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Quadtree decomposition

`S = qtdecomp(I)S = qtdecomp(I, threshold)S = qtdecomp(I, threshold, mindim)S = qtdecomp(I, threshold, [mindim
maxdim])S = qtdecomp(I, fun)`

`qtdecomp` divides a square image into four
equal-sized square blocks, and then tests each block to see if it
meets some criterion of homogeneity. If a block meets the criterion,
it is not divided any further. If it does not meet the criterion,
it is subdivided again into four blocks, and the test criterion is
applied to those blocks. This process is repeated iteratively until
each block meets the criterion. The result can have blocks of several
different sizes.

`S = qtdecomp(I)` performs
a quadtree decomposition on the intensity image `I` and
returns the quadtree structure in the sparse matrix `S`.
If `S(k,m)` is nonzero, then `(k,m)` is
the upper left corner of a block in the decomposition, and the size
of the block is given by `S(k,m)`. By default, `qtdecomp` splits
a block unless all elements in the block are equal.

`S = qtdecomp(I, threshold)` splits
a block if the maximum value of the block elements minus the minimum
value of the block elements is greater than `threshold`. `threshold` is
specified as a value between 0 and 1, even if `I` is
of class `uint8` or `uint16`. If `I` is `uint8`,
the threshold value you supply is multiplied by 255 to determine the
actual threshold to use; if `I` is `uint16`,
the threshold value you supply is multiplied by 65535.

`S = qtdecomp(I, threshold, mindim)` will
not produce blocks smaller than `mindim`, even if
the resulting blocks do not meet the threshold condition.

`S = qtdecomp(I, threshold, [mindim
maxdim])` will not produce blocks smaller than `mindim` or
larger than `maxdim`. Blocks larger than `maxdim` are
split even if they meet the threshold condition. `maxdim/mindim` must
be a power of 2.

`S = qtdecomp(I, fun)` uses
the function `fun` to determine whether to split
a block. `qtdecomp` calls `fun` with
all the current blocks of size `m`-by-`m` stacked
into an `m`-by-`m`-by-`k` array,
where `k` is the number of `m`-by-`m` blocks. `fun` returns
a logical `k`-element vector, whose values are 1
if the corresponding block should be split, and 0 otherwise. (For
example, if `k(3)` is 0, the third `m`-by-`m` block
should not be split.) `fun` must be a `function_handle`. Parameterizing
Functions, in the MATLAB Mathematics documentation, explains
how to provide additional parameters to the function `fun`.

For the syntaxes that do not include a function, the input image
can be of class `logical`, `uint8`, `uint16`, `int16`, `single`,
or `double`. For the syntaxes that include a function,
the input image can be of any class supported by the function. The
output matrix is always of class `sparse`.

I = uint8([1 1 1 1 2 3 6 6;... 1 1 2 1 4 5 6 8;... 1 1 1 1 7 7 7 7;... 1 1 1 1 6 6 5 5;... 20 22 20 22 1 2 3 4;... 20 22 22 20 5 4 7 8;... 20 22 20 20 9 12 40 12;... 20 22 20 20 13 14 15 16]); S = qtdecomp(I,.05); disp(full(S));

View the block representation of quadtree decomposition.

I = imread('liftingbody.png'); S = qtdecomp(I,.27); blocks = repmat(uint8(0),size(S)); for dim = [512 256 128 64 32 16 8 4 2 1]; numblocks = length(find(S==dim)); if (numblocks > 0) values = repmat(uint8(1),[dim dim numblocks]); values(2:dim,2:dim,:) = 0; blocks = qtsetblk(blocks,S,dim,values); end end blocks(end,1:end) = 1; blocks(1:end,end) = 1; imshow(I), figure, imshow(blocks,[])

The following figure shows the original image and a representation of the quadtree decomposition of the image.

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