Journal of Signal and Information Processing, 2013, 4, 109-113
doi:10.4236/jsip.2013.43B019 Published Online August 2013 (http://www.scirp.org/journal/jsip) 109
Image Processing Techniques in Shockwave Detection and
Modeling
Suxia Cui1, Yonghui Wang2, Xiaoqing Qian3, Zhengtao Deng3
1Department of Electrical and Computer Engineering, Prairie View A&M University, Prairie View, Texas, USA; 2Department of
Engineering Technology, Prairie View A&M University, Prairie View, Texas, USA; 3Department of Mechanical Engineering, Ala-
bama A&M University, Huntsville, Alabama, USA.
Received May, 2013.
ABSTRACT
Shockwave detection is critical in analyzing shockwave structure and location. High speed video imaging systems are
commonly used to obtain image frames during shockwave control experiments. Image edge detection algorithms be-
come natural choices in detecting shockwaves. In this paper, a computer software system designed for shockwave de-
tection is introduced. Different image edge detection algorithms, including Roberts, Prewitt, Sobel, Canny, and Lapla-
cian of Gaussian, are implemented and can be chosen by the users to easily and accurately detect the shockwaves. Ex-
perimental results show that the system meets the design requirements and can accurately detect shockwave for further
analysis and applications.
Keywords: Shock Wave Detection; Im ag e Ed ge Det ect i o n
1. Introduction
A shockwave is a strong compression wave existing in
supersonic/hypersonic flow field. Across the shockwave
gas pressure, temperature and density increases signifi-
cantly as a function of flow Mach number. Near the nose
area of a supersonic/hypersonic flight vehicle, strong
shockwaves exist. Extreme heat fluxes and heat load to
the vehicle surface requires strong thermal protection in
the nose area. Additionally, the shock standoff distance
varies drastically with the temperature for a non-ideal gas,
causing large differences in the heat transfer to the ther-
mal protection system and drag of the vehicle. Super-
sonic wind tunnel experiments are needed to provide
insight into the physics of air flow at high Mach numbers.
Knowing the location and shape of the shockwave is es-
sential to the success of vehicle design. In general, opti-
cal imaging system can be used to capture shockwave
shape, location and flow property changes near the test
article in a supersonic wind tunnel. High speed video
imaging system and Sch lieren system will normally gen-
erate significant amount of images that need to be ana-
lyzed after the experiment. Image processing techniques
can make this type of data analysis more efficient and
precise, but there exists challenges on how to pre-process
the obtained images according to the wind tunnel condi-
tion as well as dealing with large volume of data cap
tured by high speed camera. Data acquisition is per-
formed in wind tunnel, while data analysis will be com-
pleted by a powerful PC.
2. Shockwave Stand-off Distance Detectio n
A series of shockwave control experiments were con-
ducted using a supersonic wind tunnel facility. The su-
personic flow is created by a primary supersonic nozzle
to provide supersonic speed up to Mach 4. The flow
emerging from the nozzle is then exhausted as a free jet
into a windowed low pressure test cabin with extremely
low back pressure. Figure 1 shows the shockwave ex-
periment setting and a typical experimental image cap-
tured by a high speed video camera for a Mach 4 shock-
wave control experiment. The test article basic diameter
(perpendicular to the incoming flow direction) is 3cm
and the nose is spherical. The length of the cylindrical
part is around 7 cm with the total length of the model
from nose tip to cylinder base is 10cm. The shockwave
structure and location capturing device were captured by
a high speed video imaging system with speed of 2000
frames per second at 512 x 512 resolutio ns. Around 800 0
frames of image data was collected for each experi-
ment.
To ana lyze the s hock wave stand-off distance, a special
shockwave shape and stand-off distance detection algo-
rithm needs to be developed. This algorithm should be
able to accurately capture the steady shape and unsteady

Image Processing Techniques in Shockwave Detection and Modeling
110
shape change of the shockwave especially the shockwave
stand-off distance along the stagnation line. Since the
experimental image has built-in noise, a noise cancella-
tion algorithm should be incorporated in the detection
scheme. The detection algorithm should also be robust
because the large amount of unsteady shockwave images
has to be analyzed. The time history of the shockwave
stand-off distance under control conditions has to be pre-
cisely captured.
Figure 1. Aero-Test Article inside the wind tunnel and
typical shockwave image near the nose are of the test arti-
cle.
The current research focused on the development of a
new shockwave standoff distance detection algorithm. To
detect the shockwave shape and stand-off distance
through the images, image processing techniques can be
used to make this type of data analysis more efficient and
precise. In the current research, a new interactive and
user-friendly shockwave detection software was devel-
oped. This software can precisely detect the shockwave
stand-off distance in front of the test article inside a su-
personic wind tunnel.
3. Image Edge Detection Algorithms
Edge detection algorithm is the natural cho ice for detect-
ing shockwave within the obtained high speed video se-
quences. Edges are local features of images, which are
local regions with special properties. Edges are pixels
with significant local changes of intensity–large gradi-
ent–in an image. Edges typically occur on the boundary
between two different regions in an image (as shown in
Figure 2). Because important features, such as corners,
lines, curves, etc., can be extracted from the edges, edge
detection algorithms are very important in computer vi-
sion applications. Edge detection is to detect the edges
and to produce a line drawing of a scene from an image
of that scene.
There are four steps for edge detection: (1) Smoothing:
suppress as much noise as possible, without destroying
the true edges. (2) Enhancement: apply a filter to en-
hance the quality of the edges in the image (sharpening).
(3) Detection: determine which edge pixels should be
discarded as noise and which should be retained (usu ally,
thresholding provides the criterion used for detection). (4)
Localization: determine the exact location of an edge
Edge thinning and linking are usually required in this
step.
Figure 2. Image edge example: a scan line highlighted (left)
and intensity along the highlighted scan line (right).
In mathematics, derivatives are used to describe
changes of continuous functions. Applying this to 2D
images, partial derivatives can be used to express the
image intensity changes (e.g. edges). Edge points can be
detected by detecting (1) the local maxima or minima of
the first derivative and (2) the zero-crossing of the sec-
ond derivative. For 1D discrete signals, the first deriva-
tive can be approximated as



0
()
lim1( )
a
fxa fx
f
xf
a


xfx
;
and the second derivative can be approximated as
  
0
lim
a
f
xfxa
fx a




 




1fx fx



(1)2() (1)fxfx fx

 .
For 2D images, gradient can be used to describe edges.
Gradient is defined as a vector
[,]
f
f
f
x
y




,
its magnitude,
22
() ()
f
f
f
x
y

 

,
provides the edge’s strength information. For images, by
using pixel-coordinate notation (e.g., for row number
and for column number, and i
j
I
for image signal),
the gradient can be approximated as




0
,,
lim1, ,
a
Ix ayIxy
I

I
xyIxy
xa




(,1)(, )
I
ij Iij

 , and
0
(,)(, )
lim( ,1)( ,)
a
IIxy aIxy
I
xy Ixy
ya




(1,) (,)
I
ijIij

 .

Image Processing Techniques in Shockwave Detection and Modeling 111
3.1. Roberts
The Roberts method finds edges using the Roberts
approximation to the derivative. It returns edges at those
points where the gradient of I is maximum. It was one of
the first edge detectors and was initially proposed by
Lawrence Roberts [1]. The Roberts edge detector ap-
proximates the partial derivatives of the gradient as
 
,1,
IIijIij
x



1
,

1,, 1
IIij Iij
y
 
.
This approximation can be implemented by convolving
the following masks
10
01
x
M 




and
01
10
y
M



onto images. An example of Roberts edge detection is
shown in Figure 3.
Figure 3. Roberts edge detector: original image (left) and
detected edges (right) .
3.2. Prewitt
The Prewitt method finds edges using the Prewitt ap-
proximation to the derivative. It was proposed by Judith
M. S. Prewitt [2]. The Prewitt operator approximates the
partial derivatives of the gradient as

1, 1, 11, 1
IIi jIijIi j
x
 




1, 1(, 1) (1, 1)Ii jIijIi j ,

1, 11,1, 1
IIi jIi jIij
y
 




1,1( 1,)( 1,1)Ii jIi jIi j 
.
The approximation can be implemented by convolv ing
the following masks
101
101
101
x
M








and
111
000
111
y
M











onto images. An example of Prewitt edge detection is
shown in Figure 4.
Figure 4. Prewitt edge detector: original image (left) and
detected edges (right) .
3.3. Sobel
The Sobel method finds edges using the Sobel approxi-
mation to the derivative. It was proposed by Irwin E.
Sobel in 1970 [3]. A little bit different from the Prewitt
operator, the Sobel operator approximates the partial
derivatives of the gra di ent as

1, 12, 11, 1
IIi jIijIi j
x







1, 12(, 1)(1, 1)Ii jIijIi j


,

1,1 21,1,1
IIi jIi jIi j
y



 



1,12(1,)(1,1)Ii jIi jIi j

 
.
The approximation can be implemented by convolv ing
the following masks
10 1
202
10 1
x
M













and
121
000
121
y
M






onto images. An example of Sobel edge detection is
shown in Figure 5.
Figure 5. Sobel edge detector: original image (left) and de-
tected edges (right) .
Edge detection algorithms with Roberts, Prewitt, and
Sobel operators share the same procedure in detecting
edges. Main steps in edge detection with these operators:
(1) calculate partial derivatives of the image through
convolution, *
x
x
I
I
IM
x


 and *
y
y
I
I
IM
y


; (2)
calculate the magnitud e of gradient,

Image Processing Techniques in Shockwave Detection and Modeling
112
2
() ()
2
I
I
I
x
y

 

; and (3) if (, )
I
ij T
, then it
is possible an edg e point, is the threshold.
T
3.4. Canny
Also being a method which finds edges by looking for
local maxima of the gradient of the image, the Canny
algorithm, which was developed by John F. Canny in
1986 [4], introduces more steps to minimize the noise
affection. To reduce the noise effect, a low-pass Gaus-
sian filter,

22
2
2
2
1
,2
x
y
Gxy e




, (1)
is applied to the image. By finding the derivative of the
Gaussian filter, the gradient can be calculated

** *
x
x
I
I
IGIG IG
xx x
 
 
,

** *
y
Ix
I
IGIGIG
xx x
 
 
,
where 2(,)
xx
GGx


y
and 2(, )
yy
GGx


y
.
After the gradient magnitude, 22
x
y
III , is ob-
tained, two more steps are performed to identify the
edges. A non-maxima suppression algorithm is applied to
find the local maxima of the gradient magnitude, and a
hysteresis thresholding with two thresholds is applied to
get rid of extra noise and retain the real edge poin ts. This
method is therefore less likely than the others to be
fooled by noise, and more likely to detect true weak
edges. An example of Canny edge detection is shown in
Figure 6.
Figure 6. Canny edge detector: original image (left) and
detected edges (right) .
3.5. Laplacian of Gaussian
The Laplacian of Gaussian (LoG) method identifies
edges by looking for zero crossings after filtering the
image with an LoG filter [5].
In this method, a Gaussian low-pass filter as shown in
Equation (1) is applied to reduce the noise effect. Previ-
ous discussion shows that edge points can be detected by
detecting the zero-crossings of the second derivative.
Here the Laplacian operator,
22
2
22
f
f
f
x
y





is applied to find the corresponding second derivatives
and ultimately the zero- crossings. It can be shown that


22
**
I
GI G and

22 222
2
22 4
2
,(
GGxy
Gxy Gxy
xy


 

 ,)
Theoretically, the LoG function



2
,,
g
xy Gxy
has infinite extent; for a practical implementation of LoG
edge detection, however, it has to be truncated to a finite
size. It can be shown that the width of the center lobe of


,
g
xy is 22w

, and that the function
 
3w
,, ,
ˆ,2
0,
gxyx y
gxy
else





possesses around 99.7% of the energy of


,
g
xy . By
convolving the image with the appropriate LoG mask
then detecting zero crossings in the convolution output,
LoG method offers better localization. An example of
LoG edge detection is shown in Figure 7.
Figure 7. LoG edge detector: original image (left) and de-
tected edges (right) .
4. Shockwave Detection System and Results
To detect shockwave accurately and effectively, a
MATLAB-based image processing software is developed.
A user interface window is design to help users easily
load and display shockwave image sequences, as shown
in Figures 8-10 . Different edge detection methods can be
chosen to detect the shockwave. Edge detection thresh-
olds can be specified by users or automatically chosen by
the program. Users can select to display random frame or
play the image sequence continuously. In either case, the
edge detection results will be displayed at the same time.
Two sequences are tested using the software devel-
oped. Based on the edge detected using edge detection
methods, shockwave thickness is measured, results can
be seen in Table 1. From the results, we can see that,
even though they are different from each other, the edge
detection methods perform exactly the same. For se-

Image Processing Techniques in Shockwave Detection and Modeling
113
quence #1, all methods measure the shockwave thickness
as 10 pixels; while for sequence #2, all methods agree
that the shockwave th ickness is 9 pixels. Users can select
edge detection method according to their applications or
the characteristics of the image sequence. For example, if
the sequence has a higher level of noise, then “Canny” or
“LoG” can be used due to their noise resistance property.
However, these two methods have higher computational
complexities. For quick detection applications, the other
three methods may be more suitable.
Figure 8. Shockwave detection with “Roberts ” .
Figure 9. Shockwave detection with “Sobel”.
Figure 10. Shockwave detection with “Canny”.
Table 1. Shockwave thickness dete c t ion results.
Shockwave Thickness (pixels)
Edge Detection Method Sequence #1 Sequence #2
Roberts 10 9
Prewitt 10 9
Sobel 10 9
Canny 10 9
Laplacian of Gaussian 10 9
a. All edge detection methods choose thresholds automatically.
5. Conclusions, Challenges, and Future
Works
A shockwave detection system is built. The system util-
izes image edge detection algorithms to easily and accu-
rately detect shockwave. Based on the experimental re-
sults, the system meets the design requirements. How-
ever, there exists some challenges. The biggest challeng e
right now is how to deal with the large volume of data
captured by high speed camera as well as the high com-
putational comp lex image processing algorithms. To load
the whole sequence in computer, 8 GB main memory is
required. To accomplish real time processing, high-per-
formance computer system is desired. The future works
include testing this software system on the HPC system
make the system more user friendly.
6. Acknowledgements
This work was partially supported by the NSF SEED
award.
REFERENCES
[1] L. G. Roberts, “Mac hin e Perce pt i on ofThree-Dimensiona
l Solids,” Optical and Electro-Optical Information Proc-
essing, J. T. Tippett, et al., Eds., May 1965.
http://www.packet.cc/files/mach-per-3D-solids.html#*
[2] J. M. S. Prewitt, “Object enhancement and extraction,”
Picture Processing and Psychopictorics, B. Lipkin and A.
Rosenfeld, Eds., New York: Academic Press, 1970, pp.
75-149.
[3] I. E. Sobel, “Camera Models and Machine Perception,”
Stanford Doctoral Dissertation, 1970.
[4] J. Canny, “A Computational Approach to Edge Detec-
tion,” IEEE Transactions on Pattern Analysis and Ma-
chine Intelligence, Vol. PAMI-8, No. 6, 1986, pp.
679-698. doi:10.1109/TPAMI.1986.4767851
[5] D. C. Marr and E. Hildreth, “Theory of Edge Detection,”
in Proceedings of the Royal Society of London, Vol. 207,
No. 1167, Feb. 1980, pp. 187-217.
doi:10.1098/rspb.1980.0020