Solution to exercises week 8, The Multivariate Gaussian Classifier

Contents

Multivariate Gaussian classifier

We are provided with a Landsat sattelite image containing 6 image "bands". We will use each of these bands as a feature image. Lets load them, I'm saving them in a so called cell array.

tm = cell(6,1);
tm{1} = imread('tm1.png');
tm{2} = imread('tm2.png');
tm{3} = imread('tm3.png');
tm{4} = imread('tm4.png');
tm{5} = imread('tm5.png');
tm{6} = imread('tm6.png');
% We are also going to need these training and test masks. These masks
% indicate what pixels are known to belong to each class. Thus indicating
% what pixels we should use for training, and what pixels we can use to
% validate the result (test).
tm_train = imread('tm_train.png');
tm_test = imread('tm_test.png');

figure(1)
subplot(211)
imshow(tm{1},[]);
colorbar
title('Feature 1');

subplot(212)
imshow(tm{2},[]);
colorbar
title('Feature 2');

figure(2)
subplot(211)
imshow(tm{3},[]);
colorbar
title('Feature 3');

subplot(212)
imshow(tm{4},[]);
colorbar
title('Feature 4');

figure(3)
subplot(211)
imshow(tm{5},[]);
colorbar
title('Feature 5');

subplot(212)
imshow(tm{6},[]);
colorbar
title('Feature 6');

figure(4)
subplot(211)
imagesc(tm_train);
colorbar
axis image
title('Training mask');

subplot(212)
imagesc(tm_test);
colorbar
axis image
title('Test mask');
drawnow

Let's do the classification

[M,N] = size(tm_train);
res_train = zeros(M,N);
res_test = zeros(M,N);

% I have one implementation where I train the classifier, but also run the
% classifier on the trining data. Giving me the accuarcy for the classifier
% on the traning data
[class_img,error_train,confusion_train,u,c] = trainMultiGaussClassifier(tm,tm_train);
% The second implementation takes the mean values (u) and the covariance
% matrices (c) from the traning part and classifies the image. From this I
% calculate the accuracy on the test part of the image
[class_img2,error_test,confusion_test] = multiGaussClassifierNoTraining(tm,tm_test,u,c);
% Note that the two classified images will be the sam (class_img and
% class_img2) the difference is which mask I use.

% Lets make the resulting image within the training masks
res_train(tm_train==1) = class_img(tm_train==1);
res_train(tm_train==2) = class_img(tm_train==2);
res_train(tm_train==3) = class_img(tm_train==3);
res_train(tm_train==4) = class_img(tm_train==4);

% And within the test masks
res_test(tm_test==1) = class_img(tm_test==1);
res_test(tm_test==2) = class_img(tm_test==2);
res_test(tm_test==3) = class_img(tm_test==3);
res_test(tm_test==4) = class_img(tm_test==4);

% And display them
figure(5);
imagesc(class_img);
title('Classified image');
colormap jet
drawnow

figure(6);
imagesc(res_train);
title('Classified pixels in training masks');
colormap jet
drawnow

figure(7)
imagesc(res_test);
title('Classified pixels in test masks');
colormap jet
drawnow

% Lets load  the tm_classres
load tm_classres

figure(8)
imagesc(klassim)
title('Given classification (from tm classres)');
colormap jet
drawnow

p = sum(sum(class_img == klassim))*100/(N*M);
fprintf('Comparing my result with tm_classres: %f \n',p);

error_train

confusion_train

error_test

confusion_test

Comparing my result with tm_classres: 100.000000 

error_train =

    0.0807


confusion_train =

        1340           2           0         310
          43        1253           0           2
           0           0        1738           0
         131           3           0        1266


error_test =

    0.1240


confusion_test =

        1474           3           1         251
         513        2311           0           0
          14           0        1953          12
         213           2           0        1390

Exercise 4, (named Exercise 3) see the note for details

C = [1.2 0.4; 0.4 1.8];

mu1 = [0.1 ; 0.1];
mu2 = [2.1 ; 1.9];
mu3 = [-1.5 ; 2.0];

x = [1.6 ; 1.5];

g1 = -(1/2)*(x-mu1)'*inv(C)*(x-mu1)

g2 = -(1/2)*(x-mu2)'*inv(C)*(x-mu2)

g3 = -(1/2)*(x-mu3)'*inv(C)*(x-mu3)

[a,c] = max([g1 g2 g3]);
c

g1 =

   -1.1805


g2 =

   -0.1205


g3 =

   -4.7095


c =

     2

Exercise 5, (named Exercise 4) see the note for details

C = [1.1 0.3; 0.3 1.9];

mu1 = [0 ; 0];
mu2 = [3 ; 3];

x = [1.0 ; 2.2];

g1 = -(1/2)*(x-mu1)'*inv(C)*(x-mu1)

g2 = -(1/2)*(x-mu2)'*inv(C)*(x-mu2)

[a,c] = max([g1 g2]);
c


% post_id = 642; %delete this line to force new post;
% permaLink = http://inf4300.olemarius.net/2015/10/27/exercise-m-2/;

g1 =

   -1.4760


g2 =

   -1.8360


c =

     1

Published with MATLAB® R2015a