A17-Color Image Segmentation

We gathered a video of freely-falling objects, two pieces of paper with the same dimensions. One of them was crumpled. My goal is to track the distance traversed by the object from its original height as time increases. I then compared this with what should be expected theoretically. Above is the first frame of the video we gathered.

Since it is hard to segment the paper from the hand, and since in the last frames of the video, the crumpled paper had already reached the floor, I only used frames 3 to 12. For each frame, I got two portions and binarized them to track the falling papers. I then got the centroid for each portion. From the original height located in frame 1, and the y-components of the centroids, I obtained the position versus time graph for the two objects. I compared them by the theoretical values d = gt^2 where d stands for distance, g for the acceleration due to gravity and t is time. The white markings in the frames served as scale and their real world interval was 10 cm. In pixels, the interval was 33 pixels.

The final distance for the uncrumpled paper is 0.23 m, for the crumpled paper 0.60 m, and for the theoretical distance 0.78 m. We expect the final distance for the uncrumpled paper to be less than that for the crumpled paper because of drag force. The discrepancy between the measured distances versus time for the crumpled paper and the theoretical must be due to a little drag force on the crumpled paper. But at least they are of the same order of magnitude.

SELF--GRADE: 9/10

Thank you to Lei, Aiyin, Beth, Rica for the video and sliced frames.

Project - Image Deblurring

I'm still on the process of searching references:
[1] http://www.picturesolve.com,
[2] http://ieeexplore.ieee.org/iel3/4760/13241/00600843.pdf
[3] How to Sharpen an Image in Photoshop, http://www.photoshopsupport.com/tutorials/sharpen-an-image/photo-sharpening.html
[4] Sharpen Effect, http://www.websupergoo.com/helpie/source/2-effects/sharpen.htm

Hehe, we changed topic. Sharpening of images taken under a microscope. Due to the limited depth of field of the microscope, and the sample's varying topography, some parts of the image become blurred. The sharpening filter to be used is a high-boost filter given by
H = (1/9)*[-1 -1 -1; -1 w -1; -1 -1 -1]; (1)

where w = 9A-1 with A>1. The effect of the above mask is an ouput image related to the original by this equation
High-boost Output = (A - 1) Original + Highpass [2].

A20 - Neural Networks

This is another way of classifying piattos and pillows chips. First, we train our system. We have an input feature set. The columns are the features (red-and-green contrast, and area normalized to the largest area in the set) and the rows are the individuals.

x =[0.313023 0.7962447;
0.2596636 1.;
0.2721711 0.7661728;
0.3666842 0.842306;
0.8614653 0.8345313;
0.8959559 0.7132170;
0.9718898 0.5795805;
0.9224472 0.5188499]';

The first four rows pertain to piattos chips while the last four refer to pillows chips. We designate piattos as 0 and pillows as 1.Then our target set is
t = [0 0 0 0 1 1 1 1];
We input this into the neural network program and choose a test set whose member classifications we do not know.

testset = [0.3322144 0.8215565;
1.0195367 0.3562358;
0.3121461 0.9116466;
1.043473 0.3339846;
0.4000078 1.;
1.0175605 0.3679583;
0.3930316 1.;
0.9543794 0.2963204 ];

The test result is
0.1190987
0.9510804
0.0952159
0.9528344
0.1154394
0.9507229
0.1122649
0.9477875

which when binarized becomes
0
1
0
1
0
1
0
1.

Our system has classified the test samples with perfect accuracy. Indeed the test set comprises of alternating piattos and pillows photos.

SELF-GRADE: 10/10

Acknowledgment: Jeric Tugaff for the code and Cole Fabros for explaining it to me.

Mr. Tugaff's code modified to process my data:
// Simple NN that learns 'and' logic
// ensure the same starting point each timerand('seed',0);
// network def.// - neurons per layer, including input//2 neurons in the input layer, 2 in the hidden layer and 1 in the ouput layerN = [2,2,1];
// inputsx = [0.313023 0.7962447; 0.2596636 1.; 0.2721711 0.7661728; 0.3666842 0.842306; 0.8614653 0.8345313; 0.8959559 0.7132170; 0.9718898 0.5795805; 0.9224472 0.5188499]'; x2 = [0.3322144 0.8215565; 1.0195367 0.3562358; 0.3121461 0.9116466; 1.043473 0.3339846; 0.4000078 1.; 1.0175605 0.3679583; 0.3930316 1.; 0.9543794 0.2963204]';
// targets, 0 if there is at least one 0 and 1 if both inputs are 1t = [0 0 0 0 1 1 1 1];// learning rate is 2.5 and 0 is the threshold for the error tolerated by the networklp = [0.1,0];
W = ann_FF_init(N);
// 400 training cylesT = 1000;W = ann_FF_Std_online(x,t,N,W,lp,T);

A19-Probabilistic Classification

I used data from the previous activity. There were again two classes (piattos and pillows), each with four training images . There was only one test image chosen for analysis. The features set was the same as in the previous activity.

----RG----Area--Classification----

0.3130230 5428. piattos
0.2596636 6817. piattos
0.2721711 5223. piattos
0.3666842 5742. piattos
0.8614653 5689. pillows
0.8959559 4862. pillows
0.9718898 3951. pillows
0.9224472 3537. pillows

We have our global feature set

x = [0.3130230 5428.;

0.2596636 6817.;

0.2721711 5223.;

0.3666842 5742.;

0.8614653 5689.;

0.8959559 4862.;

0.9718898 3951.;

0.9224472 3537.];

and its classification vector

y = [1;1;1;1;2;2;2;2];

We separate the global feature set to class feature sets

x1 = [0.3130230 5428.; 0.2596636 6817.; 0.2721711 5223.; 0.3666842 5742.];
x2 = [0.8614653 5689.; 0.8959559 4862.; 0.9718898 3951.; 0.9224472 3537.];

We get the mean for each feature in each group

u1 = [0.3028855 5802.5];

u2 = [0.9129396 4509.75];

and the global mean vector

u = [0.6079125 5156.125];

Then we get the mean-corrected data (xnaught1 and xnaught2) and the covariance matrix for each group (c1 and c2)

xnaught1 = [- 0.2948895 271.875;

- 0.3482489 1660.875;

- 0.3357414 66.875;

- 0.2412283 585.875];

xnaught2 = [0.2535528 532.875;

0.2880434 - 294.125;

0.3639773 - 1205.125;

0.3145347 - 1619.125 ];

c1 = [0.0947876 - 205.58834;

- 205.58834 795035.89];

c2 = [0.0946674 - 224.37948;

- 224.37948 1111089.3];

The pooled within group matrix C is then

C = [0.0947275 - 214.98391;

- 214.98391 953062.61];

Its inverse is

inv(C) = [21.629463 0.0048790;

0.0048790 0.0000021];

The prior probability vector is p = [4/8; 4/8];

The linear discriminant functions yield

----f1----- ----f2----- Class

40.193166 38.215655 1.

57.712379 55.641361 1.

35.908829 33.609495 1.

46.444826 44.89887 1.

62.954231 64.805784 2.

52.618282 54.544249 2.

42.555135 44.824398 2.

35.055327 36.902364 2.

Let our test image be that of a member of the piattos group (suppose we do not know this fact). It has a feature vector of

test = [0.3322144 0.8215565];

Its f1 and f2 values are 43.269644 and 41.458361, respectively.

We show the linear discriminant functions plot and use it to classify the test image. Through the graph, we can say that the test sample is a piattos chip.

Code:

x = [0.313023 0.7962447; 0.2596636 1.; 0.2721711 0.7661728; 0.3666842 0.842306; 0.8614653 0.8345313; 0.8959559 0.7132170; 0.9718898 0.5795805; 0.9224472 0.5188499];

y = [1;1;1;1;2;2;2;2];

x1 = [0.313023 0.7962447; 0.2596636 1.; 0.2721711 0.7661728; 0.3666842 0.842306];

x2 = [0.8614653 0.8345313; 0.8959559 0.7132170; 0.9718898 0.5795805; 0.9224472 0.5188499];

u1 = mean(x1,'r');

u2 = mean(x2,'r');

u = mean(x,'r');

xnaught1 = [];

for i = 1:size(x1,1);

xnaught1(i,:) = x1(i,:) -u;

end

xnaught2 = [];

for i = 1:size(x2,1);

xnaught2(i,:) = x2(i,:) -u;

end

c1 = xnaught1'*xnaught1/size(xnaught1,1);

c2 = xnaught2'*xnaught2/size(xnaught2,1);

C = (4*c1 + 4*c2)/8;
Cinv = inv(C);

P = [4/8; 4/8];

f1 = u1*Cinv*x' - (u1*Cinv*u1')/2 + log(P(1));

f2 = u2*Cinv*x' - (u2*Cinv*u2')/2 + log(P(2));

test = [0.3322144 0.8215565];

f1test = u1*Cinv*test' - (u1*Cinv*u1')/2 + log(P(1));

f2test = u2*Cinv*test' - (u2*Cinv*u2')/2 + log(P(2));

SELF-GRADE: 9/10 . I enjoyed the activity but it took me long to do this.

A18 - Pattern Recognition

For this activity, the aim is to automatically classify images of piattos and pillows chips using features extracted from the training images. There were four training images for the piattos and another four images for the pillows. The features used were red-and-green contrast and area.
The area was obtained by simply binarizing the images and summing the pixels. red-and-green contrast is defined by the following.
We let r be the contrast in the red channel: r = (max(r) - min(r))/(max(r) + min(r))
We let g be the contrast in the green channel: g = (max(g) - min(g))/(max(g) + min(g))
The red-and-green contrast is given by the rg = sqrt(r*r + g*g).

I designated piattos as 1 and pillows as 2.


Piattos features:
---RG---- ----Area----
0.3130230 5428.
0.2596636 6817.
0.2721711 5223.
0.3666842 5742.

Pillows features:

---RG---- ----Area----

0.8614653 5689.

0.8959559 4862.

0.9718898 3951.

0.9224472 3537.

Then I input a series of images consisting of four consecutive piattos and four consecutive pillows.

Test features:

---RG---- ----Area----

0.3322144 7569.

0.3121461 8399.

0.4000078 9213.

0.3930316 9213.

1.0195367 3282.

1.043473 3077.

1.0175605 3390.

0.9543794 2730.


The output of the program below, which made use of minimum distance classification, was

1 1 1 1 2 2 2 2

The chips were correctly classified with 100% accuracy.

If I add another class, the vcut class, using the same features, the accuracy will drop to 50%. This is because piattos and vcut nearly have the same color and the same area.

//for piattos
piattos = [];
for i = 1:4
M = imread(strcat('D:\ap186\september17\piatos'+string(i)+'.jpg'));
r = M(:,:,1);
g = M(:,:,2);
contrast_r = (max(r)-min(r))/(max(r)+min(r));
contrast_g = (max(g)-min(g))/(max(g)+min(g));
piattos(1,i) = sqrt(contrast_r*contrast_r + contrast_g*contrast_g);
M_gray = im2gray(M);
M_bw = im2bw(abs(1-M_gray),0.78);
piattos(2,i) = sum(M_bw);
end

//for pillows
pillow = [];
for i = 1:4;
M = imread(strcat('D:\ap186\september17\pillow'+string(i)+'.jpg'));
r = M(:,:,1);
g = M(:,:,2);
contrast_r = (max(r)-min(r))/(max(r)+min(r));
contrast_g = (max(g)-min(g))/(max(g)+min(g));
pillow(1,i) = sqrt(contrast_r*contrast_r + contrast_g*contrast_g);
M_gray = im2gray(M);
M_bw = im2bw(abs(1-M_gray),0.6);
pillow(2,i) = sum(M_bw);
end

m = [];
m(:,1) = sum(piattos,'c')/size(piattos,2);
m(:,2) = sum(pillow,'c')/size(pillow,2);

//for test samples
test = [];
for i = 1:8
M = imread(strcat('D:\ap186\september17\test\'+string(i)+'.jpg'));
r = M(:,:,1);
g = M(:,:,2);
contrast_r = (max(r)-min(r))/(max(r)+min(r));
contrast_g = (max(g)-min(g))/(max(g)+min(g));
test(1,i) = sqrt(contrast_r*contrast_r + contrast_g*contrast_g);
M_gray = im2gray(M);
M_bw = im2bw(abs(1-M_gray),0.63);
test(2,i) = sum(M_bw);
end

//Minimum distance classification
d = [];
for i = 1:8
for j = 1:2
d(j,i) = test(:,i)'*m(:,j) - m(:,j)'*m(:,j);
end
end

d = abs(d);
x =[];
for i = 1:8
x(i) = find(d==min(d(:,i)));
end
for i = 1:length(x);
x(i) = x(i) - 2*(i-1);
end

x

SELF-GRADE: 10/10 because I have 100% accuracy

A16 - Image Color Segmentation

September 2, 2008

Suppose I have a reference image Mpatch and an image I want to segment M, they have NCC (normalized chromaticidty coordinates) components rpatch, gpatch and bpatch, and r, g, and b

Code for non-parametric image segmentation by color:


delta_pix = 0.01;
val=[];

num_=[];

num=[];

counter=1;

for i=0:delta_pix:1;

[x,y]=find((rpatch>=i) & (rpatch<(i+delta_pix)));

val(counter)=i;

num_(counter)=length(x);

counter=counter+1;

end

num = num_./((size(rpatch,1))*size(rpatch,2));

plot(val, num_);

B = zeros(size(M,1),size(M,2),3);
delta_pix = 0.01;

val=[];

num_=[];

num=[];

counter=1;

for i=0:delta_pix:1;

[x,y]=find((gpatch>=i) & (gpatch<(i+delta_pix)));

val(counter)=i;

num_(counter)=length(x);

counter=counter+1;

end

num = num_./((size(gpatch,1))*size(gpatch,2));

plot(val, num_);

for i = 0:delta_pix:1

[x,y] = find((g>=i) & (g<(i+delta_pix)));

for k=1:length(x) for l=1:length(y)

B(x(k),y(l),2) = num_((i+delta_pix)/delta_pix);

end

end

i

end
B(:,:,3) = 1-B(:,:,1)-B(:,:,2);

Code for parametric segmentation:

delta_pix = 0.01;
val=[];

num_=[];

PDF = [];

counter=1;

for i=0:delta_pix:1;

[x,y]=find((rpatch>=i) & (rpatch<(i+delta_pix)));

val(counter)=i;

num_(counter)=length(x);

counter=counter+1;

end

PDF = num_./((size(rpatch,1))*size(rpatch,2));

plot(val, PDF);

mn = find(PDF==max(PDF));

mu_red = val(mn);

sigma_red = stdev(PDF);
val=[];

num_=[];

PDF = [];

counter=1;

for i=0:delta_pix:1;

[x,y]=find((gpatch>=i) & (gpatch<(i+delta_pix)));

val(counter)=i;

num_(counter)=length(x);

counter=counter+1;

end

PDF = num_./((size(gpatch,1))*size(gpatch,2));

plot(val,PDF);

mn = find(PDF==max(PDF));

mu_green = val(mn);

sigma_green = stdev(PDF);
x = [0:delta_pix:1];

pr = (exp(-((x-mu_red)^2)/(2*sigma_red)))/(sigma_red*sqrt(2*%pi));

pg = (exp(-((x-mu_green)^2)/(2*sigma_green)))/(sigma_green*sqrt(2*%pi));

K = zeros(size(M,1),size(M,2));

for i = 0:delta_pix:1

[x,y] = find((r>=i) & (r<(i+delta_pix)));

for k=1:length(x)

for l=1:length(y)

green = round(g(x(k),y(k)));

probability = pr((i+delta_pix)/delta_pix)*pg((green+delta_pix)/delta_pix);

K(x(k),y(l)) = probability;

end

end

i

end

Display

G = im2gray(B);

L = im2gray(M);

subplot(311)

imshow(L,[]);

subplot(312)

imshow(G,[]);

Figure 1. The raw image.

Figure 2. The reference patch which belongs to the hand.

Figure 3. The raw image (top) and the maps showing the probability that a pixel belongs to the region of interest which in this case is the skin. The center image is the result of non-parametric image segmentation while the bottom image is the result of parametric image-segmentation.

Self-grade: 10/10 because I was able to finish the activity on time and my parametric and non-parametric image segmentations result looks reasonable

Thank you, Lei for helping me with histogramming.

A15 - Color Camera Processing

August 28, 2008


We performed white balancing on images under different white balancing settings. In figure 1, row 1, we see the original images under white balancing settings inside-cloudy, inside-incandescent and auto-white balance, respectively. We see that the colors they contain per point are different and the white of the first two settings do not appear white. We try to process the first two images using Reference White Algorithm (results in second column) and Gray World Algorithm (results in third column). Now their white looks whiter, with the processed image for the inside-cloudy setting closer to the AWB setting. We may say that processed images from the Gray World Algorithm are slightly darker than those from the Reference White Algorithm.Figure 1. Myriad-colored objects processed using Reference White Algorithm and Gray World Algorithm. The white patches used for processing are in the lower-right corner of the collage figure.

Next we, try processing objects with different shades of the same hue. We try this for a high contrast image (with dark and bright background), and low contrast image (bright background only). We now see that Gray World Algorithm results are brighter. And white appears whiter for the high contrast image.Figure 2. Monochromatic Objects Processed. 1st row: raw images; 2nd row: Reference White Algorithm outcomes; 3rd row: Gray World Algorithm results. Right most image: the white patch

Code for performing the Reference White and Gray World Algorithms

//1. Defining the stacksize and calling of image
n = 100000000;
stacksize(n);
M = imread('C:\Documents and Settings\AP186user20\Desktop\act15\i - incandescent.jpg');

//2. Reference White Algo
white = imread('C:\Documents and Settings\AP186user20\Desktop\act15\whitepatch_i-incandescent.jpg');
Rw = mean(white(:,:,1));
Gw = mean(white(:,:,2));
Bw = mean(white(:,:,3));

//3. Gray World Algo
K(:,:,1) = M(:,:,1)/Rw;
K(:,:,2) = M(:,:,2)/Gw;
K(:,:,3) = M(:,:,3)/Bw;
K = K/max(max(max(K)));
imwrite(K,'C:\Documents and Settings\AP186user20\Desktop\act15\ReferenceWhite_i-incandescent.jpg');

SELF-GRADE:
10/10 because I was able to finish the activity on time

CREDITS:
Rica, Aiyin, Beth for helping me acquire images and explaining the algorithms