function reconstructgray(p)
%This takes a full image, Quantizes, then reconstructs
%in gray-scale based upon resolution factor p.

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

%Defines the dimensions of the matrix.
[height, width, dim] = size(x);

%Finds out how many 8x8 blocks there are. 
h8=floor(height/8);
w8=floor(width/8);
h88=h8*8;
w88=w8*8;


x = double(x); %Converts to double percision.

%Restricts the image to dimensions divisible by 8.
x = x(1:h88,1:w88,:);

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

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

%Quanzitization Matricies. Uncomment to use.

%Hilbert 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 = QuantizeFull(xgray,Q,h8,w8);
d = deQuantizeFull(q,C,Q,h8,w8);
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 full image.
function img = QuantizeFull(xgray,Q,h8,w8)

 for i = 1:h8
     for j = 1:w8
        xb = xgray((i-1)*8+1:i*8,(j-1)*8+1:j*8);
        xb = double(xb);
        Xc = xb - 128;
        Y = dct(dct(Xc')');
        Yq = round(Y./Q);
        img((i-1)*8+1:i*8,(j-1)*8+1:j*8) = Yq;
     end
 end
 
%DeQuantizes the full image.
function img = deQuantizeFull(yq,C,Q,h8,w8)

for i = 1:h8
     for j = 1:w8
        Yq = yq((i-1)*8+1:i*8,(j-1)*8+1:j*8); 
        Ydq = Yq.*Q;
        Xdq = C'*Ydq*C;
        Xe = Xdq + 128;
        Xf = uint8(Xe);
        img((i-1)*8+1:i*8,(j-1)*8+1:j*8) = Xf;
     end
end