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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.

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`

.

`qtdecomp`

is appropriate primarily for square
images whose dimensions are a power of 2, such as 128-by-128 or 512-by-512.
These images can be divided until the blocks are as small as 1-by-1.
If you use `qtdecomp`

with an image whose dimensions
are not a power of 2, at some point the blocks cannot be divided further.
For example, if an image is 96-by-96, it can be divided into blocks
of size 48-by-48, then 24-by-24, 12-by-12, 6-by-6, and finally 3-by-3.
No further division beyond 3-by-3 is possible. To process this image,
you must set `mindim`

to 3 (or to 3 times a power
of 2); if you are using the syntax that includes a function, the function
must return 0 at the point when the block cannot be divided further.

- Anonymous Functions (MATLAB)
- Parameterizing Functions (MATLAB)
- Create Function Handle (MATLAB)

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