Various mathematical manipulations of 3D images. More...

#include <vcl_cassert.h>
#include <vcl_vector.h>
#include <vil3d/vil3d_image_view.h>
#include <vil3d/vil3d_plane.h>
#include <vcl_algorithm.h>

Functions
template<class T >
void	vil3d_math_value_range (const vil3d_image_view< T > &im, T &min_value, T &max_value)
	Compute minimum and maximum values over im.
template<class T >
void	vil3d_math_value_range_percentile (const vil3d_image_view< T > &im, const double fraction, T &value)
	Compute value corresponding to a percentile of the range of im.
template<class T >
void	vil3d_math_value_range_percentiles (const vil3d_image_view< T > &im, const vcl_vector< double > fraction, vcl_vector< T > &value)
	Compute value corresponding to several percentiles of the range of im.
template<class aT , class sumT >
void	vil3d_math_mean_over_planes (const vil3d_image_view< aT > &src, vil3d_image_view< sumT > &dest)
	Calc the mean of each pixel over all the planes.
template<class inT , class outT , class sumT >
void	vil3d_math_mean_over_planes (const vil3d_image_view< inT > &src, vil3d_image_view< outT > &dest, sumT)
	Calc the mean of each pixel over all the planes.
template<class inT , class outT , class sumT >
void	vil3d_math_rms (const vil3d_image_view< inT > &src, vil3d_image_view< outT > &dest, sumT)
	Calculate the rms of each pixel over all the planes.
template<class imT , class sumT >
void	vil3d_math_sum (sumT &sum, const vil3d_image_view< imT > &im, unsigned p)
	Compute sum of values in plane p.
template<class imT , class sumT >
void	vil3d_math_mean (sumT &mean, const vil3d_image_view< imT > &im, unsigned p)
	Mean of elements in plane p of image.
template<class imT , class sumT >
void	vil3d_math_sum_squares (sumT &sum, sumT &sum_sq, const vil3d_image_view< imT > &im, unsigned p)
	Sum of squares of elements in plane p of image.
template<class imT , class sumT >
sumT	vil3d_math_ssd (const vil3d_image_view< imT > &imA, const vil3d_image_view< imT > &imB, sumT)
	Sum of squared differences between two images.
template<class imT , class offsetT >
void	vil3d_math_scale_and_offset_values (vil3d_image_view< imT > &image, double scale, offsetT offset)
	Multiply values in-place in image view by scale and add offset.
template<class imT , class sumT >
void	vil3d_math_mean_and_variance (sumT &mean, sumT &var, const vil3d_image_view< imT > &im, unsigned p)
	Mean and variance of elements in plane p of image.
template<class imT , class sumT >
sumT	vil3d_math_dot_product (const vil3d_image_view< imT > &imA, const vil3d_image_view< imT > &imB, sumT)
	Mean and variance of elements in plane p of image.
template<class aT , class bT , class sumT >
void	vil3d_math_image_difference (const vil3d_image_view< aT > &imA, const vil3d_image_view< bT > &imB, vil3d_image_view< sumT > &im_sum)
	Compute difference of two images (im_sum = imA-imB).
template<class aT , class bT , class sumT >
void	vil3d_math_image_sum (const vil3d_image_view< aT > &imA, const vil3d_image_view< bT > &imB, vil3d_image_view< sumT > &im_sum)
	Compute sum of two images (im_sum = imA+imB).
template<class aT , class bT , class prodT >
void	vil3d_math_image_product (const vil3d_image_view< aT > &imA, const vil3d_image_view< bT > &imB, vil3d_image_view< prodT > &im_prod)
	Compute pixel-wise product of two images (im_prod = imA*imB).
template<class aT , class bT , class scaleT >
void	vil3d_math_add_image_fraction (vil3d_image_view< aT > &imA, scaleT fa, const vil3d_image_view< bT > &imB, scaleT fb)
	imA = faimA + fbimB (Useful for moving averages!).
template<class T >
void	vil3d_math_truncate_range (vil3d_image_view< T > &image, T min_v, T max_v)
	Truncate each pixel value so it fits into range [min_v,max_v].
template<class aT , class sumT >
void	vil3d_math_integral_image (const vil3d_image_view< aT > &imA, vil3d_image_view< sumT > &im_sum)
	Calc integral image im_sum(i+1,j+1,k+1)= sum (x<=i,y<=j,z<=k) imA(x,y,z).
template<class aT , class sumT >
void	vil3d_math_integral_sqr_image (const vil3d_image_view< aT > &imA, vil3d_image_view< sumT > &im_sum, vil3d_image_view< sumT > &im_sum_sq)
	Calc integral image im_sum_sq(i+1,j+1,k+1) = sum (x<=i,y<=j,z<=k) imA^2.

Detailed Description

Various mathematical manipulations of 3D images.

Author:: Tim Cootes

Definition in file vil3d_math.h.

Function Documentation

template<class aT , class bT , class scaleT >

void vil3d_math_add_image_fraction	(	vil3d_image_view< aT > &	imA,
		scaleT	fa,
		const vil3d_image_view< bT > &	imB,
		scaleT	fb
	)		`[inline]`

imA = fa*imA + fb*imB (Useful for moving averages!).

Can do running sum using vil_add_image_fraction(running_mean,1-f,new_im,f) to update current mean by a fraction f of new_im

Definition at line 491 of file vil3d_math.h.

template<class imT , class sumT >

sumT vil3d_math_dot_product	(	const vil3d_image_view< imT > &	imA,
		const vil3d_image_view< imT > &	imB,
		sumT
	)		`[inline]`

Mean and variance of elements in plane p of image.

Definition at line 353 of file vil3d_math.h.

template<class aT , class bT , class sumT >

void vil3d_math_image_difference	(	const vil3d_image_view< aT > &	imA,
		const vil3d_image_view< bT > &	imB,
		vil3d_image_view< sumT > &	im_sum
	)		`[inline]`

Compute difference of two images (im_sum = imA-imB).

Definition at line 371 of file vil3d_math.h.

template<class aT , class bT , class prodT >

void vil3d_math_image_product	(	const vil3d_image_view< aT > &	imA,
		const vil3d_image_view< bT > &	imB,
		vil3d_image_view< prodT > &	im_prod
	)		`[inline]`

Compute pixel-wise product of two images (im_prod = imA*imB).

Definition at line 449 of file vil3d_math.h.

template<class aT , class bT , class sumT >

void vil3d_math_image_sum	(	const vil3d_image_view< aT > &	imA,
		const vil3d_image_view< bT > &	imB,
		vil3d_image_view< sumT > &	im_sum
	)		`[inline]`

Compute sum of two images (im_sum = imA+imB).

Definition at line 410 of file vil3d_math.h.

template<class aT , class sumT >

void vil3d_math_integral_image	(	const vil3d_image_view< aT > &	imA,
		vil3d_image_view< sumT > &	im_sum
	)		`[inline]`

Calc integral image im_sum(i+1,j+1,k+1)= sum (x<=i,y<=j,z<=k) imA(x,y,z).

Useful thing for quickly computing mean over large regions, as demonstrated in Viola and Jones (CVPR01). The sum of elements in the ni x nj x nk volume with corner (i,j,k) is given by im_sum(i,j,k+nk)+im_sum(i+ni,j+nj,j+nk)+im_sum(i,j+nj,k)+im_sum(i+ni,j,k) -im_sum(i,j,k)-im_sum(i+ni,j+nj,k)-im_sum(i+ni,n,k_nk)-im_sum(i,j+nj,k+nk

Definition at line 560 of file vil3d_math.h.

template<class aT , class sumT >

void vil3d_math_integral_sqr_image	(	const vil3d_image_view< aT > &	imA,
		vil3d_image_view< sumT > &	im_sum,
		vil3d_image_view< sumT > &	im_sum_sq
	)		`[inline]`

Calc integral image im_sum_sq(i+1,j+1,k+1) = sum (x<=i,y<=j,z<=k) imA^2.

Also calcs integral image, im_sum(i+1,j+1,k+1 = sum (x=i,y<=j,z<=kk) imA Useful thing for quickly computing mean and variance over large regions, as demonstrated in Viola and Jones (CVPR01). The sum of elements in the ni x nj x nk volume with corner (i,j,k) is given by: im_sum(i,j,k+nk)+im_sum(i+ni,j+nj,j+nk)+im_sum(i,j+nj,k)+im_sum(i+ni,j,k) -im_sum(i,j,k)-im_sum(i+ni,j+nj,k)-im_sum(i+ni,n,k_nk)-im_sum(i,j+nj,k+nk

Definition at line 657 of file vil3d_math.h.

template<class imT , class sumT >

void vil3d_math_mean	(	sumT &	mean,
		const vil3d_image_view< imT > &	im,
		unsigned	p
	)		`[inline]`

Mean of elements in plane p of image.

Definition at line 244 of file vil3d_math.h.

template<class imT , class sumT >

void vil3d_math_mean_and_variance	(	sumT &	mean,
		sumT &	var,
		const vil3d_image_view< imT > &	im,
		unsigned	p
	)		`[inline]`

Mean and variance of elements in plane p of image.

Definition at line 338 of file vil3d_math.h.

template<class aT , class sumT >

void vil3d_math_mean_over_planes	(	const vil3d_image_view< aT > &	src,
		vil3d_image_view< sumT > &	dest
	)		`[inline]`

Calc the mean of each pixel over all the planes.

Definition at line 156 of file vil3d_math.h.

template<class inT , class outT , class sumT >

void vil3d_math_mean_over_planes	(	const vil3d_image_view< inT > &	src,
		vil3d_image_view< outT > &	dest,
		sumT
	)		`[inline]`

Calc the mean of each pixel over all the planes.

Definition at line 174 of file vil3d_math.h.

template<class inT , class outT , class sumT >

void vil3d_math_rms	(	const vil3d_image_view< inT > &	src,
		vil3d_image_view< outT > &	dest,
		sumT
	)		`[inline]`

Calculate the rms of each pixel over all the planes.

Definition at line 193 of file vil3d_math.h.

template<class imT , class offsetT >

void vil3d_math_scale_and_offset_values	(	vil3d_image_view< imT > &	image,
		double	scale,
		offsetT	offset
	)		`[inline]`

Multiply values in-place in image view by scale and add offset.

Definition at line 310 of file vil3d_math.h.

template<class imT , class sumT >

sumT vil3d_math_ssd	(	const vil3d_image_view< imT > &	imA,
		const vil3d_image_view< imT > &	imB,
		sumT
	)		`[inline]`

Sum of squared differences between two images.

Definition at line 289 of file vil3d_math.h.

template<class imT , class sumT >

void vil3d_math_sum	(	sumT &	sum,
		const vil3d_image_view< imT > &	im,
		unsigned	p
	)		`[inline]`

Compute sum of values in plane p.

Definition at line 213 of file vil3d_math.h.

template<class imT , class sumT >

void vil3d_math_sum_squares	(	sumT &	sum,
		sumT &	sum_sq,
		const vil3d_image_view< imT > &	im,
		unsigned	p
	)		`[inline]`

Sum of squares of elements in plane p of image.

Definition at line 256 of file vil3d_math.h.

template<class T >

void vil3d_math_truncate_range	(	vil3d_image_view< T > &	image,
		T	min_v,
		T	max_v
	)		`[inline]`

Truncate each pixel value so it fits into range [min_v,max_v].

If value < min_v value=min_v If value > max_v value=max_v

Definition at line 525 of file vil3d_math.h.

template<class T >

void vil3d_math_value_range	(	const vil3d_image_view< T > &	im,
		T &	min_value,
		T &	max_value
	)		`[inline]`

Compute minimum and maximum values over im.

Definition at line 20 of file vil3d_math.h.

template<class T >

void vil3d_math_value_range_percentile	(	const vil3d_image_view< T > &	im,
		const double	fraction,
		T &	value
	)		`[inline]`

Compute value corresponding to a percentile of the range of im.

Percentiles expressed as fraction, e.g. 0.05, or 0.95.

Parameters:

im	The image to examine.
fraction	The fraction of the data range (from the lower end).

Return values:

value The image data value corresponding to the specified percentile.

Note:: This function requires the sorting of large parts of the image data and can be very expensive in terms of both processing and memory.

See also:: vil3d_math_value_range_percentiles()

Definition at line 70 of file vil3d_math.h.

template<class T >

void vil3d_math_value_range_percentiles	(	const vil3d_image_view< T > &	im,
		const vcl_vector< double >	fraction,
		vcl_vector< T > &	value
	)		`[inline]`

Compute value corresponding to several percentiles of the range of im.

Percentiles expressed as fraction, e.g. 0.05, or 0.95.

Parameters:

im	The image to examine.
fraction	The fraction of the data range (from the lower end).

Return values:

value The image data value corresponding to the specified percentiles.

Note:: This function requires the sorting of large parts of the image data and can be very expensive in terms of both processing and memory.

Definition at line 91 of file vil3d_math.h.

Functions

Detailed Description

Function Documentation