function changetogray(p)
%This takes an 8x8 portion of the input picture
%and converts the image to gray-scale
%utilizing the loss of quality variable p.

%Constructs the image into a matrix.
x = imread('C:\Users\cnelso17\Desktop\project5.jpg');
x = double(x); %Define in double percision.

x = x(200:207,200:207,:); %8x8 block.

r = x(:,:,1); %Defining Red.
g = x(:,:,2); %Defining Green.
b = x(:,:,3); %Defining Blue.

%Converts to gray-scale.
xgray = .2126*r + .7152*g + .0722*b;
xgray = uint8(xgray); %Proper units.
imagesc(xgray); colormap(gray);figure(2); %Displays image.

%Choosing the quantize matrix. Uncomment to select.

%Hildberg Matrix
Q =  p*8./hilb(8); 

%JPEG standard Matrix.
% Q=p*[16 11 10 16 24 40 51 61; 12 12 14 19 26 58 60 55;
% 14 13 16 24 40 57 69 56;
% 14 17 22 29 51 87 80 62;
% 18 22 37 56 68 109 103 77;
% 24 35 55 64 81 104 113 92;
% 49 64 78 87 103 121 120 101;
% 72 92 95 98 112 100 103 99];

C = getC();
q = Quantize(xgray,Q);
d = deQuantize(q,C,Q);
imagesc(d,[0 255]);colormap(gray);

%dct function
function C = getC()
for i = 1:8
    for j = 1:8
        C(i,j) = cos((i-1)*(2*j-1)*pi/(2*8));
    end
end
C = sqrt(2/8)*C;
C(1,:) = C(1,:)/sqrt(2);

%Quantizes the 8x8.
function img = Quantize(xb,Q)
xb = double(xb);
Xc = xb - 128;
Y = dct(dct(Xc')');
Yq = round(Y./Q)
img = Yq;

%DeQuantizes the 8x8.
function img = deQuantize(Yq,C,Q)
Ydq = Yq.*Q;
Xdq = C'*Ydq*C;
Xe = Xdq + 128;
Xf = uint8(Xe);
img = Xf;