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Activity 19: Restoration of blurred image

2009-10-11T08:47:00.000-07:00

I applied motion blur on the image using the algorithm given in the procedure. I then implemented the restoration algorithm. Here are the results:

Original

Noised / Restored

The restoration was able to remove the "trace" effect of the blur but some additive artifacts still remain. The method is not in vain however, since it still was effective enough to make the text readable again.

I give myself a 10/10 because I was able to implement the algorithms successfully.

Activity 18: Noise model and basic image restoration

2009-10-11T08:02:00.000-07:00

In this activity we explore the different type of image noise and try some techniques for cleaning them. I applied 5 types of noise: impulse, uniform, exponential, gamma and gaussian. I then implemented 4 methods of noise removal: harmonic, geometric, contraharmonic and arithmetic. Here are the results:

Original image

From top to bottom:
salt and pepper / uniform / exponential / gamma / gaussian
From left to right:
arithmetic / contraharmonic / geometric / harmonic / noise only

The images get darker/brighter because I normalized them after adding the noise. For most types of noise, the arithmetic restoration yields the best results. Also, the other methods which rely on multiplication fail at places where the noise peak.

I give myself 8/10 because i wasn't able to implement the Rayleigh noise.

Activity 17: Photometric stereo

2009-10-11T07:09:00.000-07:00

In this activity we reconstructed a 3d object using image data taken from multiple angles. The source images were already given to us and so all we had to do was to write the code to implement the equations. I came up with the following shape:

I give myself a 10/10 because I successfully constructed the 3d object.

Activity 15: Probabilistic Classification

2009-10-11T06:54:00.000-07:00

This activity is an extension of activity 14. It uses LDA instead of just taking the euclidian distance in feature space. I used the same photos and features as in activity 14 but i only made use of two classes: leaf 1 and leaf 2. I simply followed the outlined LDA procedure in the link attached with the protocol and my program was able to distinguish between the two leaves for all of 4 test objects.

Classes

f1 =
- 1.3203592
  12.37927
  36.708249
  27.447476

f2 =
- 2.9090572
  10.544618
  38.737733
  29.893865

Results: first two values correspond to leaf 1, last two correspond to leaf 2

I give myself a 10/10 since I was able to implement the outlined procedure and the features I chose proved to be valid for the given set of objects.

Activity 14: Pattern Recognition

2009-10-11T06:11:00.000-07:00

In this activity we attempted automated classification. We first extracted the mean features of each class. We then classified test objects by finding the class nearest the object in feature space. I used 4 classes:

Classes
leaf 1/leaf 2/25 centavos/flower

I used 4 features: mean red, mean green, mean blue and shape. To extract a single value for shape, I used the follow function to trace the perimeter of the object the took the ratio of its square to the area. This proved to be a valid measurement as it allowed the distinction between the two leaf classes. I used 5 objects per class to get the mean values and 2 objects per class for testing. My program was able to classify each test object (two tests per class) correctly.

I give myself a 10/10 since I was able to create a program that could classify object based on both color and shape.

Activity 10: Preprocessing text

2009-08-06T13:30:00.000-07:00

In this activity we set out to clean up a scanned document to make it ready for handwriting recognition. Our main goals were to remove unecessary details, i.e. table lines, and to binarize the result. I first rotated the image such that the horizontal lines were parallel to the x axis. I did this by making sure that the maxima of the FFT of the image formed a perfectly vertical line. I then removed the horizontal lines via a vertical mask over the FFT. I then binarized the image using the im2bw function and a threshold of .38.

As an additional objective, we also sought to detect all occurences of the word "description". I did this using the correlation technique we used in activity 5.

RESULTS

Original image / horizontal lines removed / b&w

Basis for correlation

Result of correlation

The removal of the horizontal lines was quite successful. Even though the regularity of the removal is apparent (sinusoidal erasure), it works when we convert the image to B&W. As for the correlation, it works quite well as long as you take only the maxima into account.

For this activity I give myself an 8/10 since I wasn't able to take advantage of morphological operations in binarizing the image.

Activity 12: Color image segmentation

2009-08-06T10:54:00.000-07:00

For this activity we try to distinguish ROI's based on their color hues. By changing our color coordinates such that we separate value into an independent variable, we are left with a 2D color map that disregards brightness. With value aside we may now distinguish objects based on color alone.

We achieved the actual differentiation via 2 ways: parametric and non-parametric. In the parametric method, we assume that the color distribution of our object is a Gaussian curve. It is parametric in that we may adjust the standard deviation of the spread to be more or less tolerant. In the non-parametric method, we use the objects actual color distribution and we use the resulting curve for back projection.

RESULTS

Original Image

http://www.missouriplants.com/Yellowopp/Helianthus_divaricatus_flowers.jpg

Parametric approach

Non-parametric approach

It seems that the assumption of a Gaussian distribution of colors results in the manifestation of the white noise on the ROI. This is probably a reflection of the normal distribution of noise on the original image. When we remove this assumption, we get a much more solid and accurate ROI since we use prior knowledge of the objects color distribution. I also observed in my peer's (Sison) work that this method is much more effective in differentiating adjacent colors (e.g. orange and red).

I give myself a 10/10 because I was able to execute the procedure completely and efficiently.

Activity 8: Morphological Operations

2009-07-20T19:38:00.000-07:00

In this activity we were tasked to explore the properties of dilation and erosion by applying the said operations on a square, a triangle, a circle, a hollow square and a cross. We are to perform the operations using each of the following: 1) 4x4 square, 2) 2x4 rectangle, 3) 4x2 rectangle, 4) a plus sign of width 1 and length 5. My results are listed below. They are arranged in order of the operators above.

DILATION

EROSION

My predictions for the dilations were spot on except for the triangle dilated with a plus sign. I forgot to note that the bottom side should have manifested the plus sign as square 'clips'. As for the erosions, I was correct for all except the hollow squares. I thought the widths of the operators would have been enough to completely erode the corresponding edges. it seems however that except for the last case (the plus sign operator), thin lines still remained.

I give myself a grade of 9/10 because I was able to execute the procedure completely. My predictions were a bit off hence the -1.

Activity 6: Properties of the 2D Fourier Transform

2009-07-08T18:48:00.001-07:00

We seek to understand the properties of the 2D Fourier Transform by applying it to several test cases. Below are the results I've gathered:

ORIGINAL / FFT

square / square annulus / donut / slits / dots

several cases of the sin function:
3 vertical sin waves of decreasing frequencies / biased / rotated / sum of sines in x and y / previous case + rotated sines

Both the FT's of the square and the square annulus look like stars/crosses. They only differ in that the latter looks striped such that it jumps over some values. The symmetry of the FTs reflect the symmetry of the squares. The FT of a donut has a strong peak at the center and is surrounded by a symmetric pattern covering some circular area around it. This reflects the circular symmetry of the object. The FT of the slits looks like a vertical interference pattern at the center. It is as if we have recorded the interference pattern after ltting light pass through the slits. This is expected as the diffraction pattern we get from an aperature is the same its FT.

The FT of the two dots look like the superposistion of two airy disks symmetrically off center. We already found in the previous experiment that the FT of a circle is an airy disk. It is expected then that the FT of two circles is simply a superposition of two airy disks.

As the frequency of the sine wave decreases, the point corresponding to the frequency of the sine wave come closer to the center. As expected, the FT is symmetric along the X axis. Adding a bias simply adds a point at the center of the FT. Rotating the sine wave rotates the FT by the same angle. The last FT turned out as expected since it is simply a superposition of the previous FT's. It outlines a circle since we sum up rotations of the same frequencies. In addition, we still retain the four points from the previous FT.

I give myself a grade of 9/10 because I was able to execute the procedure but I feel I could do better in interpreting the results.

Activity 5: Fourier Transform and Correlation

2009-07-06T19:39:00.000-07:00

In this activity, we explored the uses of FFT and correlation in image processing. We started by taking the FFT of a circle and a character just to see how the 2D FFT function works in Scilab. I got the following results:

Original/FFT/double FFT
Top: Circle, Bottom: A

These results agree with the analytical expectation: we get an Airy disk for the circle and we inverse the image when the FFT is performed twice.

We then used FFT to convolve an image of an aperature and an image to simulate the effect of an imaging device with limited aperature. I got the following result:

Original image/ Convolution of "VIP" and circular aperature of r=40/30/20/10/5

We get an image of the original object but it is now inverted and less resolved. Decreasing the aperature size causes the image to blur and gain artifacts which somehow resemble the shape of the aperature.

Our next task was to use correlation to find a certain pattern in an image. In this case, we had an image of the line "THE RAIN IN SPAIN STAYS MAINLY IN THE PLAIN" and we had to look for the A's via correlation. Correlating the image and an image of the letter "A", I came up with the following result:

Original image/Correlation of the image and pattern

We find that the peaks of the resulting image correspond to the posistions of the A's in the image thus verifying that the method was correct.

Finally, we attempted to do edge detection by correlating small matrices of either a vertical line, a horizontal line, or a point with a given image. I came up with the following results:

Vertical/horizonal/point edge detection

We can see that the method worked as it highlighted only the parts which correspond to the types of edges being detected.

For this activity I give myself a 10/10 because I was able to complete the tasks completely and efficiently.

Activity 4

2009-07-05T07:33:00.000-07:00

In this activity we were tasked to change the improve the contrast of a grayscale image by tweaking it such that its CDF is converted to some desired curve. To do this we took the CDF of the original image then matched the pixel values with the same value on the original CDF and desired. We then edited the image such that every pixel with a given pixel value on the original image is replaced with its matched pixel value from the desired CDF. Here are my results:

BEFORE:

original image 250x250 grayscale

original PDF

original CDF

AFTER:

resulting image 250x250 grayscale

resulting PDF

resulting CDF

The resulting image had much better contrast. The details of the petals and the background are now much more easily distinguishable. The resulting CDF is quite close to the desired (linear). The few kinks on th curve are probably a result of the limitations of histograms. Since histogram values are discrete it is possible that some values on the original CDF dont have corresponding values on a desired CDF. I give myself a 9/10 for this activity because I was able to execute the procedure properly yet I believe that there is room for improvement in the method such that the resulting CDF may be exact.

Activity 2: Area estimation for images with defined edges

2009-06-24T19:48:00.000-07:00

In this activity we set out to determine the area of an ROI in a binary image by first tracing its contour then using Green's theorem to calculate the area enclosed. To prepare the image for processing, I first had to convert the image to a binary matrix using the im2bw function. I then used the follow function to trace the ROI's contour. I then implemented the discrete form of green's theorem to finally come up with the area.

After preliminary results Ifound that the area we would calculate was always lacking by half of the contours length. I speculated that the follow function traced the inner contour of the ROI, thus decreasing the area enclosed by some value. M. Sison proposed that to correct the calculated area, we simply add half the length of the contour. After testing the method over various shapes, both regular and irregular, we found the the proposed correction was indeed valid.

Sample Results

Shape 1: 200 x 200 Square

Analytical: 40000 pixels
Pixel count: 40000 pixels
Program: Analytical: 40000 pixels

Shape 2: Robot

Analytical: 32071 pixels
Pixel count: 32701 pixels
Program: 32071 pixels

Shape 3: Irregular

Analytical: N/A
Pixel count: 26526 pixels
Program: 26526 pixels

For this experiment, I give myself a score of 10/10 because I was able to implement the method properly and the results attest to the accuracy of the program.

Activity 3: Histogram and Thresholding

2009-06-22T20:15:00.001-07:00

Shape

256x256 robot saved as JPEG

Histogram

The histogram shows that the image's values are concentrated towards the 0 and 255 areas corresponding to black and white respectively. We may say the ROI and background are well separated since each corresponds to one of the narrow peaks of the histogram.

Activity 3: ImageTypes

2009-06-22T18:27:00.000-07:00

Indexed / Graphics Interchange Format (GIF)

SRC: http://www.hobby-hour.com/guitar/fender_telecaster1.gif

GIF's are indexed.

BINARY / BITMAP (BMP)

SRC :http://www.rainbarrel.com/monochrm.bmp

Checking the image properties will reveal that the image has a 1-bit bit depth (0 and 1).

True Color / Joint Photographic Experts Group (JPG)

SRC: http://www.penmachine.com/musicpages/musicimages/fender_strat_hardtail.jpg

Checking the image properties will reveal that the image has a 24-bit bit depth (256 values for each of the 3 colors).

Grayscale / Joint Photographic Experts Group (JPG)

SRC: http://press.roncarter.net/RonCarter2_300grayscale.jpg

Checking the image properties will reveal that the image has an 8-bit bit depth (256 values from white to black).

Activity 1: DIgital Scanning

2009-06-17T19:55:00.000-07:00

For this activity we "digitized" a hand-drawn plot by scanning it and then tabulating the corresponding xy values of the pixels of the points of the plot. To replicate the actual data, we had to figure out the relationship between the actual physical values and the pixel data we've gathered. To do this I measured the pixel distances between grid lines and divided them by their corresponding physical values. I found that the ratio was unconsistent and I ended up with varying ratios per area of the chart. Upon replotting the data, I dealt with this simply by using the different ratios for different points depending on their locations. I came up with the following plot:

The reconstruction was accurate for the first three points, but as the plot progressed, the digitized points (in red) start to deviate from the actual plot. Furthermore, the x=-50 and x=50 grid lines don't seem to match up. While the y deviation simply increses (the digitized points deviate downward) as the plot moves forward, the x deviation increases at the middle of the plot but recovers towards the end. The most probable reason for the error I obtained is that I failed to rotate the image before obtaining the pixel data and so when I was forced to rotate the image later on when overlaying the original, The points matched up only at certain points (probably those that were near the axis of rotation).

For this reason I can only give myself a grade of 7. I was able to follow the procedure for the most part, but a crucial error at the start of my data gathering doomed the final result.