CN104156723A - Method for extracting maximally stable extremal region with scale invariance - Google Patents

Abstract

The invention discloses a method for extracting a maximally stable extremal region with scale invariance. The method includes the steps that firstly, an initial maximally stable extremal region is detected in an original image through a maximally stable extremal region algorithm; then a scale pyramid of the initial maximally stable extremal region is built through M-scale wavelet transform, characteristic points with the scale invariance are determined in the scale pyramid according to energy operators of an M-scale wavelet transform coefficient, extremal regions corresponding to the characteristic points are obtained from all layers of images of the scale pyramid of the maximally stable extremal region, and the maximally stable extremal region with the scale invariance is extracted through the stability indexes of the extremal region in a multi-scale space; finally, the maximally stable extremal region with the scale invariance is adjusted to be in an oval shape, and the final maximally stable extremal region with the scale invariance is obtained. According to the method for extracting the maximally stable extremal region with the scale invariance, the scale invariance and the maximally stable extremal region are combined, the maximally stable extremal region is extracted, and full affine invariance is achieved.

Description

A kind of extracting method of the stable extremal region with yardstick unchangeability

Technical field:

The present invention relates to the extraction in digital picture invariant features region, especially there is the extracting method of the stable extremal region of yardstick unchangeability.

Background technology:

From image, detect characteristic area is one of primary study problem of computer vision field always.In recent years, the affine invariant features of the image region based on regional area is subject to paying close attention to more and more widely, and is successfully applied to many fields such as target identification, image retrieval, robot autonomous navigation and scene understanding and subject image classification.

Typical local feature region detection algorithm comprises: the yardstick invariant features point SIFT (scale invariant feature transform) that Lowe proposes, the affine invariant features point based on multiple dimensioned Harris angle point that Mikolajczyk and Schmid propose, the stable extremal region MSER (maximum stable extreme region) of the people such as affine constant marking area (AISR) and the Matas proposition based on information entropy that the people such as Kadir propose.In the Local affine invariant feature region detection algorithm having proposed, MSER algorithm has superior performance in many aspects, and the rotation variation to image, visual angle change, brightness variation all have good unchangeability.MSER algorithm basic thought is, for any width gray scale picture, choose from small to large all possible threshold value, obtain the many connected regions concerning this width image, finally obtain the region that is less than certain value in these regions with its area change of variation of threshold value, namely stable extremal region.Because MSER extracts from single scalogram picture, when graphical rule occurs when larger variation, the fuzzy meeting of image changes the border of stable extremal region, thereby affects the stability of Affinely invariant region.

Summary of the invention

The problem existing for MSER algorithm, the present invention is by the stability indicator of extremal region in definition multiscale space, a kind of extracting method of the stable extremal region with yardstick unchangeability is proposed, can solve first key problem in affine invariant feature extraction: the location of characteristic area, where extract feature; Meanwhile, the basis that the Affinely invariant region that this extracting method detects can be laid for follow-up image processing.

The technical scheme that the present invention takes is: a kind of extracting method of the stable extremal region with yardstick unchangeability, and its concrete steps are:

1) first use stable extremal region algorithm in original image, to detect initial stable extremal region;

2) set up the yardstick pyramid of initial stable extremal region by M dyadic wavelet transform, in the yardstick pyramid of initial stable extremal region, according to the energy operator of M dyadic wavelet transform coefficient, determine the unique point with yardstick unchangeability:

Initial stable extremal region is designated as to f (x, y), is increasing progressively yardstick M ^jdo M dyadic wavelet transform along x and y direction down, wherein M is greater than 1 real number that is less than 2, and j is the positive integer increasing progressively, and wavelet function ψ (x, y) is wherein defined as smooth function along the derivative of x and y direction, thereby obtain by increasing progressively yardstick M ^junder level and smooth stable extremal region and wavelet coefficient the MSER yardstick pyramid of composition; The wavelet transformation result of different scale when j is even number, in conjunction with the information on its adjacent position, adopts Teager energy operator to obtain energy and the corresponding mould of M system wavelet conversion coefficient carry out local non-maximum value according to this mould value and suppress, namely, compared with 8 points around, if the mould value maximum of current point, this point is confirmed as having the unique point of yardstick unchangeability, is designated as X=(x, y, M ^j), the wherein position of (x, y) representation feature point, M ^jrepresentation feature point place yardstick;

3) to each unique point of being determined by above-mentioned steps, from the pyramidal each tomographic image of yardstick of stable extremal region, obtain the extremal region corresponding with it, and by the stability indicator of extremal region in multiscale space, extract the stable extremal region with yardstick unchangeability:

First to each unique point of extracting, find out stable extremal region level and smooth under its place yardstick from the yardstick pyramid of stable extremal region the gray-scale value of middle pixel is than all large or all little connected regions of the gray-scale value of its boundary pixel point, as its corresponding extremal region; Then judge spatial stability and the dimensional stability of this extremal region, if this extremal region is all stable at metric space and pixel space, this extremal region is exactly the stable extremal region with yardstick unchangeability so;

4) finally the stable extremal region with yardstick unchangeability is adjusted to elliptical shape, so that subsequent treatment:

First according to the region of size and the deletion repetition of area change rate size or poor stability; Then according to covariance matrix, irregularly shaped region is adjusted into regular elliptical region; This elliptical region is amplified to some ratios, obtain the final stable extremal region with unchangeability.

According to the preferred version of embodiment, in the described M dyadic wavelet transform in step 2 metric space number, the maximal value J of j selects 21.

According to the preferred version of embodiment, in described step 3, stability indicator comprises the stability indicator ε (ER) of metric space and the stability indicator of pixel space

The stability indicator ε (ER) of metric space is defined as:

$\mathrm{\ϵ}\left(\mathrm{ER}\right)=\frac{{\mathrm{Er}}_{j-1}\∩{\mathrm{ER}}_j}{{\mathrm{ER}}_{j-1}\∪{\mathrm{ER}}_j}+\frac{{\mathrm{ER}}_{j+1}\∩{\mathrm{ER}}_j}{{\mathrm{ER}}_{j+1}\∪{\mathrm{ER}}_j}$

Wherein j represents the level of extremal region ER in yardstick pyramid;

The stability indicator of pixel space be defined as:

Wherein Δ is an input parameter of algorithm, || represent the gesture of set, ER ^{+ Δ}, ER ^-Δbelong to limit area, if the ε of extremal region ER (ER) exists local minimum, claim that extremal region ER is stable at metric space, if extremal region ER be local minimum, region ER is stable in pixel space so, if extremal region ER is stable at metric space and pixel space, extremal region ER is exactly the stable extremal region with yardstick unchangeability so.

According to the preferred version of embodiment, in step 4, the region of deleting according to area change rate size has: area change rate is less than 0.5 or be greater than 1 region.

According to the preferred version of embodiment, in step 4, the region of deleting according to size is: the half of the number of pixels that the pixel threshold values of establishing surface area is selected test pattern, in the time that the number of pixels of this surface area exceedes threshold values, be large area region, need to delete.

According to the preferred version of embodiment, in step 4, elliptical region amplification factor is 2.5.

Design concept of the present invention is:

In the detection algorithm of existing Local affine invariant feature region, the MSER algorithm that the people such as Matas propose, the rotation variation to image, visual angle change, brightness variation all have good robustness, but its vary stable to graphical rule is inadequate.Meanwhile, existing Multiscale Theory can be under multiple yardsticks, image to be analyzed in different resolution, and it is consistent experiencing image information from coarse to finely with human visual system.The present invention is by the stability indicator of extremal region in definition multiscale space, proposes a kind of multiple dimensioned stable extremal region detection method, and first it detect MSER on original image.Then set up the yardstick pyramid of the MSER of original image by M dyadic wavelet transform, in MSER yardstick pyramid, detect the local modulus maximum value of wavelet coefficient, determine the unique point with yardstick unchangeability.Then to each unique point of determining, utilize existing region growing algorithm to obtain the extremal region corresponding with it from the pyramidal each tomographic image of MSER yardstick, and by the stability indicator of extremal region in multiscale space, extract the stable extremal region with yardstick unchangeability.Finally the stable extremal region with yardstick unchangeability is adjusted to elliptical shape, so that subsequent treatment.

In sum, the present invention combines yardstick unchangeability and stable extremal region, has found the image-region that can extract invariant features, i.e. pixel coordinate figure.The stable extremal region detecting by the present invention, rotation variation to image, dimensional variation, brightness variation, visual angle change, noise etc. all can maintain the invariance, and have affine unchangeability completely.

Brief description of the drawings

Fig. 1 is the FB(flow block) of method described in embodiment;

Fig. 2 is the adjustment schematic diagram of covariance elliptical region;

Embodiment:

Below in conjunction with drawings and Examples data, said method is described in detail:

As shown in Figure 1, a kind of extracting method of the stable extremal region with yardstick unchangeability, comprises the steps:

The first step, the MSER implementation algorithm proposing according to people such as Murphy detects MSER in original image; (this step is utilized existing algorithm, and detailed process repeats no more, and only MSER is defined as follows :)

Gray level image I can be defined as a mapping from 2 dimension pixel coordinates to gray-scale value S, and the limit area ER in image I is a connected region, and meets the following conditions:

$\∀p\∈\mathrm{ER},\∀q\∈C\left(\mathrm{ER}\right)\→I\left(p\right)\mathrm{RI}\left(q\right)$

Wherein be related to that R is greater than relation or is less than relation, C (ER) represents the border of region ER, and q and p represent pixel.If R is greater than relation, claim that region ER is maximum value limit area, is expressed as ER+; If R is less than, claim that region ER is minimal value limit area, is expressed as ER-.Known according to above definition, limit area is that the gray-scale value of pixel in image is than all large or all little connected regions of the gray-scale value of its boundary pixel point.In order to search out stability limit region from limit area, need to ask for the stability index of limit area in pixel space

Wherein Δ is an input parameter of algorithm, || represent the gesture of set, ER ^{+ Δ}, ER ^-Δbelong to limit area.If be local minimum, region ER is exactly initial stable extremal region MSER so.

Second step, sets up the yardstick pyramid of original image MSER by M dyadic wavelet transform, determine the unique point with yardstick unchangeability in MSER yardstick pyramid:

A) start original image MSER (being designated as f (x, y)) to carry out multiple dimensioned M system wavelet transformation from j=1, obtain J the M system wavelet coefficient under different scale.For with SIFT method in the number of plies of the graphical rule considered be substantially consistent, the present embodiment choosing j=21.The wavelet function adopting when wavelet transformation is for second order splines, and this is that frequency domain is decayed fast because second order spline wavelets has tight support, and the feature such as analytical expression is relatively simple.

B) the wavelet transformation result of different scale while j being even number, in conjunction with the information on its adjacent position, adopts Teager energy operator, obtains the energy of M system wavelet conversion coefficient with and corresponding mould wherein represent that logarithm value m rounds.

C) basis value carry out local non-maximum value and suppress, namely compared with 8 points around, only have current point maximum, this point is candidate feature point, otherwise just this point is rejected from feature point detection algorithm.

M dyadic wavelet transform is wherein defined as:

Suppose that function # (x) meets and time, claim that θ (x) is smooth function.In the time that θ (x, y) is two-dimentional smooth function, the smooth function θ on image f (x, y) and different scale a _a(x, y) convolution, will make image f (x, y) by smooth, wherein ${\mathrm{\θ}}_a(x,y)=\frac{1}{a^2}\mathrm{\θ}(\frac{x}{a},\frac{y}{a}).$

Definition 2-d wavelet function is respectively:

${\mathrm{\ψ}}^{\left(1\right)}(x,y)=\frac{\mathrm{d\θ}(x,y)}{\mathrm{dx}}$

${\mathrm{\ψ}}^{\left(2\right)}(x,y)=\frac{\mathrm{d\θ}(x,y)}{\mathrm{dy}}$

Work as ψ ⁽¹⁾(x, y) and ψ ⁽²⁾(x, y) meets completeness and the stability condition of 2-d wavelet, can be used as the wavelet mother function of two-dimensional wavelet transformation.Note:

${\mathrm{\ψ}}_a^{\left(1\right)}(x,y)=\frac{1}{a^2}{\mathrm{\ψ}}^{\left(1\right)}(\frac{x}{a},\frac{y}{a})$

${\mathrm{\ψ}}_a^{\left(2\right)}(x,y)=\frac{1}{a^2}{\mathrm{\ψ}}^{\left(2\right)}(\frac{x}{a},\frac{y}{a})$

The wavelet transformation of function f (x, y) is:

$W_a^{\left(1\right)}f(x,y)=f(x,y)*{\mathrm{\ψ}}_a^{\left(1\right)}(x,y)$

$W_a^{\left(2\right)}f(x,y)=f(x,y)*{\mathrm{\ψ}}_a^{\left(2\right)}(x,y)$

For the ease of computer realization, the method for general discretize yardstick a is that a is progressively strengthened by the form of power series, even a=M ^j, M>0, j ∈ Z ⁺, j<J.If get M=2, the wavelet transformation that deserves to be called formula representative is Dyadic Wavelet Transform.And for yardstick a being done to finer division, also a can be taken as to mark or irrational number, and the wavelet transformation of now above formula representative is referred to as the wavelet transformation of M system, and its calculating often can realize by the method for frequency domain.

Can prove:

$\left[\begin{array}{c}{W}_{M^j}^{\left(1\right)}f(x,y)\\ W_{M^j}^{\left(2\right)}f(x,y)\end{array}\right]=M^j\left[\begin{array}{c}\frac{d}{\mathrm{dx}}(f(x,y)*{\mathrm{\&theta;}}_{M^j}(x,y))\\ \frac{d}{\mathrm{dy}}(f(x,y)*{\mathrm{\&theta;}}_{M^j}(x,y))\end{array}\right]=M^j\&dtri;(f(x,y)*{\mathrm{\&theta;}}_{M^j}(x,y))$

Can be found out M system wavelet coefficient by above formula be proportional to respectively yardstick M ^jlower quilt the partial derivative of the smoothed image f of institute (x, y) along continuous straight runs and vertical direction.

The 3rd step to each unique point of determining, obtains the extremal region corresponding with it from the pyramidal each tomographic image of MSER yardstick, and by the stability indicator of extremal region in multiscale space, extracts the stable extremal region with yardstick unchangeability;

The constant stable extremal region feature of yardstick that the present invention detects is the stable extremal region extracting from yardstick pyramid, not only passes through extremal region is investigated in the stability of pixel space, and the stability of metric space is investigated.Extremal region at the definition of stability of metric space is:

$\mathrm{\&epsiv;}\left(\mathrm{ER}\right)=\frac{{\mathrm{Er}}_{j-1}\&cap;{\mathrm{ER}}_j}{{\mathrm{ER}}_{j-1}\&cup;{\mathrm{ER}}_j}+\frac{{\mathrm{ER}}_{j+1}\&cap;{\mathrm{ER}}_j}{{\mathrm{ER}}_{j+1}\&cup;{\mathrm{ER}}_j}$

Wherein j represents the level of extremal region in yardstick pyramid.If the ε of extremal region ER (ER) exists local minimum, claim that extremal region ER is stable at metric space.If be local minimum, region ER is stable in pixel space so.If extremal region ER is stable at metric space and pixel space, extremal region ER is exactly the stable extremal region with yardstick unchangeability so.

The 4th step, is finally adjusted to elliptical shape by the stable extremal region with yardstick unchangeability, so that subsequent treatment such as feature description, characteristic matching.

Before carrying out elliptical region adjustment, delete some regions according to size and area change rate size.Because the region that area is larger or less has poor uniqueness, directly cause lower can matching.The Domain Stability that area change rate is larger is poor, and the less region of area change rate mostly is repeat region.The existence in these regions can increase the time complexity of algorithm.For the excessive and too small region of those area change rates, delete according to area change rate size, remove area change rate and be less than 0.5 or be greater than 1 region, the only region of Retention area rate of change between 0.5 to l:

For the larger region of area, according to the number of pixels of selected test pattern, the pixel threshold of establishing large area region is the half of full figure number of pixels, deletes this region if area pixel number is greater than this threshold value.And for the less region of area, caused by little vibration or noise because be mainly, be called noise extremal region, specifically be set as being less than structural element for area is compared with zonule, (f ⊕ b) Θ b removes these noise extremal regions to use the closure operation fb=of existing gray scale morphology, wherein f is stable extremal region image, ⊕ and Θ are respectively dilation and erosion computing, b is structural element, the size of this element can be determined according to the mean size of noise extremal region, generally should be greater than the mean size of noise extremal region, described in the present embodiment, structural element b selects the structural element of 5*5 pixel.

The characteristic area now obtaining is irregularly shaped region, and irregularly shaped region is difficult to carry out feature description.For the convenience of subsequent treatment, adopt with the following method irregularly shaped region is adjusted to ellipse.

First utilize the Pixel Information of composition irregular area to construct the second order centre distance based on vector representation.

$\mathrm{\&Sigma;}\left(R\right)=\frac{1}{\left|R\right|}\underset{X\&Element;R}{\mathrm{\&Sigma;}}{(X-E\left(X\right))(X-E\left(X\right))}^T$

Be wherein: X=[x, y] coordinate of pixel, R represents irregular area, | R| is the gesture by the set that in irregular area, all pixels form, i.e. the number of pixel in this region, E represents expectation value, T represents transposition.

The covariance matrix form of above formula being write as to dimensionality reduction, has

$U=\left[\begin{array}{cc}D\left(x\right)& \mathrm{COV}(x,y)\\ \mathrm{COV}(x,y)& D\left(y\right)\end{array}\right]$

Wherein D (x), D (y), COV (x, y) be respectively in this region the covariance of horizontal ordinate variance, ordinate variance and transverse and longitudinal coordinate a little:

$\left\{\begin{array}{c}D\left(x\right)=E\left(x^2\right)-{\left[E\left(x\right)\right]}^2\\ D\left(y\right)=E\left(y^2\right)-{\left[E\left(y\right)\right]}^2\\ \mathrm{COV}(x,y)=E\left(\mathrm{xy}\right)-E\left(x\right)E\left(y\right))\end{array}\right.$

And:

$E\left(x\right)=\frac{1}{\left|R\right|}\underset{x\&Element;R}{\mathrm{\&Sigma;}}\mathrm{xE}\left(y\right)=\frac{1}{\left|R\right|}\underset{y\&Element;R}{\mathrm{\&Sigma;}}y$

$E\left(x^2\right)=\frac{1}{\left|R\right|}\underset{x\&Element;R}{\mathrm{\&Sigma;}}{x}^{2}E\left(y^2\right)=\frac{1}{\left|R\right|}\underset{y\&Element;R}{\mathrm{\&Sigma;}}{y}^{2}E\left(\mathrm{xy}\right)=\frac{1}{\left|R\right|}\underset{y\&Element;R}{\mathrm{\&Sigma;}}\mathrm{xy}$

Wherein, | R| is the gesture by the set that in irregular area, all pixels form, i.e. pixel number in this region.

Covariance matrix U is symmetrical matrix, according to its proper vector and characteristic root, can be adjusted major and minor axis direction and the amplitude of rear ellipse, as Fig. 2 shows, and α in figure ₁and α ₂be major and minor axis amplitude, θ represents the direction of major axis, and E (x) and E (y) are the center point coordinate of elliptical region after adjusting.

Each stable extremal region has a tolerance region corresponding with it, i.e. covariance elliptical region, and the area of this elliptical region is corresponding with the size of stable extremal region.If this ellipse area is less, its conspicuousness is just poor so.In order to improve the conspicuousness in region, covariance ellipse is amplified, even now is likely included some background content of non-target in image, but according to pertinent literature, suitably increase the area in tolerance region, can greatly improve the conspicuousness in tolerance region, and Comparatively speaking the impact of background is acceptable.Given this, the present invention amplifies covariance ellipse, and reference experiment result is decided to be 2.5 by amplification factor.Because oval parameter is only determined by the space distribution of corresponding region pixel, therefore can keep good robustness by the method to affine variation.

The present embodiment is at 8 groups of cycle testss such as the Graffiti that keeps using on the consistent basis of experiment condition robot research group of Cambridge University to provide as far as possible, according to method of evaluating performance, adopt local feature region repetition rate to investigate the performance of the inventive method and MSER algorithm.Definition local feature region repetition rate is as follows:

$\mathrm{repeatability}=\frac{\mathrm{correctMathes}}{\min \mathrm{Number}}$

Wherein correctMathes represents between two width images the stable extremal region number of correct coupling, and min Number represents the smaller value of the stable extremal region number of two width images.

No matter between image, what kind of affine variation has occurred, as long as corresponding local feature region also exists in two width images, desirable Local affine invariant feature region detection algorithm just should detect them in corresponding position.Therefore under identical experiment condition, the performance that the method that repetition rate is larger has had.

Taking the 1st width image of 8 groups of cycle testss as reference picture, obtain image to be matched with reference to image scaling some scale respectively.The zoom factor of the 1st image relative reference image to be matched is that the zoom factor of 1.5, the 2 image relative reference images to be matched is 2.0, the like, the zoom factor of last image relative reference image to be matched is 5.5.By these 9 images to be matched be respectively Z1, Z2, Z3 ... and Z9.Adopt two kinds of methods to detect the local feature region (namely stable extremal region) of 9 width images, and calculate respectively the characteristic area repetition rate of 9 width image relative reference images.For 8 groups of cycle testss, the characteristic area repetition rate that two kinds of methods obtain is as shown in the table

?	Z1	Z2	Z3	Z4	Z5	Z6	Z7	Z8	Z9
										The present invention	0.86	0.81	0.77	0.70	0.65	0.63	0.51	0.42	0.35
MSER	0.85	0.78	0.71	0.61	0.44	0.21	0.17	0.09	0.03

As can be seen from the above table, in the time of image generation dimensional variation, the characteristic area repetition rate that the present invention obtains is all greater than MSER method in any case.The dimensional variation of image is larger, and the advantage of the method for the invention is more obvious.

Claims (6)

1. an extracting method with the stable extremal region of yardstick unchangeability, is characterized in that, comprises the steps:

1) first use stable extremal region algorithm in original image, to detect initial stable extremal region;

2) set up the yardstick pyramid of initial stable extremal region by M dyadic wavelet transform, in the yardstick pyramid of initial stable extremal region, according to the energy operator of M dyadic wavelet transform coefficient, determine the unique point with yardstick unchangeability:

Initial stable extremal region is designated as to f (x, y), is increasing progressively yardstick M ^jdo M dyadic wavelet transform along x and y direction down, wherein M is greater than 1 real number that is less than 2, and j is the positive integer increasing progressively, and wavelet function ψ (x, y) is wherein defined as smooth function along the derivative of x and y direction, thereby obtain by increasing progressively yardstick M ^junder level and smooth stable extremal region and wavelet coefficient the MSER yardstick pyramid of composition; The wavelet transformation result of different scale when j is even number, in conjunction with the information on its adjacent position, adopts Teager energy operator to obtain energy and the corresponding mould of M system wavelet conversion coefficient carry out local non-maximum value according to this mould value and suppress, namely, compared with 8 points around, if the mould value maximum of current point, this point is confirmed as having the unique point of yardstick unchangeability, is designated as X=(x, y, M ^j), the wherein position of (x, y) representation feature point, M ^jrepresentation feature point place yardstick;

3) to each unique point of being determined by above-mentioned steps, from the pyramidal each tomographic image of yardstick of stable extremal region, obtain the extremal region corresponding with it, and by the stability indicator of extremal region in multiscale space, extract the stable extremal region with yardstick unchangeability:

First to each unique point of extracting, find out stable extremal region level and smooth under its place yardstick from the yardstick pyramid of stable extremal region the gray-scale value of middle pixel is than all large or all little connected regions of the gray-scale value of its boundary pixel point, as its corresponding extremal region; Then judge spatial stability and the dimensional stability of this extremal region, if this extremal region is all stable at metric space and pixel space, this extremal region is exactly the stable extremal region with yardstick unchangeability so;

4) finally the stable extremal region with yardstick unchangeability is adjusted to elliptical shape:

First according to the region of size and the deletion repetition of area change rate size or poor stability; Then according to covariance matrix, irregularly shaped region is adjusted into regular elliptical region; This elliptical region is amplified to some ratios, obtain the final stable extremal region with unchangeability.

2. the extracting method according to claim 1 with the stable extremal region of yardstick unchangeability, is characterized in that, in described step 2 in M dyadic wavelet transform

3. the extracting method according to claim 1 with the stable extremal region of yardstick unchangeability, is characterized in that, in described step 3, stability indicator comprises the stability indicator ε (ER) of metric space and the stability indicator of pixel space

The stability indicator ε (ER) of metric space is defined as:

$\mathrm{\&epsiv;}\left(\mathrm{ER}\right)=\frac{{\mathrm{Er}}_{j-1}\&cap;{\mathrm{ER}}_j}{{\mathrm{ER}}_{j-1}\&cup;{\mathrm{ER}}_j}+\frac{{\mathrm{ER}}_{j+1}\&cap;{\mathrm{ER}}_j}{{\mathrm{ER}}_{j+1}\&cup;{\mathrm{ER}}_j}$

Wherein j represents the level of extremal region ER in yardstick pyramid;

The stability indicator of pixel space be defined as:

Wherein Δ is an input parameter of algorithm, || represent the gesture of set, ER ^{+ Δ}, ER ^-Δbelong to limit area, if the ε of extremal region ER (ER) exists local minimum, claim that extremal region ER is stable at metric space, if extremal region ER be local minimum, region ER is stable in pixel space so, if extremal region ER is stable at metric space and pixel space, extremal region ER is exactly the stable extremal region with yardstick unchangeability so.

4. the extracting method according to claim 1 with the stable extremal region of yardstick unchangeability, is characterized in that, the region of deleting according to area change rate size in described step 4 has: area change rate is less than 0.5 or be greater than 1 region.

5. there is according to claim 1 the extracting method of the stable extremal region of yardstick unchangeability, it is characterized in that, in described step 4, the region of deleting according to size is: the half of the number of pixels that the pixel threshold values of establishing large area region is selected test pattern, when the number of pixels of this surface area exceedes threshold values, be large area region, need to delete.

6. according to the extracting method of stable extremal region described in one of claim 1-5 with yardstick unchangeability, it is characterized in that, in described step 4, elliptical region amplification factor is 2.5.