MSER (Maximally Stable Extremal Regions) More...

#include "generic.h"

Data Structures
struct	VlMserStats
	MSER filter statistics definition. More...
struct	VlMserReg
	MSER: basic region (declaration) More...
struct	VlMserExtrReg
	MSER: extremal region (declaration) More...
struct	VlMserFilt
	MSER filter. More...
Defines
#define	VL_MSER_PIX_MAXVAL 256
	Maximum value.
#define	VL_MSER_VOID_NODE ((1ui64<<32) - 1)
	Basic region flag: null region.
Typedefs
typedef vl_uint8	vl_mser_pix
	MSER image data type.
typedef float	vl_mser_acc
	MSER accumulator data type.
Functions
Construction and Destruction
VlMserFilt *	vl_mser_new (int ndims, int const *dims)
	Create a new MSER filter.
void	vl_mser_delete (VlMserFilt *f)
	Delete MSER filter.
Processing
void	vl_mser_process (VlMserFilt f, vl_mser_pix const im)
	Process image.
void	vl_mser_ell_fit (VlMserFilt *f)
	Fit ellipsoids.
Retrieving data
vl_uint	vl_mser_get_regions_num (VlMserFilt const *f)
	Get number of maximally stable extremal regions.
vl_uint const *	vl_mser_get_regions (VlMserFilt const *f)
	Get maximally stable extremal regions.
float const *	vl_mser_get_ell (VlMserFilt const *f)
	Get ellipsoids.
vl_uint	vl_mser_get_ell_num (VlMserFilt const *f)
	Get number of ellipsoids.
vl_uint	vl_mser_get_ell_dof (VlMserFilt const *f)
	Get number of degrees of freedom of ellipsoids.
VlMserStats const *	vl_mser_get_stats (VlMserFilt const *f)
	Get statistics.
Retrieving parameters
vl_mser_pix	vl_mser_get_delta (VlMserFilt const *f)
	Get delta.
double	vl_mser_get_min_area (VlMserFilt const *f)
	Get minimum region area.
double	vl_mser_get_max_area (VlMserFilt const *f)
	Get maximum region area.
double	vl_mser_get_max_variation (VlMserFilt const *f)
	Get maximum region variation.
double	vl_mser_get_min_diversity (VlMserFilt const *f)
	Get minimum diversity.
Setting parameters
void	vl_mser_set_delta (VlMserFilt *f, vl_mser_pix x)
	Set delta.
void	vl_mser_set_min_area (VlMserFilt *f, double x)
	Set minimum region area.
void	vl_mser_set_max_area (VlMserFilt *f, double x)
	Set maximum region area.
void	vl_mser_set_max_variation (VlMserFilt *f, double x)
	Set maximum region variation.
void	vl_mser_set_min_diversity (VlMserFilt *f, double x)
	Set minimum diversity.

Detailed Description

implements the Maximally Stable Extremal Regions (MSER) feature detetctor [7] .

Maximally Stable Extremal Regions Overview

Running the MSER filter usually involves the following steps:

Initialize the MSER filter by vl_mser_new(). The filter can be reused for images of the same size.
Compute the MSERs by vl_mser_process().
Optionally fit ellipsoids to the MSERs by vl_mser_ell_fit().
Retrieve the results by vl_mser_get_regions() (and optionally vl_mser_get_ell()).
Optionally retrieve filter statistics by vl_mser_get_stats().
Delete the MSER filter by vl_mser_delete().

MSER definition

An extremal region $R_l$ of an image is a connected component of the level set $S_l = \{ x : I(x) \leq l \}$ .

For each intensity $l$ , one has multiple disjoint extremal regions in the level set $S_l$ . Let $l$ span a finite number of values $\mathcal{L}=\{0,\dots,M-1\}$ (a sampling of the image range). One obtains a family of regions $R_l$ ; by connecting two regions $R_l$ and $R_{l+1}$ if, and only if, $R_l\subset R_{l+1}$ , regions form a tree:

The maximally stable extremal regions are extremal regions which satisfy a stability criterion. Here we use a criterion which is similar but not identical to the original paper. This definition is somewhat simpler both to understand and code (it also runs faster).

Let $B(R_l)=(R_l,R_{l+1},\dots,R_{l+\Delta})$ be the branch of the tree rooted at $R_l$ . We associate to the branch the (in)stability score

$v(R_l) = \frac{|R_{l+\Delta} - R_l|}{|R_l|}.$

The score is low if the regions along the branch have similar area (and thus similar shape). We aim to select maximally stable branches; then a maximally stable region is just a representative region selected from a maximally stable branch (for simplicity we select $R_l$ , but one could choose for example $R_{l+\Delta/2}$ ).

Roughly speaking, a branch is maximally stable if it is a local minimum of the (in)stability score. More accurately, we start by assuming that all branches are maximally stable. Then we consider each branch $B(R_{l})$ and its parent branch $B(R_{l+1}):R_{l+1}\supset R_l$ (notice that, due to the discrete nature of the calculations, they might be geometrically identical) and we mark as unstable the less stable one, i.e.:

if $v(R_l)<v(R_{l+1})$ , mark $R_{l+1}$ as unstable;
if $v(R_l)>v(R_{l+1})$ , mark $R_{l}$ as unstable;
otherwise, do nothing.

This criterion selects among nearby regions the ones that are more stable. We optionally refine the selection by running (starting from the bigger and going to the smaller regions) the following tests:

$a_- \leq |R_{l}|/|R_{\infty}| \leq a_+$ : exclude MSERs too small or too big ( $|R_{\infty}|$ is the area of the image).

$v(R_{l}) < v_+$ : exclude MSERs too unstable.

For any MSER , find the parent MSER $R_{l'}$ and check if $|R_{l'} - R_l|/|R_l'| < d_+$ : remove duplicated MSERs.

parameter	alt. name	standard value	set by
$\Delta$	`delta`	5	vl_mser_set_delta()
	`max_area`	0.75	vl_mser_set_max_area()
	`min_area`	3.0/ $\|R_\infty\|$	vl_mser_set_min_area()
	`max_var`	0.25	vl_mser_set_max_variation()
	`min_diversity`	0.2	vl_mser_set_min_diversity()

Volumetric images

The code supports images of arbitrary dimension. For instance, it is possible to find the MSER regions of volumetric images or time sequences. See vl_mser_new() for further details

Ellipsoids

Usually extremal regions are returned as a set of ellipsoids fitted to the actual regions (which have arbitrary shape). The fit is done by calculating the mean and variance of the pixels composing the region:

$\mu_l = \frac{1}{|R_l|}\sum_{x\in R_l}x, \qquad \Sigma_l = \frac{1}{|R_l|}\sum_{x\in R_l} (x-\mu_l)^\top(x-\mu_l)$

Ellipsoids are fitted by vl_mser_ell_fit(). Notice that for a n dimensional image, the mean has n components and the variance has n(n+1)/2 independent components. The total number of components is obtained by vl_mser_get_ell_dof() and the total number of fitted ellipsoids by vl_mser_get_ell_num(). A matrix with an ellipsoid per column is returned by vl_mser_get_ell(). The column is the stacking of the mean and of the independent components of the variance, in the order (1,1),(1,2),..,(1,n), (2,2),(2,3).... In the calculations, the pixel coordinate $x=(x_1,...,x_n)$ use the standard index order and ranges.

Algorithm

The algorithm is quite efficient. While some details may be tricky, the overall idea is easy to grasp.

Pixels are sorted by increasing intensity.
Pixels are added to a forest by increasing intensity. The forest has the following properties:
- All the descendent of a certain pixels are subset of an extremal region.
- All the extremal regions are the descendants of some pixels.
Extremal regions are extracted from the region tree and the extremal regions tree is calculated.
Stable regions are marked.
Duplicates and other bad regions are removed.

Remarks:: The extremal region tree which is calculated is a subset of the actual extremal region tree. In particular, it does not contain redundant entries extremal regions that coincide as sets. So, for example, in the calculated extremal region tree, the parent of an extremal region $R_{l}$ may or may not correspond to $R_{l+1}$ , depending whether $q\leq l+1$ or not. These subtleties are important when calculating the stability tests.

Author:: Andrea Vedaldi

Define Documentation

#define VL_MSER_PIX_MAXVAL 256

Maximum value of the integer type vl_mser_pix.

#define VL_MSER_VOID_NODE ((1ui64<<32) - 1)

Typedef Documentation

typedef float vl_mser_acc

This is a large integer type. It should be large enough to contain a number equal to the area (volume) of the image by the image width by the image height (for instance, if the image is a square of side 256, the maximum value is 256 x 256 x 256).

typedef vl_uint8 vl_mser_pix

This is the data type of the image pixels. It has to be an integer.

Function Documentation

void vl_mser_delete ( VlMserFilt * f )

The function releases the MSER filter f and all its resources.

Parameters:

f	MSER filter to be deleted.

void vl_mser_ell_fit ( VlMserFilt * f )

Parameters:

f	MSER filter.

See also:: Ellipsoids

vl_mser_pix vl_mser_get_delta ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: value of delta.

float const * vl_mser_get_ell ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: ellipsoids.

vl_uint vl_mser_get_ell_dof ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: number of degrees of freedom.

vl_uint vl_mser_get_ell_num ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: number of ellipsoids

double vl_mser_get_max_area ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: maximum region area.

double vl_mser_get_max_variation ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: maximum region variation.

double vl_mser_get_min_area ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: minimum region area.

double vl_mser_get_min_diversity ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: value of minimum diversity.

vl_uint const * vl_mser_get_regions ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: array of MSER pivots.

vl_uint vl_mser_get_regions_num ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: number of MSERs.

VlMserStats const * vl_mser_get_stats ( VlMserFilt const * f ) [inline]

Parameters:

f	MSER filter.

Returns:: statistics.

VlMserFilt* vl_mser_new	(	int	ndims,
		int const *	dims
	)

Initializes a new MSER filter for images of the specified dimensions. Images are ndims -dimensional arrays of dimensions dims.

Parameters:

ndims	number of dimensions.
dims	dimensions.

void vl_mser_process	(	VlMserFilt *	f,
		vl_mser_pix const *	im
	)

The functions calculates the Maximally Stable Extremal Regions (MSERs) of image im using the MSER filter f.

The filter f must have been initialized to be compatible with the dimensions of im.

Parameters:

f	MSER filter.
im	image data.

void vl_mser_set_delta	(	VlMserFilt *	f,
		vl_mser_pix	x
	)		`[inline]`

Parameters:

f	MSER filter.
x	value of `delta`.

void vl_mser_set_max_area	(	VlMserFilt *	f,
		double	x
	)		`[inline]`

Parameters:

f	MSER filter.
x	maximum region area.

void vl_mser_set_max_variation	(	VlMserFilt *	f,
		double	x
	)		`[inline]`

Parameters:

f	MSER filter.
x	maximum region variation.

void vl_mser_set_min_area	(	VlMserFilt *	f,
		double	x
	)		`[inline]`

Parameters:

f	MSER filter.
x	minimum region area.

void vl_mser_set_min_diversity	(	VlMserFilt *	f,
		double	x
	)		`[inline]`

Parameters:

f	MSER filter.
x	value of `minimum` diversity.

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Data Structures

Defines

Typedefs

Functions

Detailed Description

Maximally Stable Extremal Regions Overview

MSER definition

Volumetric images

Ellipsoids

Algorithm

Define Documentation

Typedef Documentation

Function Documentation