### Table of Contents

*Maximally Stable Extremal Regions (MSER)* is a feature
detector; Like the SIFT detector, the MSER
algorithm extracts from an image `I`

a number of co-variant
regions, called MSERs. An MSER is a *stable* connected
component of some level sets of the image `I`

. Optionally,
elliptical frames are attached to the MSERs by fitting ellipses to the
regions. For a more in-depth explanation of the MSER detector, see
our API reference for
MSER

# Extracting MSERs

Each MSERs can be identified uniquely by (at least) one of its
pixels `x`

, as the connected component of the level set at
level `I(x)`

which contains `x`

. Such a pixel is
called *seed* of the region.

To demonstrate the usage of the MATLAB command `vl_mser`

we open MATLAB and load a test image

pfx = fullfile(vl_root,'data','spots.jpg') ; I = imread(pfx) ; image(I) ;

We then convert the image to a format that is suitable for the
`vl_mser`

command.

I = uint8(rgb2gray(I)) ;

We compute the region seeds and the elliptical frames by

[r,f] = vl_mser(I,'MinDiversity',0.7,... 'MaxVariation',0.2,... 'Delta',10) ;

We plot the region frames by

f = vl_ertr(f) ; vl_plotframe(f) ;

`vl_ertr`

transposes the elliptical frame and is
required here because the `vl_mser`

code assumes that the row index
is the first index, but the normal image convention assumes that this is the
`x`

(column) index.

Plotting the MSERs themselves is a bit more involved as they have
arbitrary shape. To this end, we exploit two
functions: `vl_erfill`

, which, given an image and a region
seed, returns a list of the pixels belonging to that region, and
the MATLAB built-in `contour`

, which draws the contour lines
of a function. We start by

M = zeros(size(I)) ; for x=r' s = vl_erfill(I,x) ; M(s) = M(s) + 1; end

which computes a matrix `M`

whose value are equal to the
number of overlapping extremal regions. Next, we use `M`

and `contour`

to display the region boundaries:

figure(2) ; clf ; imagesc(I) ; hold on ; axis equal off; colormap gray ; [c,h]=contour(M,(0:max(M(:)))+.5) ; set(h,'color','y','linewidth',3) ;

# MSER parameters

In the original formulation, MSERs are controlled by a single
parameter `Δ`

, which controls how the stability is
calculated. Its effect is shown in the figure below.

The stability of an extremal region `R`

is the inverse
of the relative area variation of the region `R`

when the
intensity level is increased by `Δ`

. Formally, the
variation is defined as:

|R(+Δ) - R| ----------- |R|

where `|R|`

denotes the area of the extremal region
`R`

, `R(+Δ)`

is the extremal region
`+Δ`

levels up which contains `R`

and
`|R(+Δ) - R|`

is the area difference of the two
regions.

A stable region has a small variation. The algorithm finds regions which are "maximally stable", meaning that they have a lower variation than the regions one level below or above. Note that due to the discrete nature of the image, the region below / above may be coincident with the actual region, in which case the region is still deemed maximal.

However, even if an extremal region is maximally stable, it might be rejected if:

- it is too big (see the parameter
`MaxArea`

); - it is too small (see the parameter
`MinArea`

); - it is too unstable (see the parameter
`MaxVariation`

); - it is too similar to its parent MSER (see the
parameter
`MinDiversity`

).

By default, MSERs are extracted for both dark-on-bright regions and bright-on-dark regions. To control this, parmeters `BrightOnDark`

and `DarkOnBright`

which take values 0 or 1 to enable or disable the regions. For example:

[r,f] = vl_mser(I,'MinDiversity',0.7,... 'MaxVariation',0.2,... 'Delta',10,... 'BrightOnDark',1,'DarkOnBright',0) ;

computes the regions in green in the figure below.

# Conventions

As mentioned in the introduction, `vl_mser`

uses
matrix indices as image coordinates. Compared to the usual MATLAB
convention for images, this means that the `x`

and `y`

axis are swapped (this has been done to make the
convention consistent with images with three or more dimensions). Thus
the frames computed by the program may need to be "transposed" as
in:

[r,f] = vl_mser(I) ; f = vl_ertr(f) ;

On the other hand, the region seeds `r`

are already in
row major format, which is the standard MATLAB format for pixel
indices.

Instead of transposing the frames, one can start by transposing
the image. In this case, the frames `f`

have the standard
image convention, but the region seeds are in column-major format and
may need to be "transposed" as in:

[r,f] = vl_mser(I') ; [i,j] = sub2ind(size(I'),r) ; r = ind2sub(size(I),j,i) ;

The command line utility `mser`

uses the normal image
convention (because images are rasterized in column-major
order). Therefore the image frames are in the standard format, and the
region seeds are in column major format.

In order to convert from the command line utility convention to
the MATLAB convention one needs also to recall that MATLAB coordinates
starts from (1,1), but the command line utility uses the more common
convention (0,0). For instance, let the files `image.frame`

and `image.seed`

contain the feature frames and seeds in
ASCII format as generated by the command line utility. Then

r_ = load('image.seed')' + 1 ; f_ = load('image.frame')' ; f_(1:2,:) = f_(1:2,:) + 1 ; [r,f] = vl_mser(I') ; % notice the transpose

produces identical (up to numerical noise) region
seeds `r`

and `r_`

and frames `f`

and `f_`

.