[Scipysvn] r5281  trunk/doc/source/tutorial
scipysvn@scip...
scipysvn@scip...
Sat Dec 20 05:05:18 CST 2008
Author: david.wardefarley
Date: 20081220 05:05:15 0600 (Sat, 20 Dec 2008)
New Revision: 5281
Modified:
trunk/doc/source/tutorial/ndimage.rst
Log:
Huge fixerupper. All module functions prefixed with :func: (is this correct?). All parameters enclosed in \*param\* (seemed like the closest thing in the Sphinx documentation that I could find. Tables and sectional crossreferences fixed.
Modified: trunk/doc/source/tutorial/ndimage.rst
===================================================================
 trunk/doc/source/tutorial/ndimage.rst 20081220 06:53:22 UTC (rev 5280)
+++ trunk/doc/source/tutorial/ndimage.rst 20081220 11:05:15 UTC (rev 5281)
@@ 1,42 +1,44 @@
Multidimensional image processing
==================================
+Multidimensional image processing (:mod:`ndimage`)
+=========================================================
{Peter Verveer} {verveer@users.sourceforge.net}
{Multidimensional image analysis functions}
+.. moduleauthor:: Peter Verveer <verveer@users.sourceforge.net>
.. _ndimage_introduction:
+.. currentmodule:: scipy.ndimage
+
+.. _ndimageintroduction:
+
Introduction
============
+
Image processing and analysis are generally seen as operations on
twodimensional arrays of values. There are however a number of
fields where images of higher dimensionality must be analyzed. Good
examples of these are medical imaging and biological imaging.
{numarray} is suited very well for this type of applications due
its inherent multidimensional nature. The {numarray.nd_image}
+:mod:`numarray` is suited very well for this type of applications due
+its inherent multidimensional nature. The :mod:`scipy.ndimage`
packages provides a number of general image processing and analysis
functions that are designed to operate with arrays of arbitrary
dimensionality. The packages currently includes functions for
linear and nonlinear filtering, binary morphology, Bspline
interpolation, and object measurements.
.. _ndimage_properties_shared_by_all_functions:
+.. _ndimagepropertiessharedbyallfunctions:
Properties shared by all functions
==================================
+
All functions share some common properties. Notably, all functions
allow the specification of an output array with the {output}
+allow the specification of an output array with the *output*
argument. With this argument you can specify an array that will be
changed inplace with the result with the operation. In this case
the result is not returned. Usually, using the {output} argument is
+the result is not returned. Usually, using the *output* argument is
more efficient, since an existing array is used to store the
result.
The type of arrays returned is dependent on the type of operation,
but it is in most cases equal to the type of the input. If,
however, the {output} argument is used, the type of the result is
+however, the *output* argument is used, the type of the result is
equal to the type of the specified output argument. If no output
argument is given, it is still possible to specify what the result
of the output should be. This is done by simply assigning the
@@ 51,15 +53,15 @@
{In previous versions of :mod:`scipy.ndimage`, some functions accepted the *output_type* argument to achieve the same effect. This argument is still supported, but its use will generate an deprecation warning. In a future version all instances of this argument will be removed. The preferred way to specify an output type, is by using the *output* argument, either by specifying an output array of the desired type, or by specifying the type of the output that is to be returned.}
+.. _ndimagefilterfunctions:
+
Filter functions
================
+
.. _ndimage_filter_functions:

The functions described in this section all perform some type of spatial filtering of the the input array: the elements in the output are some function of the values in the neighborhood of the corresponding input element. We refer to this neighborhood of elements as the filter kernel, which is often
rectangular in shape but may also have an arbitrary footprint. Many
of the functions described below allow you to define the footprint
of the kernel, by passing a mask through the {footprint} parameter.
+of the kernel, by passing a mask through the *footprint* parameter.
For example a cross shaped kernel can be defined as follows:
::
@@ 84,7 +86,7 @@
[0 0 1 1 1 0 0]
Sometimes it is convenient to choose a different origin for the
kernel. For this reason most functions support the {origin}
+kernel. For this reason most functions support the *origin*
parameter which gives the origin of the filter relative to its
center. For example:
@@ 115,7 +117,7 @@
[ 0 1 0 0 1 0 0]
however, using the origin parameter instead of a larger kernel is
more efficient. For multidimensional kernels {origin} can be a
+more efficient. For multidimensional kernels *origin* can be a
number, in which case the origin is assumed to be equal along all
axes, or a sequence giving the origin along each axis.
@@ 125,18 +127,18 @@
borders. This is done by assuming that the arrays are extended
beyond their boundaries according certain boundary conditions. In
the functions described below, the boundary conditions can be
selected using the {mode} parameter which must be a string with the
+selected using the *mode* parameter which must be a string with the
name of the boundary condition. Following boundary conditions are
currently supported:
 {"nearest"} {Use the value at the boundary} {[1 2 3]>[1 1 2 3 3]}
 {"wrap"} {Periodically replicate the array} {[1 2 3]>[3 1 2 3 1]}
 {"reflect"} {Reflect the array at the boundary}
 {[1 2 3]>[1 1 2 3 3]}
 {"constant"} {Use a constant value, default value is 0.0}
 {[1 2 3]>[0 1 2 3 0]}
+ ========== ==================================== ====================
+ 
+ "nearest" Use the value at the boundary [1 2 3]>[1 1 2 3 3]
+ "wrap" Periodically replicate the array [1 2 3]>[3 1 2 3 1]
+ "reflect" Reflect the array at the boundary [1 2 3]>[1 1 2 3 3]
+ "constant" Use a constant value, default is 0.0 [1 2 3]>[0 1 2 3 0]
+ ========== ==================================== ====================

The {"constant"} mode is special since it needs an additional
parameter to specify the constant value that should be used.
@@ 150,19 +152,19 @@
Correlation and convolution

 The {correlate1d} function calculates a onedimensional correlation
+ The :func:`correlate1d` function calculates a onedimensional correlation
along the given axis. The lines of the array along the given axis
 are correlated with the given {weights}. The {weights} parameter
+ are correlated with the given *weights*. The *weights* parameter
must be a onedimensional sequences of numbers.
 The function {correlate} implements multidimensional correlation
+ The function :func:`correlate` implements multidimensional correlation
of the input array with a given kernel.
 The {convolve1d} function calculates a onedimensional convolution
+ The :func:`convolve1d` function calculates a onedimensional convolution
along the given axis. The lines of the array along the given axis
 are convoluted with the given {weights}. The {weights} parameter
+ are convoluted with the given *weights*. The *weights* parameter
must be a onedimensional sequences of numbers.
{A convolution is essentially a correlation after mirroring the
@@ 170,7 +172,7 @@
in the case of a correlation: the result is shifted in the opposite
directions.}
 The function {convolve} implements multidimensional convolution of
+ The function :func:`convolve` implements multidimensional convolution of
the input array with a given kernel.
{A convolution is essentially a correlation after mirroring the
@@ 178,31 +180,31 @@
in the case of a correlation: the results is shifted in the opposite
direction.}
.. _ndimage_filter_functions_smoothing:
+.. _ndimagefilterfunctionssmoothing:
Smoothing filters

 The {gaussian_filter1d} function implements a onedimensional
+ The :func:`gaussian_filter1d` function implements a onedimensional
Gaussian filter. The standarddeviation of the Gaussian filter is
 passed through the parameter {sigma}. Setting {order}=0 corresponds
+ passed through the parameter *sigma*. Setting *order* = 0 corresponds
to convolution with a Gaussian kernel. An order of 1, 2, or 3
corresponds to convolution with the first, second or third
derivatives of a Gaussian. Higher order derivatives are not
implemented.
 The {gaussian_filter} function implements a multidimensional
+ The :func:`gaussian_filter` function implements a multidimensional
Gaussian filter. The standarddeviations of the Gaussian filter
 along each axis are passed through the parameter {sigma} as a
 sequence or numbers. If {sigma} is not a sequence but a single
+ along each axis are passed through the parameter *sigma* as a
+ sequence or numbers. If *sigma* is not a sequence but a single
number, the standard deviation of the filter is equal along all
directions. The order of the filter can be specified separately for
each axis. An order of 0 corresponds to convolution with a Gaussian
kernel. An order of 1, 2, or 3 corresponds to convolution with the
first, second or third derivatives of a Gaussian. Higher order
 derivatives are not implemented. The {order} parameter must be a
+ derivatives are not implemented. The *order* parameter must be a
number, to specify the same order for all axes, or a sequence of
numbers to specify a different order for each axis.
@@ 214,13 +216,13 @@
prevented by specifying a more precise output type.}
 The {uniform_filter1d} function calculates a onedimensional
 uniform filter of the given {size} along the given axis.
+ The :func:`uniform_filter1d` function calculates a onedimensional
+ uniform filter of the given *size* along the given axis.
 The {uniform_filter} implements a multidimensional uniform
+ The :func:`uniform_filter` implements a multidimensional uniform
filter. The sizes of the uniform filter are given for each axis as
 a sequence of integers by the {size} parameter. If {size} is not a
+ a sequence of integers by the *size* parameter. If *size* is not a
sequence, but a single number, the sizes along all axis are assumed
to be equal.
@@ 236,59 +238,59 @@
Filters based on order statistics

 The {minimum_filter1d} function calculates a onedimensional
 minimum filter of given {size} along the given axis.
+ The :func:`minimum_filter1d` function calculates a onedimensional
+ minimum filter of given *size* along the given axis.
 The {maximum_filter1d} function calculates a onedimensional
 maximum filter of given {size} along the given axis.
+ The :func:`maximum_filter1d` function calculates a onedimensional
+ maximum filter of given *size* along the given axis.
 The {minimum_filter} function calculates a multidimensional
+ The :func:`minimum_filter` function calculates a multidimensional
minimum filter. Either the sizes of a rectangular kernel or the
 footprint of the kernel must be provided. The {size} parameter, if
+ footprint of the kernel must be provided. The *size* parameter, if
provided, must be a sequence of sizes or a single number in which
case the size of the filter is assumed to be equal along each axis.
 The {footprint}, if provided, must be an array that defines the
+ The *footprint*, if provided, must be an array that defines the
shape of the kernel by its nonzero elements.
 The {maximum_filter} function calculates a multidimensional
+ The :func:`maximum_filter` function calculates a multidimensional
maximum filter. Either the sizes of a rectangular kernel or the
 footprint of the kernel must be provided. The {size} parameter, if
+ footprint of the kernel must be provided. The *size* parameter, if
provided, must be a sequence of sizes or a single number in which
case the size of the filter is assumed to be equal along each axis.
 The {footprint}, if provided, must be an array that defines the
+ The *footprint*, if provided, must be an array that defines the
shape of the kernel by its nonzero elements.
 The {rank_filter} function calculates a multidimensional rank
 filter. The {rank} may be less then zero, i.e., {rank}=1 indicates
+ The :func:`rank_filter` function calculates a multidimensional rank
+ filter. The *rank* may be less then zero, i.e., *rank* =1 indicates
the largest element. Either the sizes of a rectangular kernel or
 the footprint of the kernel must be provided. The {size} parameter,
+ the footprint of the kernel must be provided. The *size* parameter,
if provided, must be a sequence of sizes or a single number in
which case the size of the filter is assumed to be equal along each
 axis. The {footprint}, if provided, must be an array that defines
+ axis. The *footprint*, if provided, must be an array that defines
the shape of the kernel by its nonzero elements.
 The {percentile_filter} function calculates a multidimensional
 percentile filter. The {percentile} may be less then zero, i.e.,
 {percentile}=20 equals {percentile}=80. Either the sizes of a
+ The :func:`percentile_filter` function calculates a multidimensional
+ percentile filter. The *percentile* may be less then zero, i.e.,
+ *percentile* =20 equals *percentile* =80. Either the sizes of a
rectangular kernel or the footprint of the kernel must be provided.
 The {size} parameter, if provided, must be a sequence of sizes or a
+ The *size* parameter, if provided, must be a sequence of sizes or a
single number in which case the size of the filter is assumed to be
 equal along each axis. The {footprint}, if provided, must be an
+ equal along each axis. The *footprint*, if provided, must be an
array that defines the shape of the kernel by its nonzero
elements.
 The {median_filter} function calculates a multidimensional median
+ The :func:`median_filter` function calculates a multidimensional median
filter. Either the sizes of a rectangular kernel or the footprint
 of the kernel must be provided. The {size} parameter, if provided,
+ of the kernel must be provided. The *size* parameter, if provided,
must be a sequence of sizes or a single number in which case the
size of the filter is assumed to be equal along each axis. The
 {footprint} if provided, must be an array that defines the shape of
+ *footprint* if provided, must be an array that defines the shape of
the kernel by its nonzero elements.
@@ 297,15 +299,15 @@
Derivative filters can be constructed in several ways. The function
{gaussian_filter1d} described in section
:ref:`_ndimage_filter_functions_smoothing` can be used to calculate
derivatives along a given axis using the {order} parameter. Other
+:ref:`ndimagefilterfunctionssmoothing` can be used to calculate
+derivatives along a given axis using the *order* parameter. Other
derivative filters are the Prewitt and Sobel filters:
 The {prewitt} function calculates a derivative along the given
+ The :func:`prewitt` function calculates a derivative along the given
axis.
 The {sobel} function calculates a derivative along the given
+ The :func:`sobel` function calculates a derivative along the given
axis.
@@ 316,21 +318,21 @@
calculate the second derivative along a given direction and to
construct the Laplace filter:
 The function {generic_laplace} calculates a laplace filter using
 the function passed through {derivative2} to calculate second
 derivatives. The function {derivative2} should have the following
+ The function :func:`generic_laplace` calculates a laplace filter using
+ the function passed through :func:`derivative2` to calculate second
+ derivatives. The function :func:`derivative2` should have the following
signature:
{derivative2(input, axis, output, mode, cval, \*extra_arguments, \*\*extra_keywords)}
It should calculate the second derivative along the dimension
 {axis}. If {output} is not {None} it should use that for the output
 and return {None}, otherwise it should return the result. {mode},
 {cval} have the usual meaning.
+ *axis*. If *output* is not {None} it should use that for the output
+ and return {None}, otherwise it should return the result. *mode*,
+ *cval* have the usual meaning.
 The {extra_arguments} and {extra_keywords} arguments can be used
+ The *extra_arguments* and *extra_keywords* arguments can be used
to pass a tuple of extra arguments and a dictionary of named
 arguments that are passed to {derivative2} at each call.
+ arguments that are passed to :func:`derivative2` at each call.
For example:
@@ 348,7 +350,7 @@
[ 0 0 1 0 0]
[ 0 0 0 0 0]]
 To demonstrate the use of the {extra_arguments} argument we could
+ To demonstrate the use of the *extra_arguments* argument we could
do:
::
@@ 378,44 +380,44 @@
The following two functions are implemented using
{generic_laplace} by providing appropriate functions for the
+:func:`generic_laplace` by providing appropriate functions for the
second derivative function:
 The function {laplace} calculates the Laplace using discrete
+ The function :func:`laplace` calculates the Laplace using discrete
differentiation for the second derivative (i.e. convolution with
{[1, 2, 1]}).
 The function {gaussian_laplace} calculates the Laplace using
 {gaussian_filter} to calculate the second derivatives. The
+ The function :func:`gaussian_laplace` calculates the Laplace using
+ :func:`gaussian_filter` to calculate the second derivatives. The
standarddeviations of the Gaussian filter along each axis are
 passed through the parameter {sigma} as a sequence or numbers. If
 {sigma} is not a sequence but a single number, the standard
+ passed through the parameter *sigma* as a sequence or numbers. If
+ *sigma* is not a sequence but a single number, the standard
deviation of the filter is equal along all directions.
The gradient magnitude is defined as the square root of the sum of
the squares of the gradients in all directions. Similar to the
generic Laplace function there is a {generic_gradient_magnitude}
+generic Laplace function there is a :func:`generic_gradient_magnitude`
function that calculated the gradient magnitude of an array:
 The function {generic_gradient_magnitude} calculates a gradient
 magnitude using the function passed through {derivative} to
 calculate first derivatives. The function {derivative} should have
+ The function :func:`generic_gradient_magnitude` calculates a gradient
+ magnitude using the function passed through :func:`derivative` to
+ calculate first derivatives. The function :func:`derivative` should have
the following signature:
{derivative(input, axis, output, mode, cval, \*extra_arguments, \*\*extra_keywords)}
 It should calculate the derivative along the dimension {axis}. If
 {output} is not {None} it should use that for the output and return
 {None}, otherwise it should return the result. {mode}, {cval} have
+ It should calculate the derivative along the dimension *axis*. If
+ *output* is not {None} it should use that for the output and return
+ {None}, otherwise it should return the result. *mode*, *cval* have
the usual meaning.
 The {extra_arguments} and {extra_keywords} arguments can be used
+ The *extra_arguments* and *extra_keywords* arguments can be used
to pass a tuple of extra arguments and a dictionary of named
 arguments that are passed to {derivative} at each call.
+ arguments that are passed to *derivative* at each call.
 For example, the {sobel} function fits the required signature:
+ For example, the :func:`sobel` function fits the required signature:
::
@@ 428,28 +430,28 @@
[0 1 2 1 0]
[0 0 0 0 0]]
 See the documentation of {generic_laplace} for examples of using
 the {extra_arguments} and {extra_keywords} arguments.
+ See the documentation of :func:`generic_laplace` for examples of using
+ the *extra_arguments* and *extra_keywords* arguments.
The {sobel} and {prewitt} functions fit the required signature and
can therefore directly be used with {generic_gradient_magnitude}.
+The :func:`sobel` and :func:`prewitt` functions fit the required signature and
+can therefore directly be used with :func:`generic_gradient_magnitude`.
The following function implements the gradient magnitude using
Gaussian derivatives:
 The function {gaussian_gradient_magnitude} calculates the
 gradient magnitude using {gaussian_filter} to calculate the first
+ The function :func:`gaussian_gradient_magnitude` calculates the
+ gradient magnitude using :func:`gaussian_filter` to calculate the first
derivatives. The standarddeviations of the Gaussian filter along
 each axis are passed through the parameter {sigma} as a sequence or
 numbers. If {sigma} is not a sequence but a single number, the
+ each axis are passed through the parameter *sigma* as a sequence or
+ numbers. If *sigma* is not a sequence but a single number, the
standard deviation of the filter is equal along all directions.
+.. _ndimagegenericfilters:
+
Generic filter functions

.. _ndimage_genericfilters:

To implement filter functions, generic functions can be used that accept a
callable object that implements the filtering operation. The iteration over the
input and output arrays is handled by these generic functions, along with such
@@ 457,17 +459,17 @@
callable object implementing a callback function that does the
actual filtering work must be provided. The callback function can
also be written in C and passed using a CObject (see
:ref:`_ndimage_ccallbacks` for more information).
+:ref:`ndimageccallbacks` for more information).
 The {generic_filter1d} function implements a generic
+ The :func:`generic_filter1d` function implements a generic
onedimensional filter function, where the actual filtering
operation must be supplied as a python function (or other callable
 object). The {generic_filter1d} function iterates over the lines
 of an array and calls {function} at each line. The arguments that
 are passed to {function} are onedimensional arrays of the
+ object). The :func:`generic_filter1d` function iterates over the lines
+ of an array and calls :func:`function` at each line. The arguments that
+ are passed to :func:`function` are onedimensional arrays of the
{tFloat64} type. The first contains the values of the current line.
It is extended at the beginning end the end, according to the
 {filter_size} and {origin} arguments. The second array should be
+ *filter_size* and *origin* arguments. The second array should be
modified inplace to provide the output values of the line. For
example consider a correlation along one dimension:
@@ 479,7 +481,7 @@
[27 32 38 41]
[51 56 62 65]]
 The same operation can be implemented using {generic_filter1d} as
+ The same operation can be implemented using :func:`generic_filter1d` as
follows:
::
@@ 498,7 +500,7 @@
function was called.
Optionally extra arguments can be defined and passed to the filter
 function. The {extra_arguments} and {extra_keywords} arguments
+ function. The *extra_arguments* and *extra_keywords* arguments
can be used to pass a tuple of extra arguments and/or a dictionary
of named arguments that are passed to derivative at each call. For
example, we can pass the parameters of our filter as an argument:
@@ 523,11 +525,11 @@
[51 56 62 65]]
 The {generic_filter} function implements a generic filter
+ The :func:`generic_filter` function implements a generic filter
function, where the actual filtering operation must be supplied as
 a python function (or other callable object). The {generic_filter}
 function iterates over the array and calls {function} at each
 element. The argument of {function} is a onedimensional array of
+ a python function (or other callable object). The :func:`generic_filter`
+ function iterates over the array and calls :func:`function` at each
+ element. The argument of :func:`function` is a onedimensional array of
the {tFloat64} type, that contains the values around the current
element that are within the footprint of the filter. The function
should return a single value that can be converted to a double
@@ 541,7 +543,7 @@
[12 15 19 23]
[28 31 35 39]]
 The same operation can be implemented using {generic_filter} as
+ The same operation can be implemented using *generic_filter* as
follows:
::
@@ 559,15 +561,15 @@
equal to two, which was multiplied with the proper weights and the
result summed.
 When calling {generic_filter}, either the sizes of a rectangular
 kernel or the footprint of the kernel must be provided. The {size}
+ When calling :func:`generic_filter`, either the sizes of a rectangular
+ kernel or the footprint of the kernel must be provided. The *size*
parameter, if provided, must be a sequence of sizes or a single
number in which case the size of the filter is assumed to be equal
 along each axis. The {footprint}, if provided, must be an array
+ along each axis. The *footprint*, if provided, must be an array
that defines the shape of the kernel by its nonzero elements.
Optionally extra arguments can be defined and passed to the filter
 function. The {extra_arguments} and {extra_keywords} arguments
+ function. The *extra_arguments* and *extra_keywords* arguments
can be used to pass a tuple of extra arguments and/or a dictionary
of named arguments that are passed to derivative at each call. For
example, we can pass the parameters of our filter as an argument:
@@ 599,7 +601,7 @@
the filter dependening on spatial location. Here is an example of
using a class that implements the filter and keeps track of the
current coordinates while iterating. It performs the same filter
operation as described above for {generic_filter}, but
+operation as described above for :func:`generic_filter`, but
additionally prints the current coordinates:
::
@@ 645,9 +647,9 @@
[12 15 19 23]
[28 31 35 39]]
For the {generic_filter1d} function the same approach works,
+For the :func:`generic_filter1d` function the same approach works,
except that this function does not iterate over the axis that is
being filtered. The example for {generic_filte1d} then becomes
+being filtered. The example for :func:`generic_filter1d` then becomes
this:
::
@@ 688,53 +690,53 @@
[51 56 62 65]]
Fourier domain filters
======================
+
The functions described in this section perform filtering
operations in the Fourier domain. Thus, the input array of such a
function should be compatible with an inverse Fourier transform
function, such as the functions from the {numarray.fft} module. We
+function, such as the functions from the {scipy.fft} module. We
therefore have to deal with arrays that may be the result of a real
or a complex Fourier transform. In the case of a real Fourier
transform only half of the of the symmetric complex transform is
stored. Additionally, it needs to be known what the length of the
axis was that was transformed by the real fft. The functions
described here provide a parameter {n} that in the case of a real
+described here provide a parameter *n* that in the case of a real
transform must be equal to the length of the real transform axis
before transformation. If this parameter is less than zero, it is
assumed that the input array was the result of a complex Fourier
transform. The parameter {axis} can be used to indicate along which
+transform. The parameter *axis* can be used to indicate along which
axis the real transform was executed.
 The {fourier_shift} function multiplies the input array with the
+ The :func:`fourier_shift` function multiplies the input array with the
multidimensional Fourier transform of a shift operation for the
 given shift. The {shift} parameter is a sequences of shifts for
+ given shift. The *shift* parameter is a sequences of shifts for
each dimension, or a single value for all dimensions.
 The {fourier_gaussian} function multiplies the input array with
+ The :func:`fourier_gaussian` function multiplies the input array with
the multidimensional Fourier transform of a Gaussian filter with
 given standarddeviations {sigma}. The {sigma} parameter is a
+ given standarddeviations *sigma*. The *sigma* parameter is a
sequences of values for each dimension, or a single value for all
dimensions.
 The {fourier_uniform} function multiplies the input array with the
+ The :func:`fourier_uniform` function multiplies the input array with the
multidimensional Fourier transform of a uniform filter with given
 sizes {size}. The {size} parameter is a sequences of values for
+ sizes *size*. The *size* parameter is a sequences of values for
each dimension, or a single value for all dimensions.
 The {fourier_ellipsoid} function multiplies the input array with
+ The :func:`fourier_ellipsoid` function multiplies the input array with
the multidimensional Fourier transform of a elliptically shaped
 filter with given sizes {size}. The {size} parameter is a sequences
+ filter with given sizes *size*. The *size* parameter is a sequences
of values for each dimension, or a single value for all dimensions.
{This function is
only implemented for dimensions 1, 2, and 3.}
Interpolation functions
=======================
+
This section describes various interpolation functions that are
based on Bspline theory. A good introduction to Bsplines can be
@@ 743,22 +745,22 @@
2238, November 1999. {Spline prefilters} Interpolation using
splines of an order larger than 1 requires a pre filtering step.
The interpolation functions described in section
:ref:`_ndimage_interpolation` apply prefiltering by calling
{spline_filter}, but they can be instructed not to do this by
setting the {prefilter} keyword equal to {False}. This is useful if
+:ref:`ndimageinterpolation` apply prefiltering by calling
+:func:`spline_filter`, but they can be instructed not to do this by
+setting the *prefilter* keyword equal to {False}. This is useful if
more than one interpolation operation is done on the same array. In
this case it is more efficient to do the prefiltering only once
and use a prefiltered array as the input of the interpolation
functions. The following two functions implement the
prefiltering:
 The {spline_filter1d} function calculates a onedimensional spline
+ The :func:`spline_filter1d` function calculates a onedimensional spline
filter along the given axis. An output array can optionally be
provided. The order of the spline must be larger then 1 and less
than 6.
 The {spline_filter} function calculates a multidimensional spline
+ The :func:`spline_filter` function calculates a multidimensional spline
filter.
{The multidimensional filter is implemented as a sequence of
@@ 769,25 +771,25 @@
This can be prevented by specifying a output type of high precision.}
+.. _ndimageinterpolation:
+
Interpolation functions

.. _ndimage_interpolation:

Following functions all employ spline interpolation to effect some type of
geometric transformation of the input array. This requires a mapping of the
output coordinates to the input coordinates, and therefore the possibility
arises that input values outside the boundaries are needed. This problem is
solved in the same way as described in section :ref:`_ndimage_filter_functions`
+solved in the same way as described in section :ref:`ndimagefilterfunctions`
for the multidimensional filter functions. Therefore these functions all
support a {mode} parameter that determines how the boundaries are handled, and
a {cval} parameter that gives a constant value in case that the {'constant'}
+support a *mode* parameter that determines how the boundaries are handled, and
+a *cval* parameter that gives a constant value in case that the {'constant'}
mode is used.
 The {geometric_transform} function applies an arbitrary geometric
 transform to the input. The given {mapping} function is called at
+ The :func:`geometric_transform` function applies an arbitrary geometric
+ transform to the input. The given *mapping* function is called at
each point in the output to find the corresponding coordinates in
 the input. {mapping} must be a callable object that accepts a tuple
+ the input. *mapping* must be a callable object that accepts a tuple
of length equal to the output array rank and returns the
corresponding input coordinates as a tuple of length equal to the
input array rank. The output shape and output type can optionally
@@ 809,7 +811,7 @@
[ 0. 8.2625 9.6375]]
Optionally extra arguments can be defined and passed to the filter
 function. The {extra_arguments} and {extra_keywords} arguments
+ function. The *extra_arguments* and *extra_keywords* arguments
can be used to pass a tuple of extra arguments and/or a dictionary
of named arguments that are passed to derivative at each call. For
example, we can pass the shifts in our example as arguments:
@@ 835,17 +837,17 @@
[ 0. 4.8125 6.1875]
[ 0. 8.2625 9.6375]]
 {The mapping function can also be written in C and passed using a CObject. See :ref:`_ndimage_ccallbacks` for more information.}
+ {The mapping function can also be written in C and passed using a CObject. See :ref:`ndimageccallbacks` for more information.}
 The function {map_coordinates} applies an arbitrary coordinate
+ The function :func:`map_coordinates` applies an arbitrary coordinate
transformation using the given array of coordinates. The shape of
the output is derived from that of the coordinate array by dropping
 the first axis. The parameter {coordinates} is used to find for
+ the first axis. The parameter *coordinates* is used to find for
each point in the output the corresponding coordinates in the
 input. The values of {coordinates} along the first axis are the
+ input. The values of *coordinates* along the first axis are the
coordinates in the input array at which the output value is found.
 (See also the numarray {coordinates} function.) Since the
+ (See also the numarray *coordinates* function.) Since the
coordinates may be non integer coordinates, the value of the input
at these coordinates is determined by spline interpolation of the
requested order. Here is an example that interpolates a 2D array at
@@ 863,12 +865,12 @@
[ 1.3625 7. ]
 The {affine_transform} function applies an affine transformation
 to the input array. The given transformation {matrix} and {offset}
+ The :func:`affine_transform` function applies an affine transformation
+ to the input array. The given transformation *matrix* and *offset*
are used to find for each point in the output the corresponding
coordinates in the input. The value of the input at the calculated
coordinates is determined by spline interpolation of the requested
 order. The transformation {matrix} must be twodimensional or can
+ order. The transformation *matrix* must be twodimensional or can
also be given as a onedimensional sequence or array. In the latter
case, it is assumed that the matrix is diagonal. A more efficient
interpolation algorithm is then applied that exploits the
@@ 877,33 +879,33 @@
shape and type.
 The {shift} function returns a shifted version of the input, using
 spline interpolation of the requested {order}.
+ The :func:`shift` function returns a shifted version of the input, using
+ spline interpolation of the requested *order*.
 The {zoom} function returns a rescaled version of the input, using
 spline interpolation of the requested {order}.
+ The :func:`zoom` function returns a rescaled version of the input, using
+ spline interpolation of the requested *order*.
 The {rotate} function returns the input array rotated in the plane
 defined by the two axes given by the parameter {axes}, using spline
 interpolation of the requested {order}. The angle must be given in
 degrees. If {reshape} is true, then the size of the output array is
+ The :func:`rotate` function returns the input array rotated in the plane
+ defined by the two axes given by the parameter *axes*, using spline
+ interpolation of the requested *order*. The angle must be given in
+ degrees. If *reshape* is true, then the size of the output array is
adapted to contain the rotated input.
+.. _ndimagebinarymorphology:
+
Binary morphology
=================
+
.. _ndimage_binary_morphology:

 The {generate_binary_structure} functions generates a binary
+ The :func:`generate_binary_structure` functions generates a binary
structuring element for use in binary morphology operations. The
 {rank} of the structure must be provided. The size of the structure
+ *rank* of the structure must be provided. The size of the structure
that is returned is equal to three in each direction. The value of
each element is equal to one if the square of the Euclidean
distance from the element to the center is less or equal to
 {connectivity}. For instance, two dimensional 4connected and
+ *connectivity*. For instance, two dimensional 4connected and
8connected structures are generated as follows:
::
@@ 921,34 +923,34 @@
Most binary morphology functions can be expressed in terms of the
basic operations erosion and dilation:
 The {binary_erosion} function implements binary erosion of arrays
+ The :func:`binary_erosion` function implements binary erosion of arrays
of arbitrary rank with the given structuring element. The origin
parameter controls the placement of the structuring element as
 described in section :ref:`_ndimage_filter_functions`. If no
+ described in section :ref:`ndimagefilterfunctions`. If no
structuring element is provided, an element with connectivity equal
 to one is generated using {generate_binary_structure}. The
 {border_value} parameter gives the value of the array outside
 boundaries. The erosion is repeated {iterations} times. If
 {iterations} is less than one, the erosion is repeated until the
 result does not change anymore. If a {mask} array is given, only
+ to one is generated using :func:`generate_binary_structure`. The
+ *border_value* parameter gives the value of the array outside
+ boundaries. The erosion is repeated *iterations* times. If
+ *iterations* is less than one, the erosion is repeated until the
+ result does not change anymore. If a *mask* array is given, only
those elements with a true value at the corresponding mask element
are modified at each iteration.
 The {binary_dilation} function implements binary dilation of
+ The :func:`binary_dilation` function implements binary dilation of
arrays of arbitrary rank with the given structuring element. The
origin parameter controls the placement of the structuring element
 as described in section :ref:`_ndimage_filter_functions`. If no
+ as described in section :ref:`ndimagefilterfunctions`. If no
structuring element is provided, an element with connectivity equal
 to one is generated using {generate_binary_structure}. The
 {border_value} parameter gives the value of the array outside
 boundaries. The dilation is repeated {iterations} times. If
 {iterations} is less than one, the dilation is repeated until the
 result does not change anymore. If a {mask} array is given, only
+ to one is generated using :func:`generate_binary_structure`. The
+ *border_value* parameter gives the value of the array outside
+ boundaries. The dilation is repeated *iterations* times. If
+ *iterations* is less than one, the dilation is repeated until the
+ result does not change anymore. If a *mask* array is given, only
those elements with a true value at the corresponding mask element
are modified at each iteration.
 Here is an example of using {binary_dilation} to find all elements
+ Here is an example of using :func:`binary_dilation` to find all elements
that touch the border, by repeatedly dilating an empty array from
the border using the data array as the mask:
@@ 968,16 +970,16 @@
[0 0 0 0 0]]
The {binary_erosion} and {binary_dilation} functions both have an
{iterations} parameter which allows the erosion or dilation to be
+The :func:`binary_erosion` and :func:`binary_dilation` functions both have an
+*iterations* parameter which allows the erosion or dilation to be
repeated a number of times. Repeating an erosion or a dilation with
a given structure {n} times is equivalent to an erosion or a
+a given structure *n* times is equivalent to an erosion or a
dilation with a structure that is {n1} times dilated with itself.
A function is provided that allows the calculation of a structure
that is dilated a number of times with itself:
 The {iterate_structure} function returns a structure by dilation
 of the input structure {iteration}  1 times with itself. For
+ The :func:`iterate_structure` function returns a structure by dilation
+ of the input structure *iteration*  1 times with itself. For
instance:
::
@@ 996,11 +998,11 @@
If the origin of the original structure is equal to 0, then it is
also equal to 0 for the iterated structure. If not, the origin must
 also be adapted if the equivalent of the {iterations} erosions or
+ also be adapted if the equivalent of the *iterations* erosions or
dilations must be achieved with the iterated structure. The adapted
origin is simply obtained by multiplying with the number of
 iterations. For convenience the {iterate_structure} also returns
 the adapted origin if the {origin} parameter is not {None}:
+ iterations. For convenience the :func:`iterate_structure` also returns
+ the adapted origin if the *origin* parameter is not {None}:
::
@@ 1016,151 +1018,149 @@
d dilation. Following functions provide a few of these operations
for convenience:
 The {binary_opening} function implements binary opening of arrays
+ The :func:`binary_opening` function implements binary opening of arrays
of arbitrary rank with the given structuring element. Binary
opening is equivalent to a binary erosion followed by a binary
dilation with the same structuring element. The origin parameter
controls the placement of the structuring element as described in
 section :ref:`_ndimage_filter_functions`. If no structuring element is
+ section :ref:`ndimagefilterfunctions`. If no structuring element is
provided, an element with connectivity equal to one is generated
 using {generate_binary_structure}. The {iterations} parameter
+ using :func:`generate_binary_structure`. The *iterations* parameter
gives the number of erosions that is performed followed by the same
number of dilations.
 The {binary_closing} function implements binary closing of arrays
+ The :func:`binary_closing` function implements binary closing of arrays
of arbitrary rank with the given structuring element. Binary
closing is equivalent to a binary dilation followed by a binary
erosion with the same structuring element. The origin parameter
controls the placement of the structuring element as described in
 section :ref:`_ndimage_filter_functions`. If no structuring element is
+ section :ref:`ndimagefilterfunctions`. If no structuring element is
provided, an element with connectivity equal to one is generated
 using {generate_binary_structure}. The {iterations} parameter
+ using :func:`generate_binary_structure`. The *iterations* parameter
gives the number of dilations that is performed followed by the
same number of erosions.
 The {binary_fill_holes} function is used to close holes in
+ The :func:`binary_fill_holes` function is used to close holes in
objects in a binary image, where the structure defines the
connectivity of the holes. The origin parameter controls the
placement of the structuring element as described in section
 :ref:`_ndimage_filter_functions`. If no structuring element is
+ :ref:`ndimagefilterfunctions`. If no structuring element is
provided, an element with connectivity equal to one is generated
 using {generate_binary_structure}.
+ using :func:`generate_binary_structure`.
 The {binary_hit_or_miss} function implements a binary
+ The :func:`binary_hit_or_miss` function implements a binary
hitormiss transform of arrays of arbitrary rank with the given
structuring elements. The hitormiss transform is calculated by
erosion of the input with the first structure, erosion of the
logical *not* of the input with the second structure, followed by
the logical *and* of these two erosions. The origin parameters
control the placement of the structuring elements as described in
 section :ref:`_ndimage_filter_functions`. If {origin2} equals {None} it
+ section :ref:`ndimagefilterfunctions`. If {origin2} equals {None} it
is set equal to the {origin1} parameter. If the first structuring
element is not provided, a structuring element with connectivity
 equal to one is generated using {generate_binary_structure}, if
+ equal to one is generated using :func:`generate_binary_structure`, if
{structure2} is not provided, it is set equal to the logical *not*
of {structure1}.
+.. _ndimagegreymorphology:
+
Greyscale morphology
=====================
+
.. _ndimage_grey_morphology:



Greyscale morphology operations are the equivalents of binary
morphology operations that operate on arrays with arbitrary values.
Below we describe the greyscale equivalents of erosion, dilation,
opening and closing. These operations are implemented in a similar
fashion as the filters described in section
:ref:`_ndimage_filter_functions`, and we refer to this section for the
+:ref:`ndimagefilterfunctions`, and we refer to this section for the
description of filter kernels and footprints, and the handling of
array borders. The greyscale morphology operations optionally take
a {structure} parameter that gives the values of the structuring
+a *structure* parameter that gives the values of the structuring
element. If this parameter is not given the structuring element is
assumed to be flat with a value equal to zero. The shape of the
structure can optionally be defined by the {footprint} parameter.
+structure can optionally be defined by the *footprint* parameter.
If this parameter is not given, the structure is assumed to be
rectangular, with sizes equal to the dimensions of the {structure}
array, or by the {size} parameter if {structure} is not given. The
{size} parameter is only used if both {structure} and {footprint}
+rectangular, with sizes equal to the dimensions of the *structure*
+array, or by the *size* parameter if *structure* is not given. The
+*size* parameter is only used if both *structure* and *footprint*
are not given, in which case the structuring element is assumed to
be rectangular and flat with the dimensions given by {size}. The
{size} parameter, if provided, must be a sequence of sizes or a
+be rectangular and flat with the dimensions given by *size*. The
+*size* parameter, if provided, must be a sequence of sizes or a
single number in which case the size of the filter is assumed to be
equal along each axis. The {footprint} parameter, if provided, must
+equal along each axis. The *footprint* parameter, if provided, must
be an array that defines the shape of the kernel by its nonzero
elements.
Similar to binary erosion and dilation there are operations for
greyscale erosion and dilation:
 The {grey_erosion} function calculates a multidimensional grey
+ The :func:`grey_erosion` function calculates a multidimensional grey
scale erosion.
 The {grey_dilation} function calculates a multidimensional grey
+ The :func:`grey_dilation` function calculates a multidimensional grey
scale dilation.
Greyscale opening and closing operations can be defined similar to
their binary counterparts:
 The {grey_opening} function implements greyscale opening of
+ The :func:`grey_opening` function implements greyscale opening of
arrays of arbitrary rank. Greyscale opening is equivalent to a
greyscale erosion followed by a greyscale dilation.
 The {grey_closing} function implements greyscale closing of
+ The :func:`grey_closing` function implements greyscale closing of
arrays of arbitrary rank. Greyscale opening is equivalent to a
greyscale dilation followed by a greyscale erosion.
 The {morphological_gradient} function implements a greyscale
+ The :func:`morphological_gradient` function implements a greyscale
morphological gradient of arrays of arbitrary rank. The greyscale
morphological gradient is equal to the difference of a greyscale
dilation and a greyscale erosion.
 The {morphological_laplace} function implements a greyscale
+ The :func:`morphological_laplace` function implements a greyscale
morphological laplace of arrays of arbitrary rank. The greyscale
morphological laplace is equal to the sum of a greyscale dilation
and a greyscale erosion minus twice the input.
 The {white_tophat} function implements a white tophat filter of
+ The :func:`white_tophat` function implements a white tophat filter of
arrays of arbitrary rank. The white tophat is equal to the
difference of the input and a greyscale opening.
 The {black_tophat} function implements a black tophat filter of
+ The :func:`black_tophat` function implements a black tophat filter of
arrays of arbitrary rank. The black tophat is equal to the
difference of the a greyscale closing and the input.
+.. _ndimagedistancetransforms:
+
Distance transforms
===================
+
.. _ndimage_distance_transforms:

Distance transforms are used to
calculate the minimum distance from each element of an object to
the background. The following functions implement distance
transforms for three different distance metrics: Euclidean, City
Block, and Chessboard distances.
 The function {distance_transform_cdt} uses a chamfer type
+ The function :func:`distance_transform_cdt` uses a chamfer type
algorithm to calculate the distance transform of the input, by
replacing each object element (defined by values larger than zero)
with the shortest distance to the background (all nonobject
elements). The structure determines the type of chamfering that is
done. If the structure is equal to 'cityblock' a structure is
 generated using {generate_binary_structure} with a squared
+ generated using :func:`generate_binary_structure` with a squared
distance equal to 1. If the structure is equal to 'chessboard', a
 structure is generated using {generate_binary_structure} with a
+ structure is generated using :func:`generate_binary_structure` with a
squared distance equal to the rank of the array. These choices
correspond to the common interpretations of the cityblock and the
chessboard distancemetrics in two dimensions.
@@ 1168,11 +1168,11 @@
In addition to the distance transform, the feature transform can be
calculated. In this case the index of the closest background
element is returned along the first axis of the result. The
 {return_distances}, and {return_indices} flags can be used to
+ *return_distances*, and *return_indices* flags can be used to
indicate if the distance transform, the feature transform, or both
must be returned.
 The {distances} and {indices} arguments can be used to give
+ The *distances* and *indices* arguments can be used to give
optional output arrays that must be of the correct size and type
(both {Int32}).
@@ 1182,7 +1182,7 @@
27:321345, 1984.
 The function {distance_transform_edt} calculates the exact
+ The function :func:`distance_transform_edt` calculates the exact
euclidean distance transform of the input, by replacing each object
element (defined by values larger than zero) with the shortest
euclidean distance to the background (all nonobject elements).
@@ 1190,16 +1190,16 @@
In addition to the distance transform, the feature transform can be
calculated. In this case the index of the closest background
element is returned along the first axis of the result. The
 {return_distances}, and {return_indices} flags can be used to
+ *return_distances*, and *return_indices* flags can be used to
indicate if the distance transform, the feature transform, or both
must be returned.
Optionally the sampling along each axis can be given by the
 {sampling} parameter which should be a sequence of length equal to
+ *sampling* parameter which should be a sequence of length equal to
the input rank, or a single number in which the sampling is assumed
to be equal along all axes.
 The {distances} and {indices} arguments can be used to give
+ The *distances* and *indices* arguments can be used to give
optional output arrays that must be of the correct size and type
({Float64} and {Int32}).
@@ 1209,7 +1209,7 @@
in arbitrary dimensions. IEEE Trans. PAMI 25, 265270, 2003.
 The function {distance_transform_bf} uses a bruteforce algorithm
+ The function :func:`distance_transform_bf` uses a bruteforce algorithm
to calculate the distance transform of the input, by replacing each
object element (defined by values larger than zero) with the
shortest distance to the background (all nonobject elements). The
@@ 1219,17 +1219,17 @@
In addition to the distance transform, the feature transform can be
calculated. In this case the index of the closest background
element is returned along the first axis of the result. The
 {return_distances}, and {return_indices} flags can be used to
+ *return_distances*, and *return_indices* flags can be used to
indicate if the distance transform, the feature transform, or both
must be returned.
Optionally the sampling along each axis can be given by the
 {sampling} parameter which should be a sequence of length equal to
+ *sampling* parameter which should be a sequence of length equal to
the input rank, or a single number in which the sampling is assumed
to be equal along all axes. This parameter is only used in the case
of the euclidean distance transform.
 The {distances} and {indices} arguments can be used to give
+ The *distances* and *indices* arguments can be used to give
optional output arrays that must be of the correct size and type
({Float64} and {Int32}).
@@ 1241,11 +1241,11 @@
Segmentation and labeling
=========================
+
Segmentation is the process of separating objects of interest from
the background. The most simple approach is probably intensity
thresholding, which is easily done with {numarray} functions:
+thresholding, which is easily done with :mod:`numpy` functions:
::
@@ 1260,13 +1260,13 @@
[0 0 0 0 1 0]]
The result is a binary image, in which the individual objects still
need to be identified and labeled. The function {label} generates
+need to be identified and labeled. The function :func:`label` generates
an array where each object is assigned a unique number:
 The {label} function generates an array where the objects in the
+ The :func:`label` function generates an array where the objects in the
input are labeled with an integer index. It returns a tuple
consisting of the array of object labels and the number of objects
 found, unless the {output} parameter is given, in which case only
+ found, unless the *output* parameter is given, in which case only
the number of objects is returned. The connectivity of the objects
is defined by a structuring element. For instance, in two
dimensions using a fourconnected structuring element gives:
@@ 1297,7 +1297,7 @@
[0 0 0 0 1 0]]
If no structuring element is provided, one is generated by calling
 {generate_binary_structure} (see section :ref:`_ndimage_morphology`)
+ *generate_binary_structure* (see section :ref:`ndimagebinarymorphology`)
using a connectivity of one (which in 2D is the 4connected
structure of the first example). The input can be of any type, any
value not equal to zero is taken to be part of an object. This is
@@ 1323,13 +1323,13 @@
There is a large number of other approaches for segmentation, for
instance from an estimation of the borders of the objects that can
be obtained for instance by derivative filters. One such an
approach is watershed segmentation. The function {watershed_ift}
+approach is watershed segmentation. The function :func:`watershed_ift`
generates an array where each object is assigned a unique label,
from an array that localizes the object borders, generated for
instance by a gradient magnitude filter. It uses an array
containing initial markers for the objects:
 The {watershed_ift} function applies a watershed from markers
+ The :func:`watershed_ift` function applies a watershed from markers
algorithm, using an Iterative Forest Transform, as described in: P.
Felkel, R. Wegenkittl, and M. Bruckschwaiger, "Implementation and
Complexity of the WatershedfromMarkers Algorithm Computed as a
@@ 1390,7 +1390,7 @@
The result is that the object (marker=2) is smaller because the
second marker was processed earlier. This may not be the desired
effect if the first marker was supposed to designate a background
 object. Therefore {watershed_ift} treats markers with a negative
+ object. Therefore :func:`watershed_ift` treats markers with a negative
value explicitly as background markers and processes them after the
normal markers. For instance, replacing the first marker by a
negative marker gives a result similar to the first example:
@@ 1415,10 +1415,10 @@
The connectivity of the objects is defined by a structuring
element. If no structuring element is provided, one is generated by
 calling {generate_binary_structure} (see section
 :ref:`_ndimage_morphology`) using a connectivity of one (which in 2D is
 a 4connected structure.) For example, using an 8connected
 structure with the last example yields a different object:
+ calling :func:`generate_binary_structure` (see section
+ :ref:`ndimagebinarymorphology`) using a connectivity of one
+ (which in 2D is a 4connected structure.) For example, using
+ an 8connected structure with the last example yields a different object:
::
@@ 1437,14 +1437,14 @@
Object measurements
===================
+
Given an array of labeled objects, the properties of the individual
objects can be measured. The {find_objects} function can be used
+objects can be measured. The :func:`find_objects` function can be used
to generate a list of slices that for each object, give the
smallest subarray that fully contains the object:
 The {find_objects} finds all objects in a labeled array and
+ The :func:`find_objects` function finds all objects in a labeled array and
returns a list of slices that correspond to the smallest regions in
the array that contains the object. For instance:
@@ 1461,10 +1461,10 @@
[1 1 1]
[0 1 0]]
 {find_objects} returns slices for all objects, unless the
 {max_label} parameter is larger then zero, in which case only the
 first {max_label} objects are returned. If an index is missing in
 the {label} array, {None} is return instead of a slice. For
+ :func:`find_objects` returns slices for all objects, unless the
+ *max_label* parameter is larger then zero, in which case only the
+ first *max_label* objects are returned. If an index is missing in
+ the *label* array, {None} is return instead of a slice. For
example:
::
@@ 1473,7 +1473,7 @@
[(slice(0, 1, None),), None, (slice(2, 3, None),)]
The list of slices generated by {find_objects} is useful to find
+The list of slices generated by :func:`find_objects` is useful to find
the position and dimensions of the objects in the array, but can
also be used to perform measurements on the individual objects. Say
we want to find the sum of the intensities of an object in image:
@@ 1522,118 +1522,118 @@
>>> print sum(image, labels, [0, 2])
[178.0, 80.0]
The measurement functions described below all support the {index}
+The measurement functions described below all support the *index*
parameter to indicate which object(s) should be measured. The
default value of {index} is {None}. This indicates that all
+default value of *index* is {None}. This indicates that all
elements where the label is larger than zero should be treated as a
single object and measured. Thus, in this case the {labels} array
+single object and measured. Thus, in this case the *labels* array
is treated as a mask defined by the elements that are larger than
zero. If {index} is a number or a sequence of numbers it gives the
labels of the objects that are measured. If {index} is a sequence,
+zero. If *index* is a number or a sequence of numbers it gives the
+labels of the objects that are measured. If *index* is a sequence,
a list of the results is returned. Functions that return more than
one result, return their result as a tuple if {index} is a single
number, or as a tuple of lists, if {index} is a sequence.
+one result, return their result as a tuple if *index* is a single
+number, or as a tuple of lists, if *index* is a sequence.
 The {sum} function calculates the sum of the elements of the object
 with label(s) given by {index}, using the {labels} array for the
 object labels. If {index} is {None}, all elements with a nonzero
 label value are treated as a single object. If {label} is {None},
 all elements of {input} are used in the calculation.
+ The :func:`sum` function calculates the sum of the elements of the object
+ with label(s) given by *index*, using the *labels* array for the
+ object labels. If *index* is {None}, all elements with a nonzero
+ label value are treated as a single object. If *label* is {None},
+ all elements of *input* are used in the calculation.
 The {mean} function calculates the mean of the elements of the
 object with label(s) given by {index}, using the {labels} array for
 the object labels. If {index} is {None}, all elements with a
 nonzero label value are treated as a single object. If {label} is
 {None}, all elements of {input} are used in the calculation.
+ The :func:`mean` function calculates the mean of the elements of the
+ object with label(s) given by *index*, using the *labels* array for
+ the object labels. If *index* is {None}, all elements with a
+ nonzero label value are treated as a single object. If *label* is
+ {None}, all elements of *input* are used in the calculation.
 The {variance} function calculates the variance of the elements of
 the object with label(s) given by {index}, using the {labels} array
 for the object labels. If {index} is {None}, all elements with a
 nonzero label value are treated as a single object. If {label} is
 {None}, all elements of {input} are used in the calculation.
+ The :func:`variance` function calculates the variance of the elements of
+ the object with label(s) given by *index*, using the *labels* array
+ for the object labels. If *index* is {None}, all elements with a
+ nonzero label value are treated as a single object. If *label* is
+ {None}, all elements of *input* are used in the calculation.
 The {standard_deviation} function calculates the standard
+ The :func:`standard_deviation` function calculates the standard
deviation of the elements of the object with label(s) given by
 {index}, using the {labels} array for the object labels. If {index}
+ *index*, using the *labels* array for the object labels. If *index*
is {None}, all elements with a nonzero label value are treated as
 a single object. If {label} is {None}, all elements of {input} are
+ a single object. If *label* is {None}, all elements of *input* are
used in the calculation.
 The {minimum} function calculates the minimum of the elements of
 the object with label(s) given by {index}, using the {labels} array
 for the object labels. If {index} is {None}, all elements with a
 nonzero label value are treated as a single object. If {label} is
 {None}, all elements of {input} are used in the calculation.
+ The :func:`minimum` function calculates the minimum of the elements of
+ the object with label(s) given by *index*, using the *labels* array
+ for the object labels. If *index* is {None}, all elements with a
+ nonzero label value are treated as a single object. If *label* is
+ {None}, all elements of *input* are used in the calculation.
 The {maximum} function calculates the maximum of the elements of
 the object with label(s) given by {index}, using the {labels} array
 for the object labels. If {index} is {None}, all elements with a
 nonzero label value are treated as a single object. If {label} is
 {None}, all elements of {input} are used in the calculation.
+ The :func:`maximum` function calculates the maximum of the elements of
+ the object with label(s) given by *index*, using the *labels* array
+ for the object labels. If *index* is {None}, all elements with a
+ nonzero label value are treated as a single object. If *label* is
+ {None}, all elements of *input* are used in the calculation.
 The {minimum_position} function calculates the position of the
+ The :func:`minimum_position` function calculates the position of the
minimum of the elements of the object with label(s) given by
 {index}, using the {labels} array for the object labels. If {index}
+ *index*, using the *labels* array for the object labels. If *index*
is {None}, all elements with a nonzero label value are treated as
 a single object. If {label} is {None}, all elements of {input} are
+ a single object. If *label* is {None}, all elements of *input* are
used in the calculation.
 The {maximum_position} function calculates the position of the
+ The :func:`maximum_position` function calculates the position of the
maximum of the elements of the object with label(s) given by
 {index}, using the {labels} array for the object labels. If {index}
+ *index*, using the *labels* array for the object labels. If *index*
is {None}, all elements with a nonzero label value are treated as
 a single object. If {label} is {None}, all elements of {input} are
+ a single object. If *label* is {None}, all elements of *input* are
used in the calculation.
 The {extrema} function calculates the minimum, the maximum, and
+ The :func:`extrema` function calculates the minimum, the maximum, and
their positions, of the elements of the object with label(s) given
 by {index}, using the {labels} array for the object labels. If
 {index} is {None}, all elements with a nonzero label value are
 treated as a single object. If {label} is {None}, all elements of
 {input} are used in the calculation. The result is a tuple giving
+ by *index*, using the *labels* array for the object labels. If
+ *index* is {None}, all elements with a nonzero label value are
+ treated as a single object. If *label* is {None}, all elements of
+ *input* are used in the calculation. The result is a tuple giving
the minimum, the maximum, the position of the mininum and the
postition of the maximum. The result is the same as a tuple formed
 by the results of the functions {minimum}, {maximum},
 {minimum_position}, and {maximum_position} that are described
+ by the results of the functions *minimum*, *maximum*,
+ *minimum_position*, and *maximum_position* that are described
above.
 The {center_of_mass} function calculates the center of mass of
 the of the object with label(s) given by {index}, using the
 {labels} array for the object labels. If {index} is {None}, all
+ The :func:`center_of_mass` function calculates the center of mass of
+ the of the object with label(s) given by *index*, using the
+ *labels* array for the object labels. If *index* is {None}, all
elements with a nonzero label value are treated as a single
 object. If {label} is {None}, all elements of {input} are used in
+ object. If *label* is {None}, all elements of *input* are used in
the calculation.
 The {histogram} function calculates a histogram of the of the
 object with label(s) given by {index}, using the {labels} array for
 the object labels. If {index} is {None}, all elements with a
 nonzero label value are treated as a single object. If {label} is
 {None}, all elements of {input} are used in the calculation.
 Histograms are defined by their minimum ({min}), maximum ({max})
 and the number of bins ({bins}). They are returned as
+ The :func:`histogram` function calculates a histogram of the of the
+ object with label(s) given by *index*, using the *labels* array for
+ the object labels. If *index* is {None}, all elements with a
+ nonzero label value are treated as a single object. If *label* is
+ {None}, all elements of *input* are used in the calculation.
+ Histograms are defined by their minimum (*min*), maximum (*max*)
+ and the number of bins (*bins*). They are returned as
onedimensional arrays of type Int32.
Extending {nd_image} in C
============================
+.. _ndimageccallbacks:
.. _ndimage_ccallbacks:
+Extending *ndimage* in C
+
{C callback functions} A few functions in the {numarray.nd_image} take a callback argument. This can be a python function, but also a CObject containing a pointer to a C function. To use this feature, you must write your own C extension that defines the function, and define a python function that
+{C callback functions} A few functions in the {numarray.ndimage} take a callback argument. This can be a python function, but also a CObject containing a pointer to a C function. To use this feature, you must write your own C extension that defines the function, and define a python function that
returns a CObject containing a pointer to this function.
An example of a function that supports this is
{geometric_transform} (see section :ref:`_ndimage_interpolation`).
+:func:`geometric_transform` (see section :ref:`ndimageinterpolation`).
You can pass it a python callable object that defines a mapping
from all output coordinates to corresponding coordinates in the
input array. This mapping function can also be a C function, which
@@ 1660,17 +1660,17 @@
}
This function is called at every element of the output array,
passing the current coordinates in the {output_coordinates} array.
On return, the {input_coordinates} array must contain the
+passing the current coordinates in the *output_coordinates* array.
+On return, the *input_coordinates* array must contain the
coordinates at which the input is interpolated. The ranks of the
input and output array are passed through {output_rank} and
{input_rank}. The value of the shift is passed through the
{callback_data} argument, which is a pointer to void. The function
+input and output array are passed through *output_rank* and
+*input_rank*. The value of the shift is passed through the
+*callback_data* argument, which is a pointer to void. The function
returns an error status, in this case always 1, since no error can
occur.
A pointer to this function and a pointer to the shift value must be
passed to {geometric_transform}. Both are passed by a single
+passed to :func:`geometric_transform`. Both are passed by a single
CObject which is created by the following python extension
function:
@@ 1737,23 +1737,23 @@
[ 0. 4.8125 6.1875]
[ 0. 8.2625 9.6375]]
C Callback functions for use with {nd_image} functions must all
+C Callback functions for use with :mod:`ndimage` functions must all
be written according to this scheme. The next section lists the
{nd_image} functions that acccept a C callback function and
+:mod:`ndimage` functions that acccept a C callback function and
gives the prototype of the callback function.
Functions that support C callback functions

The {nd_image} functions that support C callback functions are
+The :func:`ndimage` functions that support C callback functions are
described here. Obviously, the prototype of the function that is
provided to these functions must match exactly that what they
expect. Therefore we give here the prototypes of the callback
functions. All these callback functions accept a void
{callback_data} pointer that must be wrapped in a CObject using
+*callback_data* pointer that must be wrapped in a CObject using
the Python {PyCObject_FromVoidPtrAndDesc} function, which can also
accept a pointer to a destructor function to free any memory
allocated for {callback_data}. If {callback_data} is not needed,
+allocated for *callback_data*. If *callback_data* is not needed,
{PyCObject_FromVoidPtr} may be used instead. The callback
functions must return an integer error status that is equal to zero
if something went wrong, or 1 otherwise. If an error occurs, you
@@ 1761,45 +1761,45 @@
message before returning, otherwise, a default error message is set
by the calling function.
The function {generic_filter} (see section
:ref:`_ndimage_genericfilters`) accepts a callback function with the
+The function :func:`generic_filter` (see section
+:ref:`ndimagegenericfilters`) accepts a callback function with the
following prototype:
The calling function iterates over the elements of the input and
output arrays, calling the callback function at each element. The
elements within the footprint of the filter at the current element
 are passed through the {buffer} parameter, and the number of
 elements within the footprint through {filter_size}. The
 calculated valued should be returned in the {return_value}
+ are passed through the *buffer* parameter, and the number of
+ elements within the footprint through *filter_size*. The
+ calculated valued should be returned in the *return_value*
argument.
The function {generic_filter1d} (see section
:ref:`_ndimage_genericfilters`) accepts a callback function with the
+The function :func:`generic_filter1d` (see section
+:ref:`ndimagegenericfilters`) accepts a callback function with the
following prototype:
The calling function iterates over the lines of the input and
output arrays, calling the callback function at each line. The
current line is extended according to the border conditions set by
the calling function, and the result is copied into the array that
 is passed through the {input_line} array. The length of the input
 line (after extension) is passed through {input_length}. The
+ is passed through the *input_line* array. The length of the input
+ line (after extension) is passed through *input_length*. The
callback function should apply the 1D filter and store the result
 in the array passed through {output_line}. The length of the
 output line is passed through {output_length}.
+ in the array passed through *output_line*. The length of the
+ output line is passed through *output_length*.
The function {geometric_transform} (see section
:ref:`_ndimage_interpolation`) expects a function with the following
+The function :func:`geometric_transform` (see section
+:ref:`ndimageinterpolation`) expects a function with the following
prototype:
The calling function iterates over the elements of the output
array, calling the callback function at each element. The
coordinates of the current output element are passed through
 {output_coordinates}. The callback function must return the
+ *output_coordinates*. The callback function must return the
coordinates at which the input must be interpolated in
 {input_coordinates}. The rank of the input and output arrays are
 given by {input_rank} and {output_rank} respectively.
+ *input_coordinates*. The rank of the input and output arrays are
+ given by *input_rank* and *output_rank* respectively.
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