:14
Segmentation based
6.75
2.25
8.87
1.37
9.4
12.7
24.8
11.1
20.1
00:05:14
Adaptive Weight
6.88
4.66
8.25
4.61
13.3
12.7
22.4
5.5
11.9
00:20:35
FBS 49(7)
7
3.99
12.3
3.01
8.42
12.3
23
7.5
15.1
00:00:09
FBS 45(9)
8.75
4.6
13.7
5.42
10.6
13.9
24.8
9.47
17.7
00:00:05
Variable Windows
11.13
3.12
12.4
2.42
13.3
17.7
25.5
21.2
27.3
00:00:26
Reliability
11.13
5.08
17.9
3.92
13.9
18.9
29.9
11.3
18.3
00:13:39
Multiple windows* (25W)
14.5
7.57
22.7
3.91
21.1
20.9
33.2
13.7
26.9
00:00:13
Multiple windows (9W)
14.88
7.6
25.7
7.02
33
16
36.9
10.6
26.9
00:00:04
Multiple windows (25W)
15.13
7.28
25.9
6.18
29
18
35.6
11.8
27.1
00:00:14
Gradient guided
15.25
7.41
16.2
12.9
32.3
20.1
32.8
13.5
24.9
00:00:16
Multiple windows* (9W)
15.63
9.18
22.6
6.23
28.1
21.4
34.5
13.2
26.7
00:00:04
Recursive adaptive
16.38
9.66
29.8
5.94
29.8
20.1
34.6
11.7
25.3
00:20:20
Shiftable windows
16.75
9.58
14.4
9.66
16.5
23.6
31.2
24.4
33.6
00:00:05
Multiple windows (5W)
16.88
7.62
27.2
7.55
37.2
17.4
39.7
11
27.8
00:00:02
Multiple adaptive
17
11.7
27.3
11.9
13.7
20.4
31.8
15.8
25.3
02:08:17
Multiple windows* (5W)
18.25
9.61
25.1
9.36
38.3
22.2
38
12.1
27.5
00:00:02
Max connected
21
11.8
26.4
42.5
50.9
34.5
41
17.7
22.7
01:59:09
Fixed Window (FW)
21.13
9.58
27.1
10.6
42.5
25.1
42.4
19.7
36
< 1 s
Oriented rod*
22.25
18.6
31.1
20.3
26.6
30.7
41.8
37.8
47.3
00:17:19
Oriented rod
22.5
14.2
25.8
21.9
29.8
37.5
48.6
48.5
55.5
00:17:00
Radial adaptive
23
14.8
21.8
22.4
40.4
49.6
50.1
50.2
53.6
01:06:21
Table available at: http://www.vision.deis.unibo.it/spe/SPEresults.aspx
L. DeMaeztu, S. Mattoccia, A. Villanueva, R. Cabeza, "Linear stereo matching", ICCV 2011
O(1) adaptive cost aggregation
•
Symmetric cost aggregation inspired by guided filter
•
Aggregation independent of the window size
•
Can be applied to color images (differently by
integral histogrambased methods)
•
Results comparable to state of the art
Fast/simplified adaptive cost aggregation
D. Min, J. Lu, and M. Do, ��A revisit to cost aggregation in stereo matching: how far can we reduce its computational
redundancy?��, ICCV 2011
0
10
20
30
40
50
60
0 5 10 15 20 25 30 35 40 45 50 55 60
probabilit�� %
disparit��
+
•
Asymmetric cost aggregation
•
Cost computed on a selected number of points
(determined by means of FW (5x5))
•
Matching cost computed on a subset of (fixed) points
Stefano Mattoccia
Disparity computation/optimization (3)
( )
( )
d
EdEdE
smooth
data
+
=
)(
This step aims at finding the best disparity assignment
(e.g. the best path/surface within the DSI) that minimizes a
cost function over the whole* stereo pair.
In many cases the energy function has two terms:
* subset of the stereo pair
•
The data term E
data
measure how well the assignment fits to
the stereo pair (in terms of overall matching cost).
Several approaches rely on simple pixelbased cost functions
but effective support aggregation strategies have been
successfully adopted
•
The smoothness/regularization E
smooth
term explicitly
enforces piecewise assumptions (continuity) about the scene.
This term penalizes disparity variations and large
variation are allowed only at (unknown) depth borders.
Plausibility of depth border is often related to edges.
Stefano Mattoccia
Since finding the best assignment that minimizes the energy
function a NPhard problem, approximated but effective energy
minimization strategies have been proposed.
Relevant approaches are:
 Graph Cuts [52]
 Belief Propagation [53]
 Cooperative optimization [54]
A detailed comparison of relevant energy minimization methods
can be found in [63].
An further and interesting class of approximated approaches
minimizes the energy function on a subset of points of the
stereo pair (typically along scanlines). In these cases the
energy minimization problem is efficiently solved by means
of Dynamic Programming (DP) or Scanline Optimization (SO)
techniques.
Stefano Mattoccia
Graph Cuts
V. Kolmogorov and R. Zabih, Computing visual correspondence with occlusions using graph cuts, ICCV 2001
Stefano Mattoccia
BP + segmentation
A. Klaus, M. Sormann and K. Karner, Segmentbased stereo matching using belief propagation and a
selfadapting dissimilarity measure. ICPR 2006
Stefano Mattoccia
Cooperative + segmentation
Z. Wang and Z. Zheng, A region based stereo matching algorithm using cooperative optimization, CVPR 2008
Stefano Mattoccia
Dynamic Programming (DP)

efficient (polynomial time) �� 1 sec
 enforces the ordering constraint
 accurate at depth borders and uniform regions
 streaking effect (see next slide)
Stefano Mattoccia
DP [11]
Stefano Mattoccia
Scanline Optimization (SO)

Efficient (polynomial time) �� few seconds
 Cannot enforce the ordering constraint
 accurate at depth borders and uniform regions
 overcomes the streaking effect problem (see next slide)
 high memory requirement
H. Hirschm��ller. Stereo vision in structured environments by consistent semiglobal matching.
CVPR 2006, PAMI 30(2):328341, 2008
In SO, the cost is defined as:
L(x,y,d) = C(x,y,d) + min { L(x1,y,d),
L(x1,y,d1)+ P1,
L(x1,y,d+1)+ P1,
L(x1,y,i) + P2
x
x1
L(x1,y,i)
L(x,y,d)
0
1
5
6
L(x,y,4)= C(x,y,4)+ min
L(x1,y,4)
L(x1,y, 5) + P
1
L(x1,y, 3) + P
1
L(x1,y, 7) + P
2
L(x1,y, 6) + P
2
L(x1,y, 2) + P
2
L(x1,y, 1) + P
2
L(x1,y, 0) + P
2
min L(x1,y,k)
Stefano Mattoccia
Scanline Optimization [30]
Scanline Optimization: details
2
3
0
1
4
5
6
7
Scanline 0
2
3
0
1
4
5
6
7
Scanline 1
2
3
0
1
4
5
6
7
Scanline 2
2
3
0
1
4
5
6
7
Scanline 3
2
3
0
1
4
5
6
7
Scanline 4
2
3
0
1
4
5
6
7
Scanline 5
2
3
0
1
4
5
6
7
Scanline 6
2
3
0
1
4
5
6
7
Scanline 7
2
3
0
1
4
5
6
7
Full SGM (8 scanlines, TAD color)
Stefano Mattoccia
SO + support aggregation
This method combines an effective cost aggregation strategy
with a SO based disparity computation framework.
 costs are computed by means of an effective strategy
cost aggregation strategy (Segment Support)
 disparity computation relies on SO
 uses only 4 directions
 excellent results
 very slow (due to cost aggregation strategy)
Using effective cost aggregation strategy within accurate
disparity computation frameworks is an interesting trend
successfully deployed also by other researchers [,].
S. Mattoccia, F. Tombari, and L. Di Stefano, Stereo vision enabling precise border localization within a scanline
optimization framework, ACCV 2007
Stefano Mattoccia
SO + support aggregation [29]
Stefano Mattoccia
S. Mattoccia, Improving the accuracy of fast dense stereo correspondence algorithms by enforcing local consistency
of disparity fields, 3DPVT2010
Enforcing local consistency of disparity
fields in fast SO/DP based algorithms [67]
This method aims at improving the accuracy of fast SO/DP
based algorithms by enforcing the local consistency [66]
of an initial disparity hypothesis.

evaluated deploying the initial disparity hypotheses of
CSemiglobal [30] and RealTimeGPU [70]

dramatically improves the initial disparity field

relatively fast, about 15 seconds on a standard PC with
a single core

computational optimizations/simplifications [68] enable
us to obtain almost equivalent results in less than 2
seconds on a standard multicore PC (see next slides
concerned with paper[68])
www.vision.deis.unibo.it/smatt//3DPVT2010.htm
Stefano Mattoccia
This method:
 deploys the initial dense disparity hypotheses provided by
a dense stereo algorithm (tested with fast and SO and DP
algorithms [30] and [70])
 enforces local consistency by means of the LC technique
[66] obtaining two independent disparity fields D
R
and D
T
 detects and interpolates uncertain disparity assignments
according to D
R
and D
T
PlausibilityR
PlausibilityT
LC
DR
DT
crosscheck Interpolation
R
T
D
Stefano Mattoccia
Experimental results deploying the initial disparity hypotheses
of CSemiglobal [30] available on the Middlebury web site
Experimental results according to the automatic evaluation procedure available at:
http://vision.middlebury.edu/stereo/
12
Stefano Mattoccia
CSemiglobal [30]
CSemiglobal [30]
LC
LC
LC(CSemiglobal)[67]
LC(CSemiglobal) [67]
Stefano Mattoccia
Experimental results deploying the initial disparity hypotheses
of RealTimeGPU [70] available on the Middlebury web site
Experimental results according to the automatic evaluation procedure available at:
http://vision.middlebury.edu/stereo/
49
Stefano Mattoccia
RealTimeGPU [70]
RealTimeGPU [70]
LC
LC
LC(RealTimeGPU)[67]
LC(RealTimeGPU)[67]
Stefano Mattoccia
Fast dense stereo on multicore deploying a
relaxed local consistency constraint [68]
The execution time of previously described method [67], can
be dramatically reduced according to the methodologies
proposed in [68].
Deploying the same initial disparity hypotheses (that is,
CSemiglobal and RealTimeGPU), this method enables us to
obtain almost equivalent results (see [67] in previous page)
in less than 2 seconds on a Core2 Quad CPU @ 2.49 GHz.
This methods:
 relies on a relaxed local consistency constraint
 takes advantage of coarsegrained threadlevel paralellism
S. Mattoccia, Fast locally consistent dense stereo on multicore, Sixth IEEE Embedded Computer Vision Workshop
(ECVW2010), CVPR workshop, June 13, 2010, San Francisco, USA
www.vision.deis.unibo.it/smatt/RLC stereo.htm
Original [67]
Proposed [68]
Measured speedups on a Core2 Quad CPU @ 2.49 GHz
Measurements concerned with the Teddy stereo pair
Stefano Mattoccia
CSemiglobal [30]
CSemiglobal [30]
RLC
RLC
RLC(CSemiglobal)[68]
RLC(CSemiglobal) [68]
Stefano Mattoccia
Constraining local consistency
on superpixels [69]
The effectiveness of the locally consistent technique [66]
can be further improved by constraining its behavior on
superpixels obtained by means of segmentation [50].
This method deploys a two stage strategy to constraint Local
Consistency [66] on superpixels.
During the first phase, we oversegment the reference image:
 to detect uncertain disparity measurements
 to regularize disparity within superpixels
During the second phase we relax the segmentation constraint
in order to propagate the regularized disparity assumptions.
As for previous approaches, we start with an initial disparity
hypothesis (CSemiglobal algorithms [30] available on [15])
S. Mattoccia, Accurate dense stereo by constraining local consistency on superpixels, 20th International Conference on
Pattern Recognition (ICPR2010), August 2326, 2010, Istanbul, Turkey
CSemiglobal [30]
[69]
Phase 1
Phase 2
LC
Stefano Mattoccia
Experimental results for [69] deploying the initial disparity
hypotheses of CSemiglobal [30] available on the Middlebury
evaluation site
Experimental results according to the automatic evaluation procedure available at:
http://vision.middlebury.edu/stereo/
14
Stefano Mattoccia
Disparity refinement (4)
•
Raw disparity maps computed by correspondence algorithms
contain outliers that must be identified and corrected
•
Moreover, since the disparity maps are typically computed
at discrete pixel level more accurate disparity assignments
would b desirable
•
Several approaches aimed at improving the raw disparity
maps computed by stereo correspondence algorithms have
been proposed
•
In the next slides is provided a description of some (not
mutually exclusive) relevant approaches
Stefano Mattoccia
Disparity refinement (4)
•
Raw disparity maps computed by correspondence algorithms
contain outliers that must be identified and corrected
•
Moreover, since the disparity maps are typically computed
at discrete pixel level more accurate disparity assignments
would b desirable
•
Several approaches aimed at improving the raw disparity
maps computed by stereo correspondence algorithms have
been proposed
•
A description of some (not mutually exclusive) relevant
approaches is provided in the next slides
Stefano Mattoccia
0
13
12 14
12.8
dmax1
C(x,y,d)
d
Subpixel interpolation
•
(Typically) subpixel disparity is obtained interpolating the
three matching costs with a second degree function (parabola)
•
Computationally inexpensive and reasonably accurate
•
In [55] proposed a floatingpoint free approach
•
More accurate (and computational expensive) approaches
perform directly matching cost computation on subpixel basis
L. Di Stefano, S. Mattoccia, Realtime stereo within the VIDET project RealTime Imaging, 8(5), pp. 439453, Oct. 2002
Stefano Mattoccia
Image filtering techniques
•
Median filtering
•
Morphological operators
•
Bilateral filtering [51]
Sometime the disparity maps are simply refined by means of
image filtering techniques without (explicitly) enforcing
any constraint about the underlining disparity maps.
Common image filtering operators are:
Stefano Mattoccia
Bidirectional Matching*
Bidirectional matching (BM) is a widely used technique for
detecting outliers [56] in stereo (local and global).
The correspondence problem is solved two times
 assuming left image as reference (d
LR
(x,y))
 assuming right image as reference (d
RL
(x,y))
and the disparity values that are not consistent between the
two maps are classified as outliers enforcing
d
LR
(x,y) d
RL
(x+d
LR
(x,y),y)<T
with threshold T typically set to 1
* aka LeftRight (consistency) check
P. Fua, Combining stereo and monocular information to compute dense depth maps that preserve depth discontinuities
12th. Int. Joint Conf. on Artificial Intelligence, pp 1292–1298, 1993
Stefano Mattoccia
d
LR
(x,y) d
RL
(x+d
LR
(x,y),y)<T ?
yes
no
d
LR
d
RL
Outliers detected by BM
are encoded in white
Stefano Mattoccia

useful for detecting occlusions
 preserves depth discontinuities
 (partially) effective for detecting outliers
in ambiguous regions (see figure)
 two matching phases
 implicitly enforces the uniqueness constraint
Stefano Mattoccia
Single Matching Phase (SMP) – Uniqueness+
The Single Matching Phase (SMP) approach [48] aims
at detecting unreliable disparity assignments using
a more computationally efficient technique.
 uses a single matching phase (1/2 vs BM)
 explicitly enforces the uniqueness constraint*
 dynamically updates the disparity map when the
uniqueness constraint is violated
 strengthened by additional constraints (next slides)
 effectiveness comparable to BM []
 suitable for efficient SIMD implementation
* Sometime violated (e.g. foreshortening)
Stefano Mattoccia
The correspondences are dynamically evaluated and corrected
within a single matching phase (d
RT
(x,y)).
When two correspondences fall in the same point of
the target image:
 the correspondence with the best score is kept
 the other correspondence is discarded
R
T
Stefano Mattoccia
The basic SMP approach can be strengthened by means of two
additional constraints:
Example:
repetitive pattern
Example:
uniform region
0
13
d
?
?
e(d)
0
13
d
? ? ?
e(d)
a) Distinctiveness
b) Sharpness
Stefano Mattoccia
Example of reliable
correspondence
0
13
d
e(d)
An exhaustive comparison between DM and SMP on stereo pairs
with groundtruth can be found in [48].
Outliers are
encoded in white
SMP
BM
Stefano Mattoccia
Performance evaluation [48]: SMP vs BM (PIII 800 MHz)
Stefano Mattoccia
Two fundamental assumptions:
1) disparity within each segment varies smoothly
2) each segment can be approximated with a plane
Sometime 2) is not verified (below)⇒
oversegmentation
Segmentation based outliers
identification and replacement
Stefano Mattoccia
x
y
z
x
y
z
Top view
frontal
parallel
frontal
parallel
3D view
x
z
x
z
3 DOF
3 DOF
Stefano Mattoccia
Each segment is modelled with a plane in the 3D space (3 DOF):
d(x,y) = ��
·x + ��
·y + ��
Robust plane fitting of disparity measurements:
•
RANSAC [25] (iterative)
•
Histogram Voting [54] (non iterative)
The best performing algorithms on the Middlebury dataset cast
robust plane fitting within a global energy minimization
framework.
The next slide shows robust plane fitting of disparity
measurements computed by a local approach (WTA + BM +
Histogram Voting).
Interesting research activity: replacing planes with more
complex surfaces
Stefano Mattoccia
Example of robust plane fitting
Local approach (FBS) + WTA + BM + robust plane fitting
Stefano Mattoccia
Robust interpolation of noisy measurements
•
Disparity maps always contain outliers
•
Reliable fitting with planes requires interpolation
techniques robust to outliers
Traditional approach
(Least Square (LS))
Robust interpolation
RANSAC and Histogram Voting are two techniques used in
stereo for robust interpolation of noisy disparity
measurements
Stefano Mattoccia
Accurate localization of borders and occlusions
[29] S. Mattoccia, F. Tombari, and L. Di Stefano, Stereo vision enabling precise border localization within a scanline
optimization framework, ACCV 2007
In [29] was proposed a method for accurate detection of
depth borders and occlusions.
•
This method uses the disparity maps (d
LR
and d
RL
) computed
by a (local or global) stereo correspondence algorithm
•
Borders and occlusions are detected (without global
energy minimization frameworks) enforcing, along
scanlines, constraints between occlusions (in one
image) and discontinuities (in the other image)
•
Accurate results (see the next slides)
•
Evaluated with the disparity maps provided by the
algorithm described in [29] (SO + SegmentSupport)
Stefano Mattoccia
Occlusions (yellow)
Borders (red)
Stefano Mattoccia
Occlusions (yellow)
Borders (red)
Stefano Mattoccia
Iterative approaches
L. DeMaeztu, S. Mattoccia, A. Villanueva, R. Cabeza, "Efficient aggregation via iterative blockbased
adapting support weight", IC3D 2011
Stefano Mattoccia
Computational Optimizations
Stefano Mattoccia
Hardware implementation
Open problem: radiometric variations
Courtesy of IMRA Europe, Sophia Antipolis (FR)
Left ILL(1)EXP(0)
Right ILL(3)EXP(2)
Groundtruth
TAD
ROBUST_COST_FUNCTION
Groundtruth
Left ILL(1)EXP(0)
Right ILL(3)EXP(2)
NCC
ROBUST_COST_FUNCTION
Stefano Mattoccia
Realtime applications based
on our embedded 3D camera
•
3D tracking
•
SLAM
•
Autonomous robot navigation
•
Mobility aid for visually impaired
Stefano Mattoccia
3D Tracking 1/2
Applications:
•
people counting (building, bus, train)
•
monitoring trajectories (shopping, sport)
•
safety
•
surveillance and security
Stefano Mattoccia
3D Tracking 2/2
https://www.youtube.com/watch?v=2vorrRhBssQ
•
Embedded computer + FPGA stereso camera
•
20+ fps
SLAM 1/2
•
3D scanning at 5+ fps (with bundle adjustment)
SLAM 2/2
Autonomous robot navigation
•
Realtime and reliable obstacle detection with
the 3D camera and an embedded computer at 20+ fps
•
Battery powered
www.youtube.com/watch?v=7rieq3wfGDo
Mobility aid for visually impaired 1/4
•
Wearable and lightweight (3D camera + computing
platform about 150 g) system for autonomous nav.
•
Feedback: vibrotactile and audio (by means of
bone conductive headset)
•
Enables hours of autonomous navigation with a
small battery (3200 mAh) at 15+ fps
Mobility aid for visually impaired 2/4
Pocket
battery
(3200 mA)
Stefano Mattoccia
Mobility aid for visually impaired 3/4
•
Realtime navigation example with obstacle
•
Realtime navigation example without obstacles
White: detected plane
Black: obstacles
Stefano Mattoccia
Current prototype (in the news):
http://www.rai.tv/dl/RaiTV/programmi/media/ContentItem
fbb80bea9d9644eaae621fa3b5e572a5tgr.html?
refresh_ce#p=0
https://www.youtube.com/watch?v=DQ7x3PtFkJw#t=1346
http://www.corriere.it/salute/disabilita/
14_novembre_28/dalvideotelefonosordociechiallapp
cheaiuta
badante393744a6770111e490d40eff89180b47.shtml
First prototype:
www.youtube.com/watch?v=G1UIUXUu2wY
Mobility aid for visually impaired 4/4
Stefano Mattoccia
[1] F. Tombari, S. Mattoccia, L. Di Stefano, E. Addimanda, Classification and evaluation of cost aggregation methods for
stereo correspondence,
IEEE International Conference on Computer Vision and Pattern Recognition (CVPR 2008)
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of disparity maps. In Proc. IEEE Workshop on Circuit, Systems and Signal Processing, pages 615–618, 2005
[5] M. Gerrits and P. Bekaert. Local Stereo Matching with Segmentationbased Outlier Rejection
In Proc. Canadian Conf. on Computer and Robot Vision (CRV 2006), pages 6666, 2006
[6 M. Gong and R. Yang. Imagegradientguided realtime stereo on graphics hardware
In Proc. Int. Conf. 3D Digital Imaging and Modeling (3DIM), pages 548–555, 2005
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ground control points, In Proc. Conf. on Computer Vision and Pattern Recognition (CVPR 2005), pages 1075–1082, 2005
[10] F. Tombari, S. Mattoccia, and L. Di Stefano, Segmentationbased adaptive support for accurate stereo correspondence
PSIVT 2007
[11] D. Scharstein and R. Szeliski, A taxonomy and evaluation of dense twoframe stereo correspondence algorithms
Int. Jour. Computer Vision, 47(1/2/3):7–42, 2002
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Stefano Mattoccia
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support weight",International Conference on 3D (IC3D 2011), December 78, 2011, Liege, Belgium
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Stefano Mattoccia
Stefano Mattoccia
mail: stefano.mattoccia@unibo.it
web: www.vision.deis.unibo.it/smatt
Tel: +39 051 2093860
Fax: +39 051 2093073
Address:
Department of Computer Science and Engineering (DISI)
University of Bologna
Viale Risorgimento, 2
40136 Bologna, ITALY