A Multi Patch Warping Approach for Improved Stereo Block

Matching

Mircea Paul Muresan, Sergiu Nedevschi and Radu Danescu

Dept. Computer Science Department, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

{mircea.muresan, sergiu.nedevschi, radu.danescu}@cs.utcluj.ro

Keywords: Dense Stereo, Block Matching, Slanted Surfaces, Disparity Refinement, Binary Descriptors.

Abstract: Stereo cameras are a suitable solution for reconstructing the 3D information of the observed scenes, and,

because of their low price and ease to set up and operate, they can be used in a wide area of applications,

ranging from autonomous driving to advanced driver assistance systems or robotics. Due to the high quality

of the results, energy based reconstruction methods like semi global matching have gained a lot of popularity

in recent years. The disadvantages of semi global matching are the large memory footprint and the high

computational complexity. In contrast, window based matching methods have a lower complexity, and are

leaner with respect to the memory consumption. The downside of block matching methods is that they are

more error prone, especially on surfaces which are not parallel to the image plane. In this paper we present a

novel block matching scheme that improves the quality of local stereo correspondence algorithms. The first

contribution of the paper consists in an original method for reliably reconstructing the environment on slanted

surfaces. The second contribution consists in the creation of set of local constraints that filter out possible

outlier disparity values. The third and final contribution consists in the creation of a refinement technique

which improves the resulted disparity map. The proposed stereo correspondence approach has been validated

on the KITTI stereo dataset.

1 INTRODUCTION

Stereo correspondence is one of the most researched

topics in computer vision. Using a pair of cameras

for estimating depth information remains a popular

choice mainly because of the low cost of the sensor,

and the high quality and density of the output,

comparable to the laser scanner technology (Penner

et al., 2015), (Antunes et al., 2012). The principle of

3D reconstruction from stereo image pairs is the

triangulation, which means finding the 3D point

where the rays passing through the pixels

corresponding to the same object in the two images

intersect. In practice, the images are rectified in such

a way that the corresponding points are on the same

line, and the only difference between position of an

object in the left and right image is in the column

coordinate. This difference (or offset) is called

disparity (d) and it is inversely proportional to the

object depth (Z), as described by equation 1. The term

B refers to the baseline of the stereo system and f

represents the focal length, in pixels, of the rectified

images.

Bf

d

Z

(1)

Due to an increasing number of applications

ranging from Advanced Driving Assistance Systems

(ADAS), Autonomous Driving or Biometry (Huang

et al., 2002), (Yasir Mohd Mustafah, December 2012

), (Einecke and Eggert, 2014) requiring accurate 3D

information, a wide variety of stereovision methods

have been developed. Current state-of-the-art

approaches may be classified in two main categories:

global and local stereo correspondence algorithms

(also called block matching algorithms). The global

stereo correspondence algorithms usually try to

minimize an energy function. These algorithms can

be based on belief-propagation (Yang et al., 2009),

dynamic programming (Hirschmuller, 2005), or

graph-cut techniques (Kolmogorov and Zabih, 2002).

The drawback of these methods consists in the large

memory consumption and high running time. The

semi-global matching (SGM) algorithm

(Hirschmuller, 2005) is a subclass of the global

optimization methods and, compared to the global

approaches, it has a simpler energy function to

Muresan M., Nedevschi S. and Danescu R.

A Multi Patch Warping Approach for Improved Stereo Block Matching.

DOI: 10.5220/0006134104590466

In Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017), pages 459-466

ISBN: 978-989-758-227-1

Copyright

c

2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

459

minimize, thus requiring less computational

complexity and producing good quality results. For

this reason SGM has attracted a lot of attention in the

automotive field over the years. Using modern GPUs,

SGM can be parallelized to run in real time (Haller

and Nedevschi, 2010); however, optimizations using

this hardware acceleration method are very power

demanding and the memory footprint remains very

high. In block matching algorithms (BM) the pixels

from one image are compared with the ones from the

second image and there is no energy minimization

constraint. Since single pixel matching can be

erroneous, the correspondence is done using

rectangular windows called blocks. Mainly due to

their simple computational scheme, block matching

algorithms run in less time without the need of

hardware acceleration, and require less memory. The

drawback of these algorithms is that they produce

lower quality disparity maps.

One of the reasons for which block matching fails

to reconstruct certain surfaces is that it generally

assumes the same disparity across the matching

window, and consequently it considers that the scene

consists of frontally viewed planes which are

perpendicular to the camera’s optical axis. This

assumption does not hold for the scenes observed by

ground vehicles or robots, since the surfaces and the

objects on the road can have many degrees of

orientation. A lot of research has been done in order

to tackle the shortcomings of block matching that

affect the quality of disparity maps, while

maintaining the low memory footprint and high

running speed of these algorithms. Our method

improves the quality of the stereo reconstruction on

tilted surfaces by using several oriented matching

blocks and constraining the winner disparity by

means of two flags. We also introduce a refinement

strategy that filters small errors. The remainder of the

paper is structured as follows: in the next section we

present the state of the art advancements for stereo

correspondence block matching algorithms, in

section three we illustrate the paper’s main

contributions, the fourth section contains

experimental results and implementation details, and

finally we end with the conclusions and further work

section.

2 RELATED WORK

Local stereo correspondence algorithms work by

creating finite support regions (usually called blocks)

around each interest point, and finding the

correspondence between these blocks in the left and

right images, by searching on the epipolar lines.

These methods are based on a matching metric

(Scharstein and Szeliski, 2002) and usually apply

different forms of aggregation for smoothing. The

common matching metrics are the sum of absolute

differences (SAD), the sum of squared differences

(SSD), the rank transform (RT), the census transform

(CT), or the normalized cross correlation (NCC). Due

to their low complexity requirements, block matching

methods are viable solutions for embedded

applications. A hardware solution implemented by

the TYZX Company is presented in (Woodfill et al.,

2006). This method uses an ASIC and a FPGA device

in order to compute in real time the BM stereo

correspondence using the census transform.

Modern approaches that tackle the problem of

surface orientation are presented in (Muresan et al.,

2015), (Ranft et al., 2014), (Einecke and Eggert,

2013) and (Einecke and Eggert, 2014). In (Muresan

et al., 2015) the authors create a new matching score

by shifting each individual row of the matching

descriptor in order to get the best matching score

between two features. A penalty is incorporated in the

matching score in case the best score does not come

from a fronto-parallel surface. In (Ranft et al., 2014)

the authors perform multiple operations of sheering

and scaling to the original images and compute

multiple block matching on the obtained images in

order to capture different surface orientations. The

final disparity map is obtained after fusing the

individual block matching results. In (Einecke and

Eggert, 2013) the authors perform a linear image

warping in order to capture the expected disparity for

the ground plane and in (Einecke and Eggert, 2014)

the authors perform an oriented block matching

aggregation. The authors use different penalties in

case the best matching score does not come from a

frontally viewed plane. The penalties are not

encapsulated in the final matching value. The method

presented in (Einecke and Eggert, 2015) uses

matching blocks of different shapes and sizes in order

to eliminate the effect caused by non-frontal surfaces.

This method of aggregation manages to diminish the

bloating effect caused by the usage of large

aggregation blocks and also reduce the noise caused

by small matching blocks.

3 PROPOSED SOLUTION

One of the reasons block matching stereo fails to

reconstruct certain surfaces is because of the inherent

assumption that the 3D depth of all the features within

a matching block is the same. In this section, we

VISAPP 2017 - International Conference on Computer Vision Theory and Applications

460

present an improvement of BM stereo in the presence

of slanted surfaces. Our method (Slanted Block

Matching - SBM) captures the orientation of surfaces

by warping the matching descriptor block. This

operation is performed very fast using a set of lookup

tables. After the matching operation has been

performed the obtained values are aggregated using

blocks of different shapes and sizes, which will help

reduce the errors introduced by the single pixel

matching.

Mainly due to the fact that when we are

computing the matching descriptors we are not

considering how surfaces may be oriented, we can

introduce matching errors. These errors are

aggregated in the following stages of the stereo

pipeline and lead, in the end, to a deteriorated

disparity map. In order to further reduce possible

outliers, we restrict each generated disparity value by

using a set of local constraints. The final map is

refined by removing all the small speckles resulted

from erroneous matching.

3.1 Matching Descriptors

In our work we have used binary descriptors. Our

motivation for choosing such features is that they are

usually easier to compute, they are invariant to

additive and multiplicative offsets in image intensity

values, and the time needed to compute these

descriptors is relatively small. For this reason, in our

work we have chosen a 7x9 weighted center

symmetric census approach. The center symmetric

census, expressed by equation (2), has a higher

robustness against noise than the classical census

transform, which is based on comparisons which all

involve the central pixel of the mask, due to the fact

that a noisy pixel will have only a local effect, and

will not compromise the whole metric. Furthermore,

after each comparison, instead of recording just one

bit, which is the result of the comparison, we are

memorizing two bits. By using two bits we are able

to better weight the certainty of the comparison. In

case the compared pixel is much smaller or much

larger than the value with which we are comparing,

we are storing the value of the comparison two times

whereas if the compared value is situated in an

interval with respect to the value with which we are

comparing we are storing the value of 01. This has the

advantage that if in the other image the comparison

result will be certain the effect of the Hamming

distance on the two images would not have an effect

as damaging to the final result as the classical

approaches. The analytical expression of the modified

center symmetric census (MCST_CENSUS) can be

seen in equation (3).

1

/2 /2 1

1

2

_(,) (, )

(,)( , )

0

0

/2

(, )

(,)(, )

0

Ni M j

NNMj

ij

j

N

M

MCST CENSUS u v I I

uv u v

i

j

M

II

uv uv

j

(2)

00,

,01,

11,

XtY

XY X t YANDX t Y

XtY

(3)

In equation (2), N and M denote the size of the

descriptor patch, and the

sign denotes the bitwise

concatenation operation. In equation (3), t represents

a small intensity threshold, with which we usually

compensate small variations in intensity. In our

solution the value of t has been set to 1.

In order to capture the geometry of slanted

surfaces, seven lookup tables have been created for

the right descriptor image, representing several

degrees of tilting for the descriptor block. Since the

derivative of the position (offset), for each pixel is

kept in the lookup table, computing all seven right

descriptor images is done concurrently, which is very

fast. An intuitive depiction of the slanted descriptor

windows is illustrated in figure 1.

Figure 1: Tilted Modified Center Symmetric Census

descriptor blocks.

The seven lookup tables were created on an

experimental basis. Initially we created multiple

tables with various degrees of inclination and we

gradually eliminated the lookup tables that did not

seem to offer any kind of improvement to the final

result, taking as reference the KITTI 2012 dataset.

Figure 2: Intuitive illustration of a 3x3 lookup table for

frontal (left) and slanted (right) situations.

A Multi Patch Warping Approach for Improved Stereo Block Matching

461

An intuitive example of a lookup table for a 3x3

patch is presented in figure 2. Each position records

the offset with respect to the center pixel, the first

element represents the offset with respect to the row

while the second records the offset with respect to the

column. In our case, seven 7x9 lookup tables were

created, using the modified weighted center

symmetric census descriptor. Six of the seven tables

correspond to the slanted surface scenario, and one

corresponds to the frontal surface scenario.

3.2 Shifted Window Hamming

Distance Computation

When using binary descriptors, the matching cost for

a specific position is usually computed using the

Hamming distance. Classically, given a pixel in the

left image, a search for a pixel with similar

appearance is carried out in the right image, on the

corresponding epipolar line over a number of

candidate positions (also called disparities). The

winning disparity represents the position where we

find the minimum Hamming distance.

Instead of searching for the minimum Hamming

distance between a feature in the left image and one

in the right image over multiple disparities, our

system searches for the best matching feature for the

left pixel in all seven right descriptor images over

multiple disparities. The best matching score will be

determined by the minimum Hamming distance value

between the score obtained for the fronto-parallel

case and the slanted blocks cases, to which we add a

small penalty. The value of the penalty that yields the

best results with respect to the stereo benchmark is 2,

and was determined experimentally. Analytical

representations of the mentioned operations are

depicted in equations (4), (5) and (6).

6

SI(i, j,d)= Min(Hamming(IL(i, j) , SRI ( , , )))

k=1

K

ijd

(4)

Frontal(i, j, d) = Hamming(IL(i, j), FPRI(i, j, d))

(5)

FS(i,j,d)=Min(Frontal(i,j,d),PS(i,j,d)+Penalty)

(6)

In the above equations we denote by SI the slanted

image pixel score, which represents the minimum

score obtained for all six slanted right images (SRI).

By Frontal we represent the score obtained for the

fronto-parallel case for a pixel at position i, j having

a disparity d. FPRI represents the fronto-parallel right

image. The final result of our algorithm for a pixel at

position i, j having the disparity d is denoted by

FS(i,j,d) and it is obtained by taking the minimal

value between the frontal score and the score for

slanted images at which we add a small penalty. We

are adding the small penalty because, similarly to the

work presented in (Hirschmuller, 2005), we are

trying to favour frontal surfaces. The final value FS is

stored in a cost volume C (p,d) where p represents the

pixel position and d is the corresponding disparity (7).

(,) (,)Cpd FSpd

(7)

After computing the Hamming distance, a multi

block aggregation is performed on the cost volume in

order to filter out possible outliers and reduce the

bloating effect of the resulted disparity map. The

aggregation scheme is similar to the one presented in

(Einecke and Eggert, 2015), improved by adapting

the matching blocks experimentally. The block sizes

used have the sizes: 1x155, 155x1, 17x17 and 7x7.

By A we are denoting the aggregated value and the

aggregation scheme is presented in (8).

max ,

1 155 155 1

17 17 7 7

A val val val val

xx

x

x

(8)

By ݒ݈ܽ

ௌ௭

we denote the value obtained by

summing the individual values within a block for one

of the specified sizes.

3.3 Winner Takes All

In the winner takes all stage of the stereo

correspondence pipeline, the index of minimum value

is chosen from the computed cost volume C, for a

certain pixel position p, as expressed by equation (9).

(,)

D

pargmin Cpd

d

(9)

The disparity map obtained through stereo

correspondence can also be deteriorated by several

external factors, such as reflectance, lack of texture,

repetitive patterns etc. For this reason we impose

several constraints on the created cost volume in the

winner takes all stage, such that erroneous results can

be filtered out or at least reduced. In order to

successfully select a disparity value, all imposed

constraints have to be satisfied.

To carry out this task the first step is to find for

each position the first three minimal values.

The first constraint used refers to the identification

of un-textured surfaces from the cost volume. For this

scenario we verify if the three best detected local

minima values are equal. Intuitively, we have

illustrated this phenomenon in figure 3 and equation

10.

1, 1 2 1 3

0,

min min AND min min

Periodicity

otherwise

(10)

VISAPP 2017 - International Conference on Computer Vision Theory and Applications

462

Figure 3: Graphical representation of the periodicity

phenomenon. With blue we highlight the position of three

possible minima values.

The second constraint is offering us a measure of

trust regarding the generated disparity value. This

confidence constraint is computed by using the

smallest three values in the cost volume for a pixel

position p, and finding if the ratio between the third

smallest value and the smallest value is less than a

confidence threshold. The analytical expression

depicting the usage of the confidence constraint is

illustrated in equation 11. The confidence threshold

has been set experimentally to 15.

3

1 ,

1

0,

min

ConfidenceThreshold

min

Con

othe

fidenceF

rwise

lag

(11)

In order to improve the precision of the detection,

sub- pixel interpolation is applied. For this step we

have used the symmetric V method, presented in

(Haller and Nedevschi, 2012). The sub pixel

interpolation is computed as:

int

2

31 31

23

2

21 21

2

21 21

23

2

31 31

(M M ) M M

0.5 0.25 ,

()

(M M ) M M

0.5 0.25 ,

()

final eger

Disp Disp

if M M

MM MM

if M M

MM MM

(12)

The values M

1

, M

2

, M

3

correspond to the winning

disparity and its neighbouring values. In order to

reduce small matching errors, a refinement stage is

applied to the disparity map.

3.4 Winner Takes All

By using refinement steps we hope to eliminate

remaining outliers, and obtain a better disparity map.

The first step consist of a background fill in stage,

which is performed in case of occlusions (Zbontar

and LeCun, 2015) and left-right (LR) check. The

analytical expressions for determining the condition

under which a certain disparity falls in (correct,

mismatch and occlusions) are described in equation

(13). Depending on this condition we know if

refinement is necessary or what refinement steps we

should apply. For example if the result of the

condition is mismatch we should apply a background

fill in, and in case of occlusion we should discard the

disparity value leaving an unreconstructed space.

1

,

,

,

1

RL

dD pd fordD p

R

Condition missmatch if d D pd for any other d

correct if

occlusion otherwise

(13)

In order to eliminate the remaining speckles caused

by incorrect matches, a new speckle removal

technique is presented. Classical speckle removal

techniques, based on region growing, tend to remove

speckles smaller than a predefined size, but do

nothing if the size of the speckle exceeds the imposed

limit. In our approach, even if the speckle has a larger

size, an erosion step is applied, reducing the size of

the error.

The first step of the refinement stage consists in

segmentation. For segmentation, two disparity

threshold values are used, a strong threshold value

(T2) and a weak threshold value (T1). Using the

strong and weak thresholds two segmentation limits

are created (an upper threshold limit and a lower

threshold limit). The disparity values that fall

between these limits are considered in the

segmentation region. Considering that v is the current

disparity value the upper and lower limits are

computed as shown by equation (14).

1

2

lower v T

upper v T

(14)

By using the two thresholds, we ensure that the

segmentation is robust even at object boundaries. The

threshold T1 has a smaller value than T2. After this

procedure a closing morphological operation with a

kernel of 11x11 is performed on the segmented

region. In case the detected region is a small speckle,

it will get filtered out by the erosion in the closing

operation. The final result is appended in the filtered

disparity map. A fill operation is carried out in order

to eliminate the holes caused by the closing operation.

For every pixel we are searching on all eight

directions until we find the closest two disparity

values with minimum difference. The search is

carried out over a number of k positions.

The final step in our refinement scheme consists in

a 1x9 and 9x1 median filter that removes any

remaining noise. The values for the weak and strong

thresholds for our application are 3 and 1 and the

A Multi Patch Warping Approach for Improved Stereo Block Matching

463

searching distance for the fill stage is 49 pixels. No

background interpolation step has been implemented

in our solution, therefore the final map density will be

less than 100%.

4 EXPERIMENTAL RESULTS

For evaluating our block matching approach we used

the online KITTI benchmark (Geiger et al., 2013).

This stereo dataset comprises road scenes and traffic

scenarios. We tested our results against classical

methods using multiple stereo cost functions, such as

census 7x9, modified census transform, sparse

census, and weighted center symmetric census. We

have also displayed the ranking of our method with

respect to the state of the art methods on the KITTI

site. In all the methods displayed in table I, a multi

block aggregation was used, along with the proposed

refinement functions. The differences in quality are

caused by the LUT based warping method of

computing the descriptor. The density percentage

comparison against the classical methods is computed

using the training set with the publicly available

ground truth. Table I illustrates the comparison with

classical rectangular descriptor based solutions.

The system on which we implemented our method

contains an Intel I5-2500 CPU with 3 GHz frequency.

No hardware acceleration methods have been used.

Open MP has been used to parallelize some small

parts of the code. The error threshold used in our

evaluation is 2px.

Table 1: Evaluation with respect to the classical cost

functions using KITTI Data-Set.

Method Density Out-All error

Census 99.67 % 11.865 %

WCS-CENSUS 99.98 % 11.24 %

MCT

99.68 %

11.21 %

SBM 99.97 % 8.785 %

Sparse Census 99.51 % 13.29 %

Figure 5 illustrates the results of the matching in

comparison with the 7x9 Census approach. The top

image represents the intensity image from the KITTI

dataset, the second image represents the result of the

census approach and the bottom image depicts the

result of our algorithm. It can be seen that our method

is able to better reconstruct the slanted surface in the

right side of the image. In figure 6 we illustrate yet

another situation in which our proposed solution

outperforms the classical approach. The top image

represents the left intensity image, the second image

represents the result of the sparse census method and

the last image is the image obtained with our

algorithm. In the sparse census method every second

pixel is skipped therefore resulting a sparse descriptor

pattern, not dense like in the case of 7x9 census. The

same aggregation scheme is employed in all tested

images.

Figure 4: The top image is the left intensity image, second

image depicts the disparity map using the census approach,

while the last image is the image obtained with our

algorithm.

Figure 5: The bottom image is the result of SBM, the second

image depicts the disparity map using a sparse census

descriptor and the first image represents the left intensity

image.

VISAPP 2017 - International Conference on Computer Vision Theory and Applications

464

Table 2 shows a snapshot of the comparison with

other methods present in the KITTI dataset from

2016. This overview shows that our local stereo

correspondence method achieves good results, even

surpassing some semi global approaches. The error

metric shown is out all, the percentage of erroneous

pixels out of all the pixels in the image, including the

occluded ones.

Table 2: Comparison with existing methods from the KITTI

benchmark.

Position Method Density Out-All error

32 wSGM 97.03 % 8.72 %

33 AARBM 85.80 % 8.70 %

34 DispNetC

100 %

8.11 %

35 SBM 99.97 % 8.75 %

36 AABM 100 % 8.77 %

37 rSGM 97.22 % 9.24 %

The running time of our algorithm is 0.3s per frame

on the KITTI data set images sizes. The method runs

faster when we are reducing the image sizes. The

proposed implementation can be accelerated in order

to achieve a higher running time. The improvement

of the time was not in the scope of the paper, as the

current work was focused so far only on improving

the quality of the stereo matching results.

The justification of the low memory consumption

is that the algorithm does not need the entire disparity

space to make optimizations in the cost volume; also,

we do not need to remember any past result when

generating the current disparity result. The only

additional memory necessary in comparison to the

classical BM methods is the one required for

memorizing the seven (1 frontal and six slanted)

weighted center symmetric census descriptor images

for the right intensity image. There is a linear

dependency between the amount of the memory used

depends and the size of the input images.

Figure 6: Rotation to the right of the 3D projected points in

PCL.

Figure 7: Rotation to the left of the 3D points.

Another good way of evaluating the quality of a

stereo algorithm would be to visually evaluate the 3D

points form the disparity map. In case there are errors

we would see spikes coming out of the image, or large

unreconstructed regions. We acquired a synchronized

pair of images from a set of Manta cameras. We

rectified them, applied our algorithm and projected

the 3D points using point cloud library. The result of

our algorithm can be seen in figure 6 and figure 7. We

have rotated the scene and took two snapshots in

order to illustrate how the scene can be viewed from

two vintage points.

5 CONCLUSIONS

In this paper we have presented a novel BM method

that improves the quality of the standard local stereo

correspondence methods, while keeping the lean

properties of the algorithm. The basic idea behind our

method is to use several descriptor images for the

right intensity image, each representing the result of

applying a slanted center symmetric descriptor and

keeping the best matching score over a number of

disparities. In our approach we try to favor frontal

surfaces, and so we include a small penalty each time

the best cost comes from a slanted descriptor. By

tilting the matching descriptor we ensure that the

errors created by the perspective effect or due to

slanted surfaces are not aggregated to lead to

erroneous results. Furthermore, we try to reduce

errors by imposing a set of local constraints when

generating a winning disparity. Finally we filter

erroneous speckles, obtaining an improved disparity

map. We did extensive tests on the KITTI dataset in

order to prove that our solution leads to improved

results with respect to classical and state of the art

stereo methods. We have also projected the disparity

points in order to make a visual evaluation of the 3D

reconstructed region.

Further development directions include improving

the running time of our algorithm, and the

implementation of the solution on a low cost

embedded platform. We will also continue with the

search for improving the quality of the stereo

A Multi Patch Warping Approach for Improved Stereo Block Matching

465

matching results, by verifying the relation between

block sizes, camera parameters and the used

descriptor, since variations in any of these three

parameters forces us to change the settings of the

algorithm.

ACKNOWLEDGEMENTS

This work was supported by a grant of the Romanian

National Authority for Scientific Research and

Innovation, CNCS/CCCDI – UEFISCDI, project

number PN-III-P3-3.6-H2020-2016-00252016,

within PNCDI III.

This work was supported by the MULTIFACE grant

(Multifocal System for Real Time Tracking of

Dynamic Facial and Body Features) of the Romanian

National Authority for Scientific Research, CNDI–

UEFISCDI, Project code: PN-II-RU-TE-2014-4-

1746.

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