AE 497 Final Report

By Catherine McCarthy

Supervised by Mike Bragg, Brian Woodard, Jeff Diebold

Aerospace Engineering, University of Illinois at Urbana-Champaign

Introduction:

One way that the pressure on a wing can be measured is through pressure taps. These are small

holes that are on the wing and measure the static pressure on the wing surface. Usually this static

pressure is then referenced to the static pressure in the freestream so the pressure coefficient can

be calculated. Another, more advanced, method in which the pressure on the wing can be

measured is through the use of pressure sensitive paint (PSP). This paint emits light at different

intensities based on the local pressure, and a continuous pressure distribution is obtained by

imagining the paint via an excitation light. Pressure sensitive paint requires a wind-off and wind-

on picture. Pervious experiments on swept wings at UIUC found that there was a significant

amount of noise on the tip of the wing model due to model deflection caused by aerodynamic

loads, resulting in misalignment between the wind-on and wind-off images. A solution to this is

to use image registration, which identifies physical markers on the surface of the model and

aligns the two images based on those marker points using computer software. Pressure taps on

the wing are commonly used as markers. Therefore, these pressure taps’ use are two-fold. They

allow collection of static pressure measurements, and for the pressure sensitive paint to be

aligned.

Last semester, I performed experiments utilizing a code that had been created by a previous

student. I created four different types of maker patterns, and attached them to plates that were

then attached to an apparatus. I would then take pictures of the plates at different angles of

deformation. The plate was rigidly deflected in increments of 3 degrees, ranging from 3 to 30

degrees, with no deformation representing the wind-off image. I would then receive alignment

measurements in both the x and y directions, and have the root mean square error calculated for

each deformation.

After performing the experiments, it was discovered that there were some inconsistencies in the

data. In the majority of the data, there were some noticeable rises and falls that did not follow

what was predicted to take place. In all the data, there was no clear pattern amongst the different

marker styles. The only tentative conclusion that could be made was that the small, close

together markers had a relatively regular data set, giving the appearance that that was the optimal

marker setup.

The majority of these problems with the data can be attributed to some problems that arose in the

code that was then being utilized. A problem that arose from the code was that it occasionally

had a challenging time determining where the ‘beginning’ of the plate was. Oftentimes the

bottom row of the wind-off image would be aligned with the third or fourth row of the wind-on

image. The corresponding markers would be manually moved to make sure that the two images

were aligned properly. However, a problem with this method is it leads to the possibility of

human error, as the alignment points may no longer be located at the exact center of the dot. This

happened most often with large degrees of deflection, and may account for the spike specifically

in the large, far apart data at the 24 degree mark.

Another problem that could lead to this data is the method in which the code was finding the

center of the markers. The Matlab code was initially creating a gray threshold, then converting

the picture to binary in order to locate the center of mass for each dot. However, depending on

what that grayscale is, the program may not have been able to have a perfect circle with the

binary image, leading to an incorrect center point. This would also lead to misalignment, and

could account for some of the spikes that were seen in the data.

Finally, another potential reason for the poor data could have been due to the cropping technique

utilized with the close-together plates. The program ran too slow, and was causing problems to

occur with the image processing. To resolve this, the image was cropped down length-wise,

creating a long, skinny plate equivalent, which could have also led to inaccurate data.

It was because of this that this semester was spent attempting to create a new code with updated

measurement techniques. Once this code would be completed, then the previous plate experiment

could be reattempted.

Experimental Methods/Results:

As previously stated, the largest goal associated with the code that was being used previously

was the inability of the program to find the center of each marker. I began with performing some

research on Otsu’s Method, which was the current threshold method being utilized. In order to

implement Otsu’s Method, an image must first be transformed into black and white. Then, it

utilizes a

“Relatively straightforward analysis which finds that threshold which minimizes the within-class

variance of the thresholded black and white pixels. In other words, this approach selects the

threshold which results in the tightest clustering of the two groups represented by the foreground

and background pixels” (Solomon 266).

However, some of the concerns that arose with Otsu’s method was the inability to define what

exactly that threshold was. Consequently, it was difficult to determine if the markers being found

using this method were actually remaining in the shape we wanted. In order to test this theory,

and to see how far off the actual image was, I started by implementing the code to stop after

Otsu’s method and return the black and white image after thresholding. In order to test this code,

I took a small cropped version of the entire plate (Figure 1).

Figure 1. Cropped Image of Small, Close Together Marker Plate

I then ran it through the Otsu’s Method (Figure 2).

Figure 2. Small, Close Together Markers after Otsu’s Method

As we can see, the markers are not in perfect circles like we would like. This could lead to an

inaccurate center, which could then lead to poor data like that which was seen previously.

My next thought was to attempt to use a smoothing technique in order to help with the

inconsistencies being produced with Otsu’s Method. I first used the fspecial command so apply a

rectangular averaging filter, and then applied this filter using imfilter. Using this filter, anything

outside the bounds of the array specified in the average filter would be assumed equal to the

nearest array border value. The results from this are shown in Figure 3. The smoothing did not

appear to be of any help in creating a more accurate representation of the markers.

Figure 3. Image after Otsu’s Method Followed by Smoothing Filter

My next method that I attempted was to utilize a minimum perimeter polygon technique. The

basic idea for this technique, as outlined by Gonzalez, is that a digital boundary can be

approximated by utilizing a polygon. The goal of this polygon approximation is “to capture the

essence of a shape in a given boundary using the fewest possible number of vertices”. I quickly

learned that this was certainly a time-consuming manner, and was never able to successfully find

the outlines of the markers like I had hoped. An image of the unsuccessful image processing is

shown in Figure 4.

Figure 4. Image after Utilizing Polygonal Approximations

Finally, I attempted to utilize a template matching technique:

“Given an image f(x,y), the correlation problem is to find all places in the image that match a

given subimage w(x,y) (called a mask or template). Usually, w(x,y) is much smaller than f(x,y).

The method of choice for matching by correlation is to use the correlation coefficient” (Gonzalez

681-2).

The image used as a template is shown in Figure 5, and the corresponding correlation can be

seen in Figure 6.

Figure 5. Template Image Figure 6. Image after Correlation

Due to the poor photo editing software I used on my computer, I was only able to get the

template image small enough to cover two markers, instead of the ideal one. However, for testing

purposes, this was not a large factor. In the correlation image, there was a gradual brightening as

correlation increased. I believe that the reason for the strange fading in and out on the edges of

the image is due to the fact that a template of two markers was used when running the program.

After this correlation method was implemented, it was still necessary to find the center of each

marker. I did this by using the matlab command findpeaks, which has the ability to find local

maxima. Using this command, the maximum pixel values are found in each region of the image,

and then marked with a blue ‘x’. Figure 7 shows the image after it has been altered with

findpeaks.

Figure 7. Image after Finding Peaks in Markers

Once again, I believe that the reason for the off-center “peaks” is due to the correlation image

created using a template with two markers on it. While these peaks were the closest thing

achieved to finding a promising center of the markers, some of the centers found were

unfortunately still not perfectly center.

Conclusions:

While a variety of image processing methods were utilized during this semester, the most

promising seems to be using template matching in order to create a correlation image that can

then be used to find the center of the markers. This would prove helpful to the group as well

since the markers may not necessarily always be circular. By using the template matching

method, any type of marker can be utilized.

The next step would be to find this “peak” at a subpixel resolution. A list of the correlation at

each individual point, or perhaps within a certain region where the markers are known to be, can

be created, and then the program can interpolate over these values. By interpolating over the

entire surface, a more accurate representation of the center peak can hopefully be created. Once

this is done, then the root mean square error can be recalculated in the manner it was calculated

previously. With that, we can reevaluate the data with the original plates that were made, and

update the previous conclusions.

References

Gonzalez, R. C., Woods, R. E., & Eddins, S. L. (2009). Digital image processing using Matlab

(2nd ed.). Gatesmark.

Solomon, C., & Breckon, T. (2011). Fundamentals of digital image processing. John Wiley &

Sons.