s:
In the second image of your question, the two-level wavelet transform is displayed. With your code example using dwt2
, you are only doing a single-level decomposition. To do a two-level decomposition, you can use the wavedec2
function with N=2
. To create the plot as shown, you have to take a closer look at the return values of wavedec2
:
(Image by Mathworks, from [2])
The vector C
contains all the approximation coefficients, stored in a column-wise fashion. S
is the so-called "book-keeping" matrix, as it contains information on how the data is stored.
Now the first image, cA2
in the example above, is the first 32*32 entries of C
. Using ii
and jj
as index variables, we can get the relevant parts of C
and use reshape
to get back to the image format:
ii = 1; jj = prod(S(1,:));
cA2 = reshape(C(ii:jj),S(1,:));
The other second-level coefficients are similarly obtained:
ii = jj+1; jj = ii + prod(S(2,:)) - 1;
cH2 = reshape(C(ii:jj),S(2,:));
ii = jj+1; jj = ii + prod(S(2,:)) - 1;
cV2 = reshape(C(ii:jj),S(2,:));
ii = jj+1; jj = ii + prod(S(2,:)) - 1;
cD2 = reshape(C(ii:jj),S(2,:));
The first-level coefficients can also be obtained in the same way, using the third row of S
:
ii = jj+1; jj = ii + prod(S(3,:)) - 1;
cH1 = reshape(C(ii:jj),S(3,:));
ii = jj+1; jj = ii + prod(S(3,:)) - 1;
cV1 = reshape(C(ii:jj),S(3,:));
ii = jj+1; jj = ii + prod(S(3,:)) - 1;
cD1 = reshape(C(ii:jj),S(3,:));
Now the plot can simply be created by arranging the images as desired:
imshow([[cA2,cH2; cV2,cD2],cH1;cV1,cD1],'Colormap',pink)
To add borders, you can use the rectangle
function and the information from S
:
% Small rectangles
rectangle('Position',[0,0,S(1,1),S(1,2)],'LineWidth',2,'EdgeColor','y');
rectangle('Position',[S(1,1),0,S(1,1),S(1,2)],'LineWidth',2,'EdgeColor','y');
rectangle('Position',[0,S(1,2),S(1,1),S(1,2)],'LineWidth',2,'EdgeColor','y');
rectangle('Position',[S(1,1),S(1,2),S(1,1),S(1,2)],'LineWidth',2,'EdgeColor','y');
% Large rectangles
rectangle('Position',[0,S(3,2),S(3,1),S(3,2)],'LineWidth',2,'EdgeColor','y');
rectangle('Position',[S(3,1),0,S(3,1),S(3,2)],'LineWidth',2,'EdgeColor','y');
rectangle('Position',[S(3,1),S(3,2),S(3,1),S(3,2)],'LineWidth',2,'EdgeColor','y');