Activity 19. Restoration of Blurred Image

A grayscale image were selected and processed using Scilab. Noise(Gaussian) was then introduced to the image. The parameter a, b and T was varied to see the their effects to the degraded image. The degraded images are shown in Figure 1.

Figure1. Original and Degraded images(a=b=0.001, a=b=0.1 and a=b=0.01)

From the images in figure 1, it can be seen that the amount of blurring increases as the value of a and b increases.

The degraded image were then subjected to Weiner Filtering. The resulting images are shown below.

For a=b=0.1 and T=1:

Figure2. Filtered images(K=0.0001 and K=0.001)

For a=b=0.01 and K=0.0001:

Figure3. Filtered images(T=10 and T=1000)

It can be observed from Figures 2 and 3 that as the value of parameter T increases the enhanced image becomes sharper. The opposite behaviour is observed for the parameter K. As K increases, the image becomes more blurred and degraded.

In summary, a grayscale image was degraded using gaussian noise. The degraded image was then subjected to Weiner filtering. The parameters of the noise and filter were varied to observe its effect to the enhanced image. It was observed that as the value of a and b decreases, degradation of the image becomes lesser. It was also observed that the enhanced image becomes clearer and sharper when the parameter T is increased and the parameter K is decreased. It can therefore be recommended that a low value of K and a high value of T be used in enhancing a degraded image.

I will give myself 10/10 in this activity.

*** My thanks to Rommel for helping me in this activity.

Activity 18. Noise Model and Basic Image Restoration

An image with 3 different levels of grayscale values was processed using Scilab. Different kinds of noise were introduced to the image. The PDF of the original image and the image with noise was generated. The original image and the image with noise are shown in Figure 1. It can be seen that the amount of distortion in the image varies with the kind of noise introduced to the original image.

Figure1. Original image and images with different noise(from the left: Original, Exponential, Gamma, Gaussian, Salt and Pepper, Uniform Function and Rayleigh)

The PDF of the original image and the images with noise is shown in Figure 2. The PDF exhibits 3 peaks due to the different gray levels of the selected image.

Figure2. PDF of the original image and images with Noise((from the left: Original, Gaussian, Gamma, Exponential, Salt and Pepper and Uniform Function)

The image with noise was then enhanced using different filters. The image with gaussian noise were then subjected to different filters. The resulting images are shown in Figure 3.

Figure3. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with exponential noise:

Figure4. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with gamma noise:

Figure5. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with salt and pepper noise:

Figure6. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with uniform noise:

Figure7. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with Rayleigh noise:

Figure8. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

A grayscale image was then selected. The selected image were then subjected with different kinds of noise. The resulting images are shown in figure 9.

Figure9. Original image and images with different noise(from the left: Original, Exponential, Gamma, Gaussian, Salt and Pepper, Uniform Function and Rayleigh)

The generated images with noises were then subjected to different filters. For the image with gaussian noise:

Figure10. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with Gamma noise:

Figure11. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with Rayleigh noise:

Figure12. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with Salt and Pepper noise:

Figure13. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with Exponential noise:

Figure14. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

For the image with Uniform noise:

Figure15. Enhanced images using different filters(Arithmetic, Contraharmonic, Geometric and Harmonic Mean Filter)

In summary, different kinds of noise were introduced to a selected image. The images with noise were generated using some Scilab functions. Built-in filters in Scilab were then used to enhanced the noise containing image. From the generated filtered images, it was observed that there is no universal filter that can produce the best image for all kinds of noises. A certain filter is suited for a certain noise.

I will grade myself 10/10 for completing this activity.

***Earl helped a lot in formulating the Scilab code used in this activity.

Activity 17. Photometric Stereo

In this activity, the an object was recreated using photometric stereo in Scilab.

The images of an object illuminated by a light source located from four different locations were used in this activity. The images and the locations of the light source are shown below.

Figure1. Images rendered in Matlab


Figure2. Locations of Light Sources

The images from a Matlab file ('photos.mat') was loaded in Scilab using the Scilab command loadmatfile. The surface normal(n) of the images were then computed in Scilab using the equations given below.

where:

After the surface normals were computed, the elevation z was then computed using the following equations:

The integral function in the given equations was evaluated using the cumsum function in Scilab. The computed elevation was then used to generate the 3D plot of the object. The generated plot is shown below.

Figure3. 3D plot of the object

I will give myself 10/10 for completing this activity.

Activity 16. Neural Networks

In this activity, objects were classified using neural networks. Only two types and two features were used for this activity. The two types of bottle caps(Coke and Sprite) were used as samples to test the efficiency of neural networks as classifiers. The coke bottle caps were tagged with the value of 1 while the sprite bottle caps were given the value of 0. The training set used to train the neural network is given below. The first column is the area of the object while the second column is the color level of the object.

x=[0.929186603, 0.58557;
0.653588517, 0.147957;
0.908133971, 0.615335;
0.579904306, 0.145402;
0.655502392, 0.164236;
0.956937799, 0.630004;
0.902392344, 0.638101;
0.679425837, 0.14559;
0.650717703, 0.15673;
0.677511962, 0.140274;
0.968421053, 0.618755;
0.914832536, 0.635996;
0.742583732, 0.147524;
0.96937799, 0.62855;
0.923444976, 0.642857;
0.717703349, 0.135958;
0.800956938, 0.157814;
1, 0.613532;
0.983732057, 0.668547;
0.7215311, 0.137754;];

The first column was normalized in order for the maximum area calculated will be equal to 1. Using the provided source code(from Cole Fabros' work), the objects were classified using neural networks in Scilab. The source code is provided below.

rand('seed',0);
N=[2,2,1];

x=[0.929186603, 0.58557;0.653588517,0.147957;0.908133971, 0.615335;0.579904306, 0.145402;0.655502392, 0.164236;0.956937799, 0.630004;0.902392344, 0.638101;0.679425837, 0.14559;0.650717703, 0.15673;0.677511962, 0.140274;0.968421053, 0.618755;0.914832536, 0.635996;0.742583732, 0.147524;0.96937799, 0.62855;0.923444976, 0.642857;0.717703349, 0.135958;0.800956938, 0.157814;1, 0.613532;0.983732057, 0.668547;0.7215311, 0.137754;];

x1=x';
t=[0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 1 1 0 0 1 ];
l=[0.1,0];
W=ann_FF_init(N);

T=1000;

W=ann_FF_Std_online(x1,t,N,W,l,T);

A=ann_FF_run(x1,N,W);

The output values of the program is shown below.

A=[0.0698714 0.9559284 0.0604605 0.9617354 0.9494504 0.0532122 0.0541484

0.9547831 0.952926 0.9568003 0.0555345 0.0539992 0.9485505 0.0529052

0.0518202 0.9552809 0.9369444 0.0551047 0.0441003 0.9543265]

The values in A were then rounded off. The resulting values are the same with the target values t given in the source code above. This means that the objects were successfully classified using neural networks. This result is for N=[2,2,1].

round(A)=[ 0. 1. 0. 1. 1. 0. 0. 1. 1. 1. 0. 0. 1. 0. 0. 1. 1. 0. 0. 1.]

For N=[2,5,1],

A=[ 0.0550852 0.9665592 0.0434460 0.9728303 0.9595599 0.0347047 0.0358142

0.9653303 0.9633175 0.9674942 0.0375346 0.0356348 0.9586883 0.0343439

0.0330257 0.9658597 0.9464930 0.0370670 0.0238807 0.9648412]

round(A)=[ 0. 1. 0. 1. 1. 0. 0. 1. 1. 1. 0. 0. 1. 0. 0. 1. 1. 0. 0. 1.]


If the learning rate was changed to a higher value the output A changes. The result is given below.

A=[ 0.0156586 0.9922242 0.0111422 0.9941406 0.9898376 0.0081610 0.0085014

0.9918369 0.9911437 0.9925391 0.0091049 0.0084479 0.9895962 0.0080486

0.0076092 0.9920324 0.9849933 0.0089606 0.0049144 0.9916999 ]

This result was calculated when the learning rate is 0.9. Comparing the values of A when the learning rate is 0.1 and when the learning rate is 0.9, it can be observed that the values of A are nearer to the target values when the learning rate is 0.9. These means that a higher learning rate produces a more accurate result.

I will give myself 10/10 for getting accurate results.

Activity 15. Probabilistic Classification

The goal of this activity is to classify 20 objects according to their classes.

The objects used in this activity are 10 Coke and 10 Sprite bottle caps. The image of the objects were taken and converted into a binary image using Scilab. The original image and the binary image are shown in Figure 1.

Figure1. Original and Binary image of the previous image

The objects were then classified using the same method employed on activity 14. The plot showing the classification of the samples used is shown in Figure 2.

Figure2. Classification of Objects

As seen in Figure 2, the classification of the samples is well separated. Linear Discriminant Analysis(LDA) was then used to further classify the samples. The plot of the classification using LDA is shown in Figure 3. A line separating the 2 groups was drawn to show the boundary between the two groups of samples. The separation between the two groups is small but is sufficient to show the classification of each sample.

Figure3. LDA

For completing this activity successfully, I will give myself 10/10.

***Earl tips helped a lot.