function [outputPicture] = smoothMe (inputPicture)
G=fspecial('gaussian', [10 10],3); %Create Gaussian mask
outputPicture = conv2(inputPicture,G,'same'); %Convolve the grayscale image with Gaussian filters
end

Ex1 :
Lena = imread('lena.png'); %import image png

figure;
image(Lena) %Display the initial image

GLena=rgb2gray(Lena) %Convert the Lena image to grayscale

figure;
colormap(gray)
imagesc(GLena) %display the gray scaled image

SmoothLena = smoothMe(GLena) %blurred image of Lena with Gaussian filter

figure;
colormap(gray)
imagesc(SmoothLena) %display the result

function [H_outputPicture, V_outputPicture] = sobelOperators(inputPicture)
%Convolve the grayscale image with horizontal Sobel filters
H_outputPicture = conv2(inputPicture, [1 2 1; 0 0 0; -1 -2 -1])
%Convolve the grayscale image with vertical Sobel filters
V_outputPicture = conv2(inputPicture, [1 0 -1; 2 0 -2; 1 0 -1])

end

Ex2 :
Lena = imread('lena.png'); %import image rgb

figure;
image(Lena) %Display the initial image

GLena = rgb2gray(Lena) %Convert the Lena image to grayscale

figure;
colormap(gray)
imagesc(Glena) %Display the gray scaled image

(H_SobelLena, V_SobelLena) = sobelOperators(GLena) %Apply sobel filters

figure;
colormap(gray)
imagesc(H_SobelLena) %Display the result of the horizontal Sobel filters

figure;
colormap(gray)
imagesc(V_SobelLena) %Display the result of the vertical Sobel filters

function[ match ] = recogniseFace( Unknown_face, Train_face )

%Training
[U,S,D]=svds(Train_Face, 30) %First 30 Eigen vectors
1TFaces= U'*Train_Face %low dimension Training Face with 20 dimension

%Prediction
1UnknownFace = U'*Unknown_Face
EuclideanDist=sqrt(sum((1TFaces-repmat(1UnknownFace,[1 34])).^2))
[match_score, match]=min(EuclideanDist);

end

Ex3 :
load A
load UnknownFace

RealFace = reshape(UnknownFace, [100 100]);
figure;
colormap(gray)
imagesc(RealFace) %Visualisation of the Unknown face

match = recogniseFace(UnknownFace, A) %Reconignition process using PCA on the database A of 34 known register
FoundFace = reshape(A(:, match), [100 100]); %Face that have been detected
figure;
colormap(gray)
imagesc(FoundFace) %Visualisation of the detected face

function [ ranks, frequency ] = querystring( query, Tf, uniqueCell )

queryCell = strsplit(query)';
number_of_documents=size(Tf,2);

for i = 1 : size(queryCell,1)
	frequency(i,1:number_of_documents)= Tf(find(strcmp(uniqueCell,queryCell(i))),:);
end

frequency=sum(frequency);
[frequency, ranks]=sort(frequency,'descend');

end

[ranks, frequency]=querystring('superhero comic film', tfidfM, uniqueCell);
ranks(1:10) %top position is document 433

function [tfidfM] = tfidf(Tf)
%Input Tf is the term frequency matrix (importance of a document to a term)
%N is the total number of documents in the corpus
N = size(Tf, 2); %number of columns
n = sum (Tf > 0, 2); %n(t) is the number of the documents in the corpus that contains term t
idf = log(N./(1+n)); %Inverse Document Frequency

%Term frequency inverse document frequency Matrix
tfidfM = Tf.*repmat(idf,[1 size(Tf, 2)]);

end

function [ s ] = kalmanfilter( s )
%Kalman filter store state in variable s
%s is a structure with field
%s.x = state variables
%s.F = transformation matrix
%s.P = covariance of variables (how to initialize? with R)
%s.R = covariance of sensor (Radar) / sampling error
%s.z = new observation

%preduction
s.x = s.F * s.x
s.P = s.F * s.P * s.F';

%update
K = s.P * inv(s.P + s.R)
s.x = s.x + K *(s.z - s.x);
s.P = s.P - K * s.P;
end