Development of stereo matching algorithm based on sum of absolute RGB color differences and gradient matching

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 3, June 2020, pp. 2375∼2382
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i3.pp2375-2382 Ì 2375
Development of stereo matching algorithm based on sum of
absolute RGB color differences and gradient matching
Rostam Affendi Hamzah1
, M. G. Yeou Wei2
, N. Syahrim Nik Anwar3
1
Fakulti Teknologi Kejuruteraan Elektrik and Elektronik , Universiti Teknikal Malysia Melaka, Malaysia
2,3
Fakulti Kejuruteraan Elektrik, Universiti Teknikal Malysia Melaka, Malaysia
Article Info
Article history:
Received Dec 19, 2017
Revised Dec 11, 2019
Accepted Dec 18, 2019
Keywords:
Bilateral filtering
Computer vision
Gradient matching
Stereo matching
Stereo vision
ABSTRACT
This article presents local-based stereo matching algorithm which comprises a devel-
opment of an algorithm using block matching and two edge preserving filters in the
framework. Fundamentally, the matching process consists of several stages which
will produce the disparity or depth map. The problem and most challenging work
for matching process is to get an accurate corresponding point between two images.
Hence, this article proposes an algorithm for stereo matching using improved Sum
of Absolute RGB Differences (SAD), gradient matching and edge preserving filters.
It is Bilateral Filter (BF) to surge up the accuracy. The SAD and gradient matching
will be implemented at the first stage to get the preliminary corresponding result, then
the BF works as an edge-preserving filter to remove the noise from the first stage.
The second BF is used at the last stage to improve final disparity map and increase
the object boundaries. The experimental analysis and validation are using the Mid-
dlebury standard benchmarking evaluation system. Based on the results, the proposed
work is capable to increase the accuracy and to preserve the object edges. To make the
proposed work more reliable with current available methods, the quantitative measure-
ment has been made to compare with other existing methods and it shows the proposed
work in this article perform much better.
Copyright c 2020 Insitute of Advanced Engineeering and Science.
All rights reserved.
Corresponding Author:
Rostam Affendi Hamzah,
Fakulti Teknologi Kejuruteraan Elektrik and Elektronik,
Universiti Teknikal Malaysia Melaka,
Malaysia.
Email: rostamaffendi@utem.edu.my
1. INTRODUCTION
Computer vision is interdisciplinary field that comprises methods for acquiring, processing
and analyzing and image understanding from digital images or videos. It is artificial intelligence to mimic
the human visual system. Stereo vision is a part of them and the process to get the information such as
object detection, recognition and depth estimation is called as stereo matching. This process starts with
corresponding from one point on reference image to another point on the target image. These images can be two
or more. In this article, the images are using from the stereo camera input which is also known as stereo
images. The matching algorithm from the matching process produces disparity map. This map consists of depth
information which is valuable for many applications such as virtual reality [1], 3D surface reconstruction [2],
face recognition [3] and robotics automation [4-5]. The stereo baseline can be setup in a wide or short
baseline [6] distance which depends on the applications. To determine the range or distance estimation,
the triangulation function is applied to each of the pixel on the disparity map. Therefore, to get an accu-
rate result, the matching process requires complex and challenging solution for depth or distance estimation.
It requires precise function on the propose framework. Fundamentally, matching algorithm consists of multiple
Journal homepage: http://ijece.iaescore.com/index.php/IJECE

2376 Ì ISSN: 2088-8708
stages which was proposed by Szeliski and Scharstein [7]. First stage, matching cost computes the preliminary
matching point of stereo image. Second stage, the filtering is utilized to reduce the preliminary noise of the first
stage. Then, disparity selection and optimization stage normalizes the disparity value each pixel on the image.
Last stage is to refine the final result and also known as disparity map post-processing step.
In stereo matching development, there are two major approaches available in developing the algorithm
framework. It is local methods as published in [8-10] and global method [11]. Mostly local methods use local
properties or local contents using windows-based technique such as fixed windows implemented in [12-13],
adaptive window [14], convolution neural network [15] and multiple windows [16]. In common, Winner-
Takes-All (WTA) strategy is applied for local based optimization. It is low computational complexity and fast
execution time [17-19]. Local method such implemented in [20] that used plane fitting technique to increase
the accuracy at the final stage. This method also known as RANSAC that efficiently works on the low textured
areas. However, the error still occurred on the object edges. Their method requires several iterations for plane
fitting process. If wrong iterations, then it will affect the results. Commonly, local methods show fast running
time, but low accuracy on the edges due to improper selection of windows sizes. Hence, to get an accurate
result for the local approach is a challenge to the researchers.
Another approach in stereo matching algorithm to produce the disparity map is global optimization
method. Fundamentally, this method uses energy-based function which is known as Markov Random Field
(MRF). The method in global optimization such as Belief Propagation (BP) [21] and Graph Cut
(GC) [22] produce accurate results. Each pixel of interest calculation requires all pixel’s energy in dispar-
ity map. It calculates neighboring or nearby pixels using maximum flow and the selection is made based on
the minimum cut-off energy on the disparity map. The algorithms implemented using global optimization
approach normally involve high computational requirement due to all pixel’s energy calculation and absorp-
tion. Global methods involve iterations which increase the execution time each disparity map reconstruction.
This article aims to produce accurate results and competitive with some established methods. The first function
or stage will be implemented using improved Sum of Absolute Differences (SAD) [23] with gradient match-
ing. Then, the second stage utilizes the edge preserving filter which is known as Bilateral Filter (BF) [24].
This filter is capable to remove noise and preserved object edges. The third stage is optimization based on
WTA strategy. Last stage, the BF is applied once again to remove unwanted or remaining invalid pixels.
The BF is also capable to increase the accuracy at object boundaries.
2. RESEARCH METHOD
The diagram of the proposed work is dispalyed by Figure 1. The stereo matching algorithm starts
with STEP 1 to get the preliminary disparity map. The improved SAD has been proposed which the weighted
technique is used on the block matching process. The combination of improved SAD with gradient match-
ing in this article should be able to increase the effectiveness of corresponding process and accuracy. Then at
STEP 2, the BP is utilized to reduce the noise and preserved the object edges. The BP is capable to efficiently
remove noise on the low texture regions and sharping the object boundaries. The optimization uses WTA
strategy which this method normalizes the floating points numbers and selects minimum disparity values on
the disparity map. Final stage at STEP 4 is also using the BP but with the disparity values. This filter is a type
of nonlinear filter and capable to improve final disparity map.
Figure 1. A flowchart of the proposed algorithm.
Int J Elec & Comp Eng, Vol. 10, No. 3, June 2020 : 2375 – 2382

Int J Elec & Comp Eng ISSN: 2088-8708 Ì 2377
2.1. Matching cost computation
The first stage of the proposed framework is using the weighted SAD. The preliminary disparity map
is produced at this stage. Hence, robust function must be used to increase the effectiveness on the dispar-
ity map. The problem on matching process at this stage on the low texture regions must be at minimum.
The weight is proposed at SAD to improve the values on the low texture regions. Thus, the consistency of the
weight at the low texture region is capable to make the matching process accurate and reduces the mismatch
or invalid pixels. The RGB values are used with the weight of sum of intensity differences on right image Ir
and left image Il which is given by (1):
SAD(x, y, d) =
1
W
(x,y)∈w
|Ii
l (x, y)i − Ii
r(x − d, y)| (1)
where (x, y) are the coordinates pixel of interest with d represents the disparity value, W is the proposed
weight, RGB channels numbers are i and w represents kernel of SAD algorithm. The second part is gradient
matching components. It contains the magnitude differences from each image. There will be two directions
that need to be calculated on this gradient differences. Vertical direction Gy and horizontal direction of Gx are
the directions with the equations are given by (3) and (2):
Gy =


1
0
−1

 ∗ Im (2)
Gx = 1 0 −1 ∗ Im (3)
where Im is input image and ∗ represents convolution operation on the gradient matching. The Gx and Gy are
the gradient magnitude for m which is given by (4):
m = G2
x + G2
y (4)
(5) is the gradient matching kernel G(x, y, d).
G(x, y, d) = |ml(x, y) − mr(x − d, y)| (5)
The matching cost function at this stage is given by (6) where the input volume of SAD(x, y,d) and G(x, y,d)
are combined together.
MC(x, y, d) = SAD(x, y, d) + G(x, y, d) (6)
2.2. Cost aggregation
This second stage more likely to filter the preliminary disparity map from stage one. Normally the
preliminary disparity map contains high noise and it must be removed. Some of invalid and uncertainties
pixels are constructed during the matching process. Hence, at this stage the filter must be robust and is capable
to remove high noise of invalid pixels and preserved the object boundaries. The BP is used due to strong
preserving object edges and at the same time efficient to remove high noise especially on the plain color and
low texture regions. (7) is the BF function used in this article.
WBF
(p, q) =
q∈wB
exp −
|p − q|2
σ2
s
exp −
|Ip − Iq|2
σ2
c
(7)
where p is the location pixel of interest at (x,y), wB and q are window size of BF and neighboring
pixels respectively. The σs denotes a factor of spatial adjustment and σc equals to similarity factor for the color
detection. The p − q is spatial Euclidean interval and |Ip − Iq| denotes the Euclidean distance in color space.
Hence, (8) is the cost aggregation function of BF with the matching cost computation input.
C(p, d) = WBF
(p, q)MC(p, d) (8)
Development of stereo matching algorithm based on... (Rostam Affendi Hamzah)

2378 Ì ISSN: 2088-8708
2.3. Disparity optimization
This stage optimizes the disparity values on disparity map. The normalization is based on the
minimum disparity values with the floating-point number which the WTA is selected in this article. The WTA
is normally being used in the local based methods due to fast implementation. The WTA function is given
by (9).
dx,y = argmind∈DC(p, d) (9)
where D represents a set of valid disparity values for an image and C(p, d) denotes the second stage of
aggregation step. Fundamentally, after this stage the disparity map still contains noise or invalid pixels.
Thus, this map needs to be improved and the last stage is will remove remaining noise.
2.4. Disparity refinement
The last stage of the algorithm framework is known as refinement or post processing stage. It has
several continuous processes which starts with handling the occlusion regions, filling the invalid pixels and
filtering final disparity map. The left-right consistency checking process is conducted to identify occlusion
areas and some invalid pixels. Then, these invalid pixels are restored with valid pixel values through the filling
process. Some of artifacts and unwanted pixels will be removed using the BF and at the same time preserved
the object boundaries. The BF smoothes the final disparity map as indicates by (7).
3. RESULT AND ANALYSIS
This section explains about the disparity map results that will be represented by color-scale intensity.
The different color tones show that the respected objects are mapped based on the disparity values and the
distance sensor (i.e., stereo camera). Most probably the lighter intensity volume indicates that the object is
closer to the sensor. The experimental analysis has been executed on a personal computer with Windows 10,
3.2GHz and 8G RAM. The input images are from the Middlebury stereo evaluation dataset [24] which contains
15 standard images and must be submitted online. These images are very complex, and each image consists
of different characteristics and properties such as light settings objects depth, incoherence regions, different
resolutions and low texture areas. The values of {w, σs, σc, wB} are {9x9, 17, 0.4, 11x11}.
Figure 2 shows a sample Jadeplant image (i.e., left and right) from the Middlebury training dataset
with different brightness and high contrast. Generally, due to the brightness difference, these input images are
very challenging to be matched. It contains different pixel values at the same corresponding point. However, the
proposed algorithm is correctly discovered the disparity locations. The level of disparity contour are precisely
assigned and object distance are well-recognized. Figure 3 shows the final disparity map results of 15 training
images from the Middlebury dataset. The accuracy attributes for error evaluation are nonocc (non-occluded)
and all error. The nonocc error is the error evaluation based on the non-occluded regions on disparity map while
all error represents the all pixels’ evaluation on an image of disparity map. Within these 15 images, Pipes and
Jadeplant images are the most difficult images to be matched. These images comprise several piping lines and
leaves with different sizes respectively. Yet, the propose algorithm can reconstruct almost accurate disparity
map with clear discontinuities regions. Fundamentally, real images from the Middlebury are difficult and very
challenging to get an accurate corresponding point. It was developed to test the robustness of an algorithm
where same corresponding point maybe contains different pixel values. Additionally, each image contains
difference characteristics such as plain color objects, shadow, discontinuity regions and occluded areas.
With referring to Figure 3, the disparity maps of low texture surfaces such as Motorcycle, Motorcy-
cleP, Playtable and PlaytableP are well recreated with different depth and disparity contour. Other regions
difficult to be matched are plain colour objects and shadow such as images of ArtL, Recycle, Piano and
PianoL. These regions consist of similar pixel values and possibility to get wrong matching are very high.
The disparity maps from the proposed work display almost accurate matching for these images. It shows that the
proposed work is able to get correct matching pixels on these regions and robust against the plain colour areas.
The quantitative measurement from the Middlebury online results are given in Tables 1 and 2. These results
are produced by the Middlebury online benchmarking evaluation system with two error attributes as explained
above. Some established methods are also included in these Tables to show the competitiveness of the proposed
work. Overall, an average error measurement is assessed to rank the best results. For Table 1, the proposed
method is ranked at top of the table with 6.11%, and Table 2 with 9.15%. It shows that the proposed work
is competitive with other recently published methods and can be used as a complete algorithm. The proposed

work is rank at top compared to [15-17,19,25,26] for nonocc error. The weight average error is 6.11% where
Jadepl, Playrm and Vintge images are the lowest error produced. For the all error attribute in Table 2, the
proposed work is produced at 9.15% which is the lowest average error. It shows that the proposed work in this
article is competitive with some established methods.
Figure 2. Different brightness and contrast of the input Jadeplant stereo images. Accurate disparity map result
is produced by the proposed work compared to the image without the proposed work. The plant structures are
clearly displayed and smooth disparity map can be notiﬁed
Figure 3. These ﬁnal disparity images are from the Middlebury dataset which the results tabulated in
Table 1 and Table 2
Table 1. The nonocc error results using the Middlebury dataset. The comparison results with other published
methods
Algorithms Adiron ArtL Jadepl Motor MotorE Piano PianoL Pipes Playrm Playt PlayP Recyc Shelvs Teddy Vintge Weight Ave
Proposed Algorithm 3.66 4.23 19.54 3.11 3.87 5.01 11.02 6.32 5.11 24.85 5.10 3.33 7.52 2.21 7.90 6.11
SNCC [19] 2.89 4.05 18.10 2.68 2.52 3.52 7.08 6.14 5.64 45.40 3.13 2.90 7.59 1.58 13.50 6.97
ELAS [26] 3.09 4.72 29.70 3.28 3.29 4.30 8.31 5.61 6.00 21.80 2.84 3.09 9.00 2.36 10.90 7.22
MPSV [15] 3.83 6.00 19.70 5.85 5.53 5.68 34.30 9.59 5.86 15.30 4.20 4.59 13.00 3.70 14.30 8.81
ADSM [16] 13.30 6.10 15.00 3.67 5.67 7.08 20.60 6.57 13.20 23.10 3.55 5.76 17.20 3.05 10.10 8.95
DoGGuided [17] 15.20 9.57 27.10 5.64 8.31 8.09 32.40 9.67 14.00 24.50 5.32 5.56 16.20 4.15 15.00 12.00
BSM [25] 7.27 11.40 30.50 6.67 6.52 10.80 32.10 10.50 12.50 24.40 12.80 7.42 16.40 4.88 32.80 13.40

2380 Ì ISSN: 2088-8708
Table 2. The all error results using the Middlebury dataset. These comparisons show the competitiveness of
the proposed method
Algorithms Adiron ArtL Jadepl Motor MotorE Piano PianoL Pipes Playrm Playt PlayP Recyc Shelvs Teddy Vintge Weight Ave
Proposed Algorithm 4.74 7.45 27.21 5.57 5.54 6.01 11.64 11.77 7.31 27.05 8.54 3.86 9.21 3.33 8.87 9.15
SNCC [19] 3.63 6.78 39.80 5.12 5.11 4.65 8.23 11.80 8.05 45.60 4.36 3.29 8.10 2.55 14.80 10.40
ELAS [26] 4.08 7.18 52.80 5.39 5.45 4.96 9.00 10.70 7.94 23.20 3.83 3.78 9.46 3.34 11.60 10.60
ADSM [16] 14.30 10.60 34.10 6.00 8.00 7.37 20.40 12.10 16.90 25.50 5.84 5.83 17.20 4.11 11.10 12.30
MPSV [15] 5.87 9.43 40.20 9.11 8.80 7.03 34.20 15.80 8.58 16.90 5.89 6.78 13.70 4.82 16.80 12.70
DoGGuided [17] 20.10 28.00 56.50 13.80 16.80 13.40 37.30 23.80 30.30 30.80 13.00 9.13 19.00 13.40 23.60 22.30
BSM [25] 12.70 28.70 58.70 14.80 14.70 16.00 35.80 24.50 29.40 31.00 20.20 12.10 19.20 14.30 39.30 23.50
To verify the potentiality of the proposed algorithm, the images from the KITTI [27] are also tested.
These images are more difficult and challenging to be matched. It contains complex edges and structures such
as shadow, plain color surfaces, high different contrast and brightness areas with large untextured regions.
The experimental results are shown in Figure 4. The disparity map results show accurate disparity values
estimation in grayscale. As for reference, the signage, a cyclist, trees and cars, are well-reconstructed with
correct disparity level. It shows the proposed work in this article capable to work with difficult stereo images
from real environment.
Figure 4. The disparity map results from the KITTI training dataset. This article utilizes images from the
number of #000004 10-#000007 10
4. CONCLUSION
In this work, the combination of SAD algorithm based RGB color and gradient matching are producing
accurate results. The second stage where edge preserving filter is utilized. The BF at the aggregation stage is
capable to filter high noise and conserve the object boundaries of the preliminary disparity map. The WTA
strategy was implemented at the optimization stage to normalize the floating points numbers to the disparity
values. The second edge preserving filter was used at the last stage of the proposed work using the same
BF. This nonlinear filter removed remaining noise and increase the efficiency of final disparity map. Overall,
these edge preserving filters used in the proposed framework were able to remove noise especially on the low
texture regions and able to preserve the object edges as shown by Figure 2. The quantitative measurement
from the standard benchmarking Middlebury system also demonstrated low average errors were produced by
the proposed framework at 6.11% and 9.15% of non-occluded and all pixel errors respectively. The training
images are shown by Figure 3. From real images of the KITTI, the proposed work was also demonstrated
accurate results.

ACKNOWLEDGEMENT
This project was sponsored by a grant from the Universiti Teknikal Malaysia Melaka with the Number:
JURNAL/2018/FTK/Q00008.
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BIOGRAPHIES OF AUTHORS
Rostam Affendi Hamzah was graduated from Universiti Teknologi Malaysia where he received his
B.Eng majoring in Electronic Engineering. Then he received his M. Sc. majoring in Electronic
System Design engineering from the Universiti Sains Malaysia in 2010. In 2017, he received PhD
majoring in Electronic Imaging from Universiti Sains Malaysia. Currently he is a lecturer in the
Universiti Teknikal Malaysia Melaka teaching digital electronics, digital image processing and
embedded system.
Melvin Gan Yeou Wei was born in 1992, Melvin Gan Yeou Wei graduated from Universiti Teknikal
Malaysia Melaka where he received his B.Eng majoring in Electrical in 2017. Currently, he is
pursuing a Master Degree in the Universiti Teknikal Malaysia Melaka.
Nik Syahrim Nik Anwar was born in 1981, Nik Syahrim graduated from University of Applied
Science Heilbronn, Germany where he received his Diplom in Mechatronik und Mikrosystemtechnik
majoring in Mechatronics in 2006. In 2010 he received his M. Sc. majoring in Mechatronics from the
University of Applied Science Aachen, Germany. In 2018, he received PhD majoring in Electrical
from the Universiti Sains Malaysia. Currently he is a lecturer in Universiti Teknikal Malaysia Melaka
teaching Electrical and Mechatronics subjects.

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