Detection Hyperbola and Distinguish

4.2 Experimental Results

4.2.2 Detection Hyperbola and Distinguish

(a) (b)

Fig. 4- 5 This morphological structures, their sizes are:

9 " 20, 15 "18

4.2.2 Detection Hyperbola and Distinguish

After using the morphological hit-or-miss transform, we’ll get the locations marked with the red points. There are three steps we proposed, first, setting the hit percentage (

h%) and the miss percentage (

m%). It can help to detect the similar hyperbola on the higher allowed error rate. We marked them the red points. In Fig. 4- 5, we have defined the subset of white elements is the part of hit; the subset of red elements is the part of miss; finally, the subset of the block elements don’t care. Images on the top of the Fig. 4- 6 show that Morphological hit-or-miss transform finds the possible locations of hyperbolas. In step2, we filter the wrong locations such as the double reflection and noises. In Fig. 4- 6(a), (1) though (4), we found four locations, due to the double refection wave is under the hyperbola, we remove the (4) location. In Fig. 4- 6(b), (3) location is same as the above situation, we still remove it.

According to the hyperbolas size is similar in an image, we compare the rectangle proportion of the (1) and (2) binary images and remove (1). In Fig. 4- 6(c), (3),(4),(6) are also the double refection waves, we still remove them. Finally, the same as Fig. 4- 6(d), we also remove (3).

According to the

(x, y) coordinate, we achieve to detection the correct hyperbola locations.

The morphological hit and miss percentages (h%/m%) are:

90 /90%, 90 /90%, 95 /90%, 95 /90% , respectively. These percentages are high, it prove that

(a) (b)

(c) (d)

Fig. 4- 6 Morphological hit-or-miss transform find the possible locations of hyperbolas and detect the correct hyperbolas using the condition we proposed. We mark the locations in programming by using the red points.

(1)

(2)

(3)

(4)

(1) (2)

(3)

(1) (2)

(3) (4)

(5)

(6) (1)

(2)

(3) (3)

(1)

After getting the locations, we manually get other coordinates to be the parabola inputs.

In chapter3, we discussed the parabola formula: y =m(x! p)² +q, where the m is the unknown parameter, the formula is: ₂

)

points. In Fig. 4- 7, (1)-(3) are the coordinates selected by us manually, (1) and (2) are the

! parabola line1 and line2. The area is the parabola model that between the two parabola lines.

Lines in Fig. 4- 7(4) are symmetry to these in (3).

Fig. 4- 7 The parabola model

Image on the top of Fig. 4- 8 shows the parabola model, we separate the hyperbola from background. Our emphasis is to select all the pixels of the hyperbolas, respectively. Focusing on the histograms of each hyperbola, we can detect the new thresholding value for them. Fig.

4- 9 show the histograms of hyperbolas in image1 through image4. When we re-measure the new threshold values for each histogram, the formula is:

max(gray " level) " min(gray " level)

( )

/2 + min(gray " level)

that is the middle value of each local histogram, respectively.

The new threshold value for each hyperbola of images: image1 is 129/129/112; image2 is 125;

image3 is 162/127/112; image4 is 138/145. Fig. 4- 8 shows the results of enhancing the local

and clear edge. In Fig. 4- 8(d), due to the white model is too close to the background pixels, we use the red color to replace the white color. We compare our approach with other methods, only the result of IRON pipes is close to other methods even not better, the PVC and PE pipes have the perfect effect. According to the new threshold value, we believe that processing the local areas for GPR images will obtain better result than global images. Our propose method is significance for weak image with low contrast or high contrast.

(a) (b)

(c) (d)

Fig. 4- 8 The results of using the parabola model.

(1) (2)

(3)

(a) (b)

(1) (2)

(c)

(d)

Fig. 4- 9 Image1 through Image4’s each histogram of hyperbolas.

We record the experiment data and initial setting in Table 4- 3 for reference.

Table 4- 3 The record of the setting and the data GPR

Images

Size Hyperbola number

Threshol d: [0,255]

Hit-or-miss Structure

Rate:

Local Threshold

Image 1 100*216 3 158 2 90/90 129,129,112

Image 2 172*112 1 140 2 90/90 125

Image 3 109*393 3 130 1 95/90 162,127,112

Image 4 48*129 2 156 1 95/90 138,145

In the following we’ll discuss our proposed method and the traditional methods. Due to the results of the Sobel and Prewitt methods is similar, we only shows the results of Sobel.

In Fig. 4- 10 through Fig. 4- 13 show the results of image1 through image4 using the methods is (a) the original image (b) histogram equalization (c) the Laplacian (d) the Sobel (e) the morphological contrast enhancement (f) our propose method, respectively. We discuss following conclusion and record the result of experiments in Table 4- 4. We note the best effect using a block star. In the traditional methods, image1, amage2, image4 has the better effect in Morphological contrast enhancement than others and image3 is in Histogram Threshold. However our proposed method is still have the best effect than above traditional methods. However, in Fig. 4- 12(f), our propose method has non-complete hyperbola in the IRON pipe, but the morphological contrast enhancement product the complete and clear hyperbola of IRON pipes. In Fig. 4- 13(f), although our propose method have the better effect than others and we can accept the result, the parabola model is not match hyperbola perfectly.

We believe it can be improved in the future. According to above conclusion, our proposed methods have the pretty good results.

Table 4- 4 The results of experiments

Histogram

Equalization Laplacian Sobel

Morphological Gradient Enhancement

Our propose method

Image1

*

^Better

Image2

*

^Better

Image3

*

^Better

Image4

*

^Better

(a) (b)

(e) (f)

Fig. 4- 10 The Image1 of (a) The original image (b) Histogram equalization

(a) (b) (c)

(d) (e) (f)

Fig. 4- 11 The Image2 of (a) The original image (b) Histogram equalization

(a) (b)

(e) (f)

Fig. 4- 12 The Image3 of (a) The original image (b) Histogram equalization

(a) (b)

(e) (f)

Fig. 4- 13 The Image4 of (a) The original image (b) Histogram equalization

CHAPTER 5 Conclusions and Future Work

5.1 Conclusions

In this thesis, we propose a parabola model for local image enhancement. We also propose a morphological hi-or-miss transform with match percentage. We focus on how to detect hyperbolas and how to forecast hyperbolas. In this way, we’ll get the local areas of hyperbolas and enhance the GRP images easier.

Using simple structuring elements we can detect typical hyperbolas fast. Through comparing the results of our experiments with other methods, we concluded that the tradition methods processing global GPR images only get better results on low contrast images, and the limit effect on high contrast images of all the weak images. The global image processing usually cause noise enhancement and some hyperbola still weak after enhancing. Thus, we process hyperbolas with local areas and obtain better effect than methods with global areas.

Our proposed methods can process low and high contrast of weak images and obtain better and clearer effect than tradition methods. However, we still take note of the IRON pipes.

When the IRON pipes is fairly clear, sometime tradition methods will have better results than ours, even the IRON pipes do not need process. Finally, although our proposed methods enhance the resolution of hyperbola effectively, and separate it from background, we still have other questions. When there are more noises or objects in the images, we’ll face with the increasing error rate of detecting hyperbola locations, that is because noise or objects

sometimes have the similar features.

From the results shown in Chapter 4, we can conclude that our method has some advantages as described below.

1. Morphological operators involve simple logical operations and can be implemented in parallel, making real-time applications possible.

2. Morphological structuring elements provide the high freedom.

3. Morphological hit-or-miss transform with the hit and miss percentage can detect the features of hyperbola effectively.

4. Our proposed methods are fast and simple on detecting and enhancing and perform good precisions.

5. Parabola model provides a forecast shape for pipes.

According to above viewpoints, the local GPR image processing is feasible and

expectation. There are more important work for us to do that, and beside the sturdy methods for detecting hyperbola (ex the more fitter structuring elements), the parabola model can be created automatically and forecasted sturdily. Such as more researches, how to filter noises effect and hold the significance information is the feature direction of the GPR pipes images for discussing deeply.

On the application, the GPR system is imported from foreign, the software is also designed from foreign. If we can design the software force on GPR data in Taiwan. We believe it is helpful and have higher value for research for exports and researcher. The advance resolutions and the sturdy distinguishing effect of GPR images reduce the time and the cost that is used to apply in our life. No matter what it is in the research or the probable work, it will have the positive value.

5.2 Future Work

We introduce the future work in the following topics. According to the research of the GPR images, we still have more discussions in research following the data complexity

increased. Focus on our proposed methods, we’ll discuss in three directions: first, other noises and hyperbolas and hyperbola detection; second, automatically; third, the 3-D model and the user interface.

Due to the non-even underground in Taiwan, there are more noises in the probed data.

There are no deeply discussed in the noises of pipes images. We hope to discuss and research fitten denoisy methods coordinated with the pipes images database. We only prove the outlook here. On the other hand, in hyperbolas, beside the complete hyperbolas, there still have other types of hyperbolas, one of them is the type of cross hyperbolas that are more important sin our application. In Fig. 5- 1, we show the example of this case, the cross

hyperbolas is not the complete hyperbola. Our proposed morphological hit-or-miss transform method can detection this case, but we’ll alter the parabola model. We show the simple model in Fig. 5- 2, we only add one coordinate

(x₂, y₂) to plot the non-complete parabola line.

Fig. 5- 1 The different situation of hyperbolas

Peak

(x₁, y₁)

(x₂, y₂)

Line1

Fig. 5- 2 The altered parabola model

Type II: Automatically

In the thesis, we manually create the threshold value and the parabola model coordinates.

However, when we have great amount of data, we’ll automatically process them for bring big benefit. In the following, we’ll describe some concepts. Our experiment shows if there are different strength hyperbolas in an image, it is hard using a single threshold value to hold the features of hyperbolas. When the complexity increases, we can use the multilevel threholding to create images class in detail. On the other hand in parabola model, due to fact that a high brightness hyperbola and a low brightness hyperbola, their thickness is also closer, as shown in Fig. 5- 3. When we obtain the locations of hyperbola (just like(1), something it shift to other location), we can regard the red curve line in the middle as the edge between the hyperbola with high brightness and the one with low brightness. When we move along the curve line, we’ll obtain the coordinate (1) in the max slope of the red curve line (Fig. 5- 3(b)).

According to the two different brightness hyperbola’s thickness is closer, and the areas of from (1) to (2) and from (1) to (3) are low frequency, we can set the (1) is the center and measure the coordinates of (2) and (3). In the edge disappear location, we can define the coordinate of (4) and (5). The great amount of data processed automatically will reduce the cost for us.

(a) (b)

Fig. 5- 3The illustration of the parabola model creating automatically (a) The real image, (b) The schema of (a)

Type III: The 3-D Model and The User Interface

We show the GRP images can be shown with the pseudo-color or 3-D image technique beside the 8-bit gray value images. Different with the original images, the two methods will burden more cost. However, we have the benefit in more diversification showing. We believe that only the higher complexity GPR images can be considered using the above two methods.

We will show the examples about pseudo-color and 3-D images in our data in Fig. 5- 4 and Fig. 5- 5. Thus, we believe that design a useful and multi-function software is necessary for exporter and researcher. The other important development is the 2-D images translated to the 3-D model. In Fig. 5- 6, when we probe the pipes and draw three detection lines, we’ll obtain three section drawings. We plot the red curve lines as the hyperbola for example. An

important technique is to use many 2-D GPR images to translate to the 3-D object model. The research about this is widely discussed. Through our proposed method to enhance pipes images, we can predict the locations of pipes images and build the 3-D model more easily. To detect the location of pipes images and build more complete database is the future focal point to be discussed.

(1) (2)

(3)

(4)

(5)

Maximal curvalture

Fig. 5- 4 The pseudo-color of the Image1

Fig. 5- 5 The example of 3-D image of Image2

Fig. 5- 6 The illustration of 3-D model of the pips images.

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