Namespace of morphological tree-related routines. More...

Namespaces
namespace	filter
	Namespace for attribute filtering.
namespace	impl
namespace	internal
Classes
struct	asc_propagation
class	data
class	depth1st_piter
struct	desc_propagation
struct	dn_leaf_piter
struct	dn_node_piter
struct	dn_site_piter
struct	up_leaf_piter
struct	up_node_piter
struct	up_site_piter
struct	way_of_propagation
Functions
template<typename A , typename T >
mln::trait::ch_value< typename T::function, typename A::result >::ret	compute_attribute_image (const Accumulator< A > &a, const T &t, mln::trait::ch_value< typename T::function, A >::ret *accu_image=0)
	Compute an attribute image using tree with a parent relationship between sites.
template<typename A , typename T , typename V >
mln::trait::ch_value< typename T::function, typename A::result >::ret	compute_attribute_image_from (const Accumulator< A > &a, const T &t, const Image< V > &values, mln::trait::ch_value< typename T::function, A >::ret *accu_image=0)
	The same as compute_attribute_image but uses the values stored by `values` image instead.
template<typename I , typename N , typename S >
mln::trait::ch_value< I, typename I::psite >::ret	compute_parent (const Image< I > &f, const Neighborhood< N > &nbh, const Site_Set< S > &s)
	Compute a tree with a parent relationship between sites.
template<typename I , typename N >
data< I, p_array< typename I::psite > >	dual_input_max_tree (const Image< I > &f, const Image< I > &m, const Neighborhood< N > &nbh)
	Compute the dual input max tree using mask-based connectivity.
template<typename T , typename I >
bool	is_a_node (const Image< T > &parent, const typename T::psite &p, const Image< I > &f)
template<typename T , typename I >
bool	is_root (const Image< T > &parent, const typename T::psite &p, const Image< I > &f)
template<typename I , typename N >
mln::trait::ch_value< I, typename I::psite >::ret	max (const Image< I > &f, const Neighborhood< N > &nbh)
template<typename I , typename N >
data< I, p_array< typename I::psite > >	max_tree (const Image< I > &f, const Neighborhood< N > &nbh)
	Compute a canonized max-tree.
template<typename I , typename N >
data< I, p_array< typename I::psite > >	min_tree (const Image< I > &f, const Neighborhood< N > &nbh)
	Compute a canonized min-tree.
template<typename T , typename I , typename S >
p_array< typename T::psite >	nodes (const Image< T > &parent, const Image< I > &f, const Site_Set< S > &s)
template<typename T , typename A , typename P , typename W >
void	propagate_if (const T &tree, Image< A > &a_, const way_of_propagation< W > &prop_, const Function_v2b< P > &pred_, const typename A::value &v)
template<typename T , typename A , typename P >
void	propagate_if (const T &tree, Image< A > &a_, const desc_propagation &prop_, const Function_v2b< P > &pred_)
template<typename T , typename A , typename W >
void	propagate_if_value (const T &tree, Image< A > &a_, const way_of_propagation< W > &prop, const typename A::value &v)
template<typename T , typename A , typename W >
void	propagate_if_value (const T &tree, Image< A > &a_, const way_of_propagation< W > &prop_, const typename A::value &v, const typename A::value &v_prop)
template<typename T , typename A >
void	propagate_node_to_ancestors (typename A::psite n, const T &t, Image< A > &a_, const typename A::value &v)
template<typename T , typename A >
void	propagate_node_to_ancestors (typename A::psite n, const T &t, Image< A > &a_)
template<typename T , typename A >
void	propagate_node_to_descendants (typename A::psite n, const T &t, Image< A > &a_, unsigned *nb_leaves=0)
template<typename T , typename A >
void	propagate_node_to_descendants (typename A::psite n, const T &t, Image< A > &a_, const typename A::value &v, unsigned *nb_leaves=0)
template<typename T , typename A >
void	propagate_node_to_descendants (typename A::psite &n, const T &t, Image< A > &a_, unsigned *nb_leaves=0)
template<typename T , typename F >
void	propagate_representative (const T &t, Image< F > &f_)
	Propagate the representative node's value to non-representative points of the component.

Detailed Description

Namespace of morphological tree-related routines.

Function Documentation

template<typename A , typename T >

mln::trait::ch_value< typename T::function, typename A::result >::ret mln::morpho::tree::compute_attribute_image	(	const Accumulator< A > &	a,
		const T &	t,
		mln::trait::ch_value< typename T::function, A >::ret *	accu_image = `0`
	)			`[inline]`

Compute an attribute image using tree with a parent relationship between sites.

In the attribute image, the resulting value at a node is the 'sum' of its sub-components value + the attribute value at this node.

Warning: s translates the ordering related to the "natural" childhood relationship. The parenthood is thus inverted w.r.t. to s.

It is very convenient since all processing upon the parent tree are performed following s (in the default "forward" way).

FIXME: Put it more clearly...

The parent result image verifies:

p is root iff parent(p) == p
p is a node iff either p is root or f(parent(p)) != f(p).

Parameters:

`[in]`	a	Attribute.
`[in]`	t	Component tree.
`[out]`	accu_image	Optional argument used to store image of attribute accumulator.

Returns:: The attribute image.

Definition at line 216 of file compute_attribute_image.hh.

References mln::morpho::tree::internal::compute_attribute_image(), mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename A , typename T , typename V >

mln::trait::ch_value< typename T::function, typename A::result >::ret mln::morpho::tree::compute_attribute_image_from	(	const Accumulator< A > &	a,
		const T &	t,
		const Image< V > &	values,
		mln::trait::ch_value< typename T::function, A >::ret *	accu_image = `0`
	)			`[inline]`

The same as compute_attribute_image but uses the values stored by values image instead.

Parameters:

`[in]`	a	Attribute.
`[in]`	t	Component tree.
`[in]`	values	Value image.
`[out]`	accu_image	Optional argument used to store image.

Returns:

Definition at line 233 of file compute_attribute_image.hh.

References mln::morpho::tree::internal::compute_attribute_image(), mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename I , typename N , typename S >

mln::trait::ch_value< I, typename I::psite >::ret mln::morpho::tree::compute_parent	(	const Image< I > &	f,
		const Neighborhood< N > &	nbh,
		const Site_Set< S > &	s
	)			`[inline]`

Compute a tree with a parent relationship between sites.

Warning: s translates the ordering related to the "natural" childhood relationship. The parenthood is thus inverted w.r.t. to s.

It is very convenient since most processing routines upon the parent tree are performed following s (in the default "forward" way). Indeed that is the way to propagate information from parents to children.

The parent result image verifies:

p is root iff parent(p) == p
p is a node iff either p is root or f(parent(p)) != f(p).

The choice "s means childhood" is consistent with labeling in binary images. In that particular case, while browsing the image in forward scan (video), we expect to find first a tree root (a first point, representative of a component) and then the other component points. Please note that it leads to increasing values of labels in the "natural" video scan.

Since mathematical morphology on functions is related to morphology on sets, we clearly want to keep the equivalence between "component labeling" and "component filtering" using trees.

FIXME: Put it more clearly... Insert pictures!

A binary image:

| | - -
| | - |
- - - -
- | | -

where '|' means true and '-' means false.

Its labeling:

0 1 1 0 0
0 1 1 0 2
0 0 0 0 0
0 0 3 3 0

The corresponding forest:

x o . x x
x . . x o
x x x x x
x x o . x

where 'x' means "no data", 'o' is a tree root (representative point for a component), and '.' is a tree regular (non-root) point (in a component by not its representative point).

The forest, with the parent relationship looks like:

o < .
^ r
. . o

o < .

Definition at line 286 of file compute_parent.hh.

References mln::morpho::tree::internal::compute_parent_dispatch(), mln::morpho::tree::internal::compute_parent_tests(), mln::trace::entering(), and mln::trace::exiting().

Referenced by mln::morpho::tree::internal::compute_parent_dispatch(), mln::morpho::tree::data< I, S >::data(), and max().

template<typename I , typename N >

morpho::tree::data< I, p_array< typename I::psite > > mln::morpho::tree::dual_input_max_tree	(	const Image< I > &	f,
		const Image< I > &	m,
		const Neighborhood< N > &	nbh
	)			`[inline]`

Compute the dual input max tree using mask-based connectivity.

Parameters:

`[in]`	f	The original image.
`[in]`	m	The connectivity mask.
`[in]`	nbh	The neighborhood of the mask.

Returns:: The computed tree.

Definition at line 109 of file dual_input_tree.hh.

References mln::morpho::tree::internal::dual_input_max_tree_dispatch(), mln::trace::entering(), mln::exact(), and mln::trace::exiting().

template<typename T , typename I >

bool mln::morpho::tree::is_a_node	(	const Image< T > &	parent,
		const typename T::psite &	p,
		const Image< I > &	f
	)			`[inline]`

Definition at line 91 of file utils.hh.

References mln::exact().

Referenced by mln::morpho::tree::data< I, S >::children(), and nodes().

template<typename T , typename I >

bool mln::morpho::tree::is_root	(	const Image< T > &	parent,
		const typename T::psite &	p,
		const Image< I > &	f
	)			`[inline]`

Definition at line 72 of file utils.hh.

References mln::exact().

template<typename I , typename N >

mln::trait::ch_value< I, typename I::psite >::ret mln::morpho::tree::max	(	const Image< I > &	f,
		const Neighborhood< N > &	nbh
	)			`[inline]`

Definition at line 62 of file morpho/tree/max.hh.

References compute_parent(), mln::trace::entering(), mln::exact(), mln::trace::exiting(), and mln::data::sort_psites_increasing().

template<typename I , typename N >

data< I, p_array< typename I::psite > > mln::morpho::tree::max_tree	(	const Image< I > &	f,
		const Neighborhood< N > &	nbh
	)			`[inline]`

Compute a canonized max-tree.

Parameters:

`[in]`	f	The input image.
`[in]`	nbh	The neighborhood.

Returns:: The corresponding max-tree structure.

Definition at line 100 of file component_tree.hh.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), and mln::data::sort_psites_increasing().

template<typename I , typename N >

data< I, p_array< typename I::psite > > mln::morpho::tree::min_tree	(	const Image< I > &	f,
		const Neighborhood< N > &	nbh
	)			`[inline]`

Compute a canonized min-tree.

Parameters:

`[in]`	f	The input image.
`[in]`	nbh	The neighborhood.

Returns:: The corresponding min-tree structure.

Definition at line 77 of file component_tree.hh.

References mln::trace::entering(), mln::exact(), mln::trace::exiting(), and mln::data::sort_psites_decreasing().

template<typename T , typename I , typename S >

p_array< typename T::psite > mln::morpho::tree::nodes	(	const Image< T > &	parent,
		const Image< I > &	f,
		const Site_Set< S > &	s
	)			`[inline]`

Definition at line 110 of file utils.hh.

References mln::exact(), and is_a_node().

template<typename T , typename A , typename P , typename W >

void mln::morpho::tree::propagate_if	(	const T &	tree,
		Image< A > &	a_,
		const way_of_propagation< W > &	prop_,
		const Function_v2b< P > &	pred_,
		const typename A::value &	v
	)			`[inline]`

Propagate nodes checking the predicate pred in the way defined by way_of_propagation.

Parameters:

	tree	Component tree used for propagation.
	a_	Attributed image where values are propagated.
	prop_	Propagate node in acsendant or descendant way.
	pred_	Predicate that node must check to be propagated.
	v	Value to be propagated. (By default `v` is the value at the node being propagated).

Definition at line 293 of file propagate_if.hh.

References mln::exact(), and mln::morpho::tree::internal::propagate_if().

Referenced by mln::morpho::tree::filter::subtractive().

template<typename T , typename A , typename P >

void mln::morpho::tree::propagate_if	(	const T &	tree,
		Image< A > &	a_,
		const desc_propagation &	prop_,
		const Function_v2b< P > &	pred_
	)			`[inline]`

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 310 of file propagate_if.hh.

References mln::exact(), and mln::morpho::tree::internal::propagate_if().

template<typename T , typename A , typename W >

void mln::morpho::tree::propagate_if_value	(	const T &	tree,
		Image< A > &	a_,
		const way_of_propagation< W > &	prop,
		const typename A::value &	v
	)			`[inline]`

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 278 of file propagate_if.hh.

References mln::pw::cst(), mln::exact(), mln::morpho::tree::internal::propagate_if(), and mln::pw::value().

template<typename T , typename A , typename W >

void mln::morpho::tree::propagate_if_value	(	const T &	tree,
		Image< A > &	a_,
		const way_of_propagation< W > &	prop_,
		const typename A::value &	v,
		const typename A::value &	v_prop
	)			`[inline]`

Propagate nodes having the value v in the way defined by way_of_propagation.

Parameters:

	tree	Component tree used for propagation.
	a_	Attributed image where values are propagated.
	prop_	Propagate node in acsendant or descendant way.
	v	Value that node must have to be propagated.
	v_prop	Value to propagate (By default it is the value at the node being propagated).

Definition at line 262 of file propagate_if.hh.

References mln::pw::cst(), mln::exact(), mln::morpho::tree::internal::propagate_if(), and mln::pw::value().

template<typename T , typename A >

void mln::morpho::tree::propagate_node_to_ancestors	(	typename A::psite	n,
		const T &	t,
		Image< A > &	a_,
		const typename A::value &	v
	)

Propagate a value v from a node n to its ancestors.

Parameters:

`[in]`	n	Node to propagate.
`[in]`	t	Component tree used for propagation.
`[in]`	a_	Attribute image where values are propagated.
`[in]`	v	Value to propagate.

Definition at line 170 of file propagate_node.hh.

References mln::exact().

Referenced by propagate_node_to_ancestors().

template<typename T , typename A >

void mln::morpho::tree::propagate_node_to_ancestors	(	typename A::psite	n,
		const T &	t,
		Image< A > &	a_
	)			`[inline]`

Propagate the node's value to its ancestors.

Parameters:

`[in]`	n	Node to propagate.
`[in]`	t	Component tree used for propagation.
`[in,out]`	a_	Attribute image where values are propagated.

Definition at line 197 of file propagate_node.hh.

References mln::exact(), and propagate_node_to_ancestors().

template<typename T , typename A >

void mln::morpho::tree::propagate_node_to_descendants	(	typename A::psite	n,
		const T &	t,
		Image< A > &	a_,
		unsigned *	nb_leaves = `0`
	)			`[inline]`

Definition at line 155 of file propagate_node.hh.

References mln::exact(), and propagate_node_to_descendants().

template<typename T , typename A >

void mln::morpho::tree::propagate_node_to_descendants	(	typename A::psite	n,
		const T &	t,
		Image< A > &	a_,
		const typename A::value &	v,
		unsigned *	nb_leaves = `0`
	)			`[inline]`

Propagate a value v from a node n to its descendants.

Parameters:

`[in]`	n	Node to propagate.
`[in]`	t	Component tree used for propagation.
`[in]`	a_	Attribute image where values are propagated.
`[in]`	v	Value to propagate.
`[out]`	nb_leaves	Optional. Store the number of leaves in the component.

Definition at line 120 of file propagate_node.hh.

References mln::exact().

Referenced by propagate_node_to_descendants().

template<typename T , typename A >

void mln::morpho::tree::propagate_node_to_descendants	(	typename A::psite &	n,
		const T &	t,
		Image< A > &	a_,
		unsigned *	nb_leaves = `0`
	)			`[inline]`

Propagate the node's value to its descendants.

Parameters:

`[in]`	n	Node to propagate.
`[in]`	t	Component tree used for propagation.
`[in]`	a_	Attribute image where values are propagated.
`[out]`	nb_leaves	Optional. Store the number of leaves in the component.

template<typename T , typename F >

void mln::morpho::tree::propagate_representative	(	const T &	t,
		Image< F > &	f_
	)			`[inline]`

Propagate the representative node's value to non-representative points of the component.

Parameters:

	t	Component tree.
	f_	Value image.

Definition at line 65 of file propagate_representative.hh.

References mln::exact().

mln::morpho::tree Namespace Reference

Namespaces

Classes

Functions

Detailed Description

Function Documentation