CN101996325A - Improved method for extracting characteristic point from image - Google Patents

Abstract

The invention proposes an improved method for extracting feature points in an image. First compute the integral image corresponding to the input image. In the scale space, the corresponding Hessian matrix determinant value is calculated for the image with the filter corresponding to a certain layer and the layer. The elements in the Hessian matrix include the convolution of the filter coverage area with the second-order partial derivatives of the Gaussian distribution function with respect to x, the second-order partial derivatives with respect to x and y, and the second-order partial derivatives with respect to y, respectively. The values corresponding to the convolutional elements are computed with a modified filter shape. The basic idea of filter design is to assign weights to the pixels in different regions of the filter to calculate the approximate value of the convolution of the corresponding region, so as to improve the time efficiency of calculation and improve the robustness to rotation and perspective transformation. Local extremum points are detected in different layers of the scale space and a series of determinants of the Hessian matrix calculated in the layers in the three-dimensional space, and the filtered local extremum point position information and the layer and level information constitute the Information about the final feature points.

Description

The method of unique point in a kind of improved extraction image

Technical field

The invention belongs to the method for unique point in a kind of improved extraction image.Specifically, be a kind of local feature in the computer vision field extract in the method for detected characteristics point, specially refer to and utilize improved filter shape on metric space, to calculate Hessian matrix determinant and find out the process of extreme point with definite character pair point.

Background technology

Local feature has extensively applied to the many aspects of computer vision field, aspects such as for example image registration, Target Recognition, objective retrieval.In the current research, local feature has unchangeability for geometric transformation, illumination conversion, for noise, block and background interference all has good robustness, and has very high discrimination between feature.These all become an important topic of its computer vision field research in the last few years.

The leaching process of the local feature of current main-stream mainly comprised for two steps: feature point detection process and descriptor computation process.In the feature point detection process, typically use a series of wave filter and be used for input picture, and in filtered result, choose the some position (for example extreme point) that possesses some characteristic, as detected unique point; In descriptor computation process, choosing with the unique point is a certain specific region (this zone is usually relevant with information such as yardstick) at center, through determining principal direction, asking a series of processes such as gradient, the distribution of Gauss's weights, obtain the descriptor vector of this unique point correspondence.

Summary of the invention

The present invention proposes the method for unique point in a kind of improved extraction image.It is at present based on a kind of improvement of detection of Hessian matrix determinant.Than previous feature point detecting method, the feature point detecting method among the present invention particularly has higher robustness at institute's detected characteristics point aspect rotation change and view transformation.

The technical problem to be solved in the present invention: according to existing feature point detecting method based on the Hessian determinant, the filter shape of structure sub-circular, propose a kind of improved under rotation and visual angle change feature point detection of robust more.

The method of unique point in a kind of improved extraction image that the present invention proposes, its step comprises:

(1) integral image computation process.For a width of cloth input picture I, calculate its integral image I _∑Certain position x=(x, y) ^T, T represents (x, y) this 1 * 2 transpose of a matrix, integral image I _∑(x) corresponding value herein, be meant by the promptly upper left corner of image origin and position x=(x, y) ^TThe summation of all pixel values in the determined rectangular area, i.e. integral image I _∑(x) computation process is expressed as

$I_{\mathrm{\Σ}}\left(x\right)=\underset{i=0}{\overset{i\≤x}{\mathrm{\Σ}}}\underset{j=0}{\overset{j\≤y}{\mathrm{\Σ}}}I(x,y)$

The pixel value summation I of certain rectangular area ABCD of input picture I correspondence _∑(reg _ABCD) calculation expression be

I _∑(reg _ABCD)＝I _∑(A)-I _∑(B)+I _∑(C)-I _∑(D)

I wherein _∑(A), I _∑(B), I _∑(C), I _∑(D) represent corresponding to an A B, C, the integral image I at D place respectively _∑(x) value.

(2) on metric space, use the wave filter with similar shape of improved different size corresponding to different scale to calculate approximate Hessian determinant and be used for feature point detection.

For input picture I, calculate corresponding Hessian determinant of a matrix value according to different filter size.The Hessian matrix representation is

$H(x,\mathrm{\σ})=\left[\begin{array}{cc}{L}_{\mathrm{xx}}(x,\mathrm{\σ})& L_{\mathrm{xy}}(x,\mathrm{\σ})\\ L_{\mathrm{xy}}(x,\mathrm{\σ})& L_{\mathrm{yy}}(x,\mathrm{\σ})\end{array}\right]$

L _Xx(x, σ) the expression Gaussian function is about the second order local derviation of x and the image I value in the convolution at x place, and wherein σ is the variance of Gaussian function; L _Xy(x, σ) and L _Yy(x, σ) meaning of Denging in like manner can get.And approximate Hessian determinant det (H _Approx) be expressed as

det(H _approx)＝D _xxD _yy-(wD _xy) ²

D wherein _Xx, D _Xy, D _YyRepresent respectively by about x second order local derviation, about x and y second order local derviation with carry out correspondence about the wave filter of y second order local derviation and calculate L _Xx, L _Xy, L _YyApproximate value.Weight w in the formula=0.9.

(a) D _YyComputing method be, wave filter is divided into the length of side that is equal to size and is 9 square area of (2k-1), according to from left to right, order from top to bottom is called upper left district reg _{Lt_sq}, Zhong Shang district reg _{Ct_sq}, upper right district reg _{Rt_sq}, Zuo Zhong district reg _{Lc_sq}, center reg _{Cc_sq}, You Zhong district reg _{Rc_sq}, lower-left district reg _{Lb_sq}, middle inferior segment reg _{Cb_sq}, bottom right district reg _{Rb_sq}Having only four districts of a public vertex with the center is upper left district, upper right district, lower-left district, bottom right district.In these four zones, get respectively that with the center length of side on a public summit to be arranged be the square area of k, be called reg _{Lt_sq_sub}, reg _{Rt_sq_sub}, reg _{Lb_sq_sub}With reg _{Rb_sq_sub}

When k is odd number, at Zuo Zhong district reg _{Lc_sq}He Youzhong district reg _{Lc_sq}The square area reg that to get a length of side respectively be k _{Lc_sq_sub}And reg _{Rc_sq_sub}, these two square area are right after center reg respectively _{Cc_sq}The left side, their Center-to-Center district reg _{Cc_sq}Be centered close on the same horizontal line; At You Zhong district reg _{Lc_sq}In can get a symmetrical square area reg equally _{Lc_sq_sub}When k is even number, at Zuo Zhong district reg _{Lc_sq}The square area reg that to get two length of sides be k _{Lc_sq_sub_1}And reg _{Lc_sq_sub_2}, they all are next to center reg _{Cc_sq}The left side, at You Zhong district reg _{Rc_sq}In get two symmetrical square area reg _{Rc_sq_sub_1}And reg _{Rc_sq_sub_2}, they all are next to center reg _{Cc_sq}The right side, reg _{Lc_sq_sub_1}And reg _{Rc_sq_sub_1}The upper end all be positioned at from center reg _{Cc_sq}The upper end begin to count

Individual position, reg _{Lc_sq_sub_2}And reg _{Rc_sq_sub_2}The vertical position of upper end all be positioned at begin to count from the upper end of center

Individual position;

The calculating formula of Dyy is

D _XxComputing method be

(b) D _XyComputing method be, be the center of circle with the center of wave filter, be diameter with 2k+1, do a border circular areas; Remove the horizontal symmetry axis and the vertical axis of symmetry part of wave filter, this border circular areas is divided into the sector region of four pi/2 sizes; Upper left, upper right, lower-left, lower right area are called reg _{Lt_fan}, reg _{Rt_fan}, reg _{Lb_fan}, reg _{Rb_fan}Note and upper left sector region reg _{Lt_fan}The length of side be that the external square area of k is reg _{Lt_fan_sq}, promptly it has a summit to overlap with the center of circle of this sector region, has two limits to overlap with outermost two radiuses of sector region; External square area reg _{Lt_fan_sq}Point to sector region reg _{Lt_fan}The diagonal line in the center of circle and sector region reg _{Lt_fan}The intersection point of arc, be positioned at the end points in the sector region outside with this diagonal line, the square area of formation is called reg _{Lt_fan_sq_1}With regional reg _{Lt_fan_sq}In connect, with reg _{Lt_fan_sq_1}External and have a summit to be positioned at sector region reg _{Lt_fan}Be symmetrical in reg on the arc _{Lt_fan_sq}Cornerwise two square area be called reg _{Lt_fan_sq_2_l}, reg _{Lt_fan_sq_2_r} With regional reg _{Lt_fan_sq}In connect, with reg _{Lt_fan_sq_2_l}External and position, a summit and sector region reg arranged _{Lt_fan}Square area on the arc is called reg _{Lt_fan_sq_3_l}In like manner can get reg _{Lt_fan_sq_3_r}, reg _{Lt_fan_sq_4_l}, reg _{Lt_fan_sq_4_r}Etc. a series of square area; Reg then _{Lt_fan}The calculation expression of approximate region summation be

I _∑(reg _{lt_fan_approx})≈I _∑(reg _{lt_fan_sq})-[I _∑(reg _{lt_fan_sq_1})+

I _∑(reg _{lt_fan_sq_2_l})+I _∑(reg _{lt_fan_sq_2_r})+I _∑(reg _{lt_fan_sq_3_l})+I _∑(reg _{lt_fan_sq_3_r})+...]

In like manner obtain the expression formula of other fan-shaped approximate regions; Final D _XyCalculation expression be

D _xy＝I _∑(reg _{lt_fan_approx})-I _∑(reg _{rt_fan_approx})+I _∑(reg _{rb_fan_approx})-I _∑(reg _{lb_fan_approx})

According to different filter size, calculate the value of the Hessian matrix determinant on the corresponding metric space.Metric space can be divided into a series of layer, and each layer comprises a series of levels again.The k value that each level is corresponding different.The k value of the level correspondence in the ground floor is respectively and is not less than 2 tolerances is 1 integer ordered series of numbers.The k value of the level correspondence in the second layer is respectively: be not less than 3 tolerances and be 2 integer ordered series of numbers.The k value of the level correspondence in the 3rd layer is respectively: be not less than 5 tolerances and be 4 integer ordered series of numbers.The k value of the level correspondence in the 4th layer is respectively: be not less than 9 tolerances and be 8 integer ordered series of numbers.The k value of the level correspondence in the n layer is respectively: be not less than 2 ^N-l+ 1 tolerance is 2 ^N-lThe integer ordered series of numbers.For each position in the metric space, the Hessian matrix determinant according to the wave filter of different k value correspondingly-sized calculates is used for follow-up extreme point testing process.

(3) dot information of the extreme value correspondence of the Hessian determinant in the metric space is as final detected unique point.For a series of Hessian determinant that calculates on the metric space, in each layer, for some positions, check that whether it is the extreme point in the zone of 3 * 3 * 3 in the adjacent level up and down, if extreme point that should the zone, so just it is chosen for detected unique point in the corresponding metric space, the characteristic of correspondence dot information comprises the positional information at this extreme point place and extreme point corresponding level number and level number in metric space.

Description of drawings

Fig. 1 is the process flow diagram of feature point detecting method.

Fig. 2 is that certain regional gray-scale value summation is calculated in the integral image.

Fig. 3 a, b are for calculating D _YySynoptic diagram.

Fig. 4 a, b are D _YyInstance graph.

Fig. 5 is for calculating D _XySynoptic diagram.

Fig. 6 a, b, c, d are for calculating D _XyInstance graph.

Specific embodiments

As shown in Figure 1, the method key step of the unique point in the improved extraction image can be described as: integral image calculates, use improved filter shape to calculate the value of corresponding Hessian matrix determinant on different metric spaces, the extreme point in the metric space detects to obtain final characteristic point position and yardstick information.

The value of certain pixel location correspondence in the integral image of one width of cloth input picture, i.e. all gray-scale value sums from the image origin rectangle that to be the upper left corner constituted to this point.For certain position x=in the input picture (x, y) ^T, the transposition of T representing matrix, its integral image values I _∑(x) equation expression is

$I_{\mathrm{\Σ}}\left(x\right)=\underset{i=0}{\overset{i\≤x}{\mathrm{\Σ}}}\underset{j=0}{\overset{j\≤y}{\mathrm{\Σ}}}I(x,y)$

Gray area among Fig. 2 and can carry out computing by the integral image values on four angles, corresponding rectangular area and obtain.The pixel value summation I of rectangular area ABCD _∑(reg _ABCD) calculation expression be

I _∑(reg _ABCD)＝I _∑(A)-I _∑(B)+I _∑(C)-I _∑(D)

I wherein _∑(A), I _∑(B), I _∑(C), I _∑(D) represent corresponding to an A B, C, the integral image values at D place respectively.

The expression formula of Hessian matrix is

$H(x,\mathrm{\σ})=\left[\begin{array}{cc}{L}_{\mathrm{xx}}(x,\mathrm{\σ})& L_{\mathrm{xy}}(x,\mathrm{\σ})\\ L_{\mathrm{xy}}(x,\mathrm{\σ})& L_{\mathrm{yy}}(x,\mathrm{\σ})\end{array}\right]$

L _Xx(x, σ) the expression Gaussian function is about the second order local derviation of x

With the value of image I in the convolution at x place, wherein σ is the variance of Gaussian function.L _Xy(x, σ) and L _Yy(x, σ) meaning of Denging in like manner can get.The determinant of Hessian matrix correspondence has been described the amplitude with the gradient of rate of gray level on this aspect on the curved surface of the gray-scale value formation of image.

Because the second-order partial differential coefficient of Gaussian function is a series of floating-point fractional value under the situation of discrete picture, complexity computing time of the convolution of itself and original image is higher.In this patent, adopt D _Xx, D _Xy, D _YyRepresent L respectively _Xx, L _Xy, L _YyApproximate value.Then Hessian determinant of a matrix calculation expression is

det(H _approx)＝D _xxD _yy-(wD _xy) ²

Weights are w=0.9 in the formula, are used for the calculating of balance Hessian determinant.

D _YyCalculating as shown in Figure 3.The square of outermost is the peripheral profile of wave filter that is used to calculate Hessian matrix determinant among the present invention.Its length of side is 3 odd-multiple, is expressed as 2k-1.The value of k illustrates in the back.The left figure of Fig. 3 and right figure are the D when k is respectively odd and even number _YyCalculate synoptic diagram.In the filter shape of left figure, comprise up and down two white portions, middle black region and remaining gray area part.Wherein the top white portion is made up of three squares.The big foursquare length of side is 2k-1, is positioned at the center of the level of whole filter.Two little foursquare length of sides of both sides are k, and lower edge and foursquare lower edge broad in the middle are positioned on the same horizontal line.Below white portion and top white portion are the shape of symmetry about the central horizontal line.Middle black region is different according to its shape of parity of k.When k was odd number, middle its length of side of big square was 2k-1, and the little square length of side of both sides is k, and three foursquare centers all are positioned on the horizontal symmetry axis.When k was even number, the centre was still the big square that the length of side is 2k-1, and the shape of both sides is respectively two squares that a unit difference is arranged on the upright position that overlap on together.This is because when k is even number, is the square of k with the length of side, and a whole pixel value can not be got in its center.Thereby the upper end position at two foursquare centers of the same side lay respectively at from the centre foursquare top position downwards number the

With

Individual position.Thereby be under the situation of even number at k, two pairs of squares of both sides are nonoverlapping in the zone that one-row pixels is all arranged up and down.In the right side area of correspondence, can get the zone of k correspondence under different odd even situations equally.

The weights of the part of black are-2 among the figure, and the weights of white are+1, and grayish weights are 0, and the weights of Dark grey part are-1.

D _YyComputing method promptly multiply each other each several part among the figure and weights exactly, and the result of the addition of all products is exactly D _YyValue.Promptly as described in the summary of the invention.Under the situation that is k=3 and k=4 shown in Fig. 4, calculate corresponding D _YyThe shape synoptic diagram.D _XxComputing method similar, just calculate D _YyThe direction of used shape has been reversed an angle of 90 degrees.

D _XyComputing method as shown in Figure 5.This is that a radius is r, angle be pi/2 a sector region with and be the external square area of the length of side with r.Diagonal line AC and arc BMD meet at M.MH ₁With MF ₁Perpendicular with AB and AD respectively.AF then ₁MH ₁It is a square.H ₁T ₁Be parallel to AC again, and T ₁G ₁With T ₁H ₂Again respectively with AD and MH ₁Perpendicular.H ₁G ₁T ₁H ₂It promptly is a square.And the like, H ₁G ₁T ₁H ₂, H ₂G ₂T ₂H ₃, H ₃G ₃T ₃H ₄... and with its regional F about the AC symmetry ₁E ₁U ₁F ₂, F ₂E ₂U ₂F ₃, F ₃E ₃U ₃F ₄... Deng all is square, and one of its summit all is positioned on the arc BMD.

Under the situation of known r,,, can obtain H by separating the analytic equation group with the initial point of a C as plane coordinate system _i(x _i, coordinate (x r) _i＜0) and the length of side s of all square area _iThe result is shown in following formula:

${\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="DEST\_PATH\_HSB00000410132600013.png,DEST\_PATH\_HSB00000410132600014.png"\; state="\{\{state\}\}">s</figure-callout>}}_1=\stackrel{\&OverBar;}{{\mathrm{<figure-callout\; id="1"\; label="AH"\; filenames="DEST\_PATH\_HSB00000410132600013.png,DEST\_PATH\_HSB00000410132600014.png"\; state="\{\{state\}\}">AH</figure-callout>}}_1}=\frac{\sqrt{2}}{2}\&CenterDot;\stackrel{\&OverBar;}{\mathrm{AM}}=(1-\frac{\sqrt{2}}{2})r,$ $s_i=\stackrel{\&OverBar;}{H_i{H}_{i-1}}=x_i-x_{i-1},i=\mathrm{2,3,4},...)$

$x_1=-\frac{\sqrt{2}}{2}r,$ $x_i=-\frac{r+x_{i-1}-\sqrt{r^2-2{\mathrm{rx}}_{i-1}-x_{i-1}^2}}{2},i=\mathrm{2,3,4},...$

Can solve x _iSeries of results be x ₁=-0.707r, x ₂=-0.545r, x ₃=-0.442r, x4=-0.371r ...s _iSeries of results be s ₁=0.293r, s ₂=0.163r, s ₃=0.103r, s ₄=0.071r .....x _iValue all be rounded up to integer.Thereby among the figure a series of square area and can obtain by above-mentioned coordinate relation.Thereby the gray-scale value sum of sector region BMDC can obtain by following formula is approximate

$I_{\mathrm{\&Sigma;}}\left({\mathrm{fan}}_{\mathrm{MBCD}}\right)\&ap;I_{\mathrm{\&Sigma;}}\left({\mathrm{reg}}_{\mathrm{ABCD}}\right)-I_{\mathrm{\&Sigma;}}\left({\mathrm{reg}}_{{\mathrm{AF}}_1{\mathrm{MH}}_1}\right)-(I_{\mathrm{\&Sigma;}}\left({\mathrm{reg}}_{H_1{G}_1{T}_1{H}_2}\right)+I_{\mathrm{\&Sigma;}}\left({\mathrm{reg}}_{H_2{G}_2{T}_2{H}_3}\right)+...)$

$-(I_{\mathrm{\&Sigma;}}\left({\mathrm{reg}}_{F_1{E}_1{U}_1{F}_2}\right)+I_{\mathrm{\&Sigma;}}\left({\mathrm{reg}}_{F_2{E}_2{U}_2{F}_3}\right)+...)$

In addition, the zone of some grey is arranged in Fig. 5, these zones can be omitted with respect to other bigger square area for the influence of testing process and be disregarded.Calculate square area that fan-shaped approximate gray-scale value sum need deduct to H ₃G ₃T ₃H ₄Size can satisfy the requirement of robustness.Calculate littler square again, its complexity increases and the detection effect is not greatly improved.

For other three sector regions, can be with reference to the method for Fig. 5.Fig. 6 has showed at k=2, k=3, k=4, the wave filter situation under the situation of k=7.The part of black is given weights-1 among the figure, and the weights of white portion are+1, and the part weights of grey are 0.Each several part is corresponding D with the product of separately weights and the result of addition _XyValue.

The calculating of Hessian determinant is carried out on metric space.Metric space is divided into a series of layer, and each layer is divided into a series of level again.The k value of the level correspondence in the ground floor is respectively and is not less than 2 tolerances is 1 integer ordered series of numbers.The k value of the level correspondence in the second layer is respectively: be not less than 3 tolerances and be 2 integer ordered series of numbers.The k value of the level correspondence in the 3rd layer is respectively: be not less than 5 tolerances and be 4 integer ordered series of numbers.The k value of the level correspondence in the 4th layer is respectively: be not less than 9 tolerances and be 8 integer ordered series of numbers.The k value of the level correspondence in the n layer is respectively: be not less than 2 ^N-1+ 1 tolerance is 2 ^N-1The integer ordered series of numbers.In the real process, satisfy institute's detected characteristics point and be for the preferred version of the robustness of affined transformation and illumination variation, often get metric space preceding 4 layers, and each layer is divided into 4 levels.The k value sequence that each layer correspondence is different.The k value sequence of the 1st layer of correspondence is: 2,3,4,5.The k value sequence of the 2nd layer of correspondence is: 3,5,7,9.The k value sequence of the 3rd layer of correspondence is: 5,9,13,17.The k value sequence of the 4th layer of correspondence is: 9,17,25,33.

In metric space, detect extreme point, as detected unique point about the Hessian determinant.Its testing process is as follows, for certain position that is in the metric space, the value of its Hessian determinant, with in neighbouring level and this layer in close position totally 26 values compare, if this value is local extreme value, think that then this position and corresponding layer and hierarchical information have constituted the information of passing through the detected unique point of this method.

Claims (7)

1. an improved method for extracting feature points in an image, characterized in that it comprises the following steps: (1) Calculate the integral image; (2) In the scale space, use two-dimensional filters with different sizes of second-order partial derivatives to calculate the approximate Hessian determinant of the integral image for feature point detection; (3) The point information corresponding to the extreme value of the Hessian determinant in the scale space is used as the finally detected feature point information. 2. the method for feature point in the improved extracting image according to claim 1 is characterized in that: for an input image I, calculate its integral image I _∑ ; A certain position x=(x, y) wherein On ^T , T represents the transposition of the 1×2 matrix (x, y), and the value of the integral image I _∑ (x) refers to the point and position x=(x, y) ^T The sum of all pixel values in the determined rectangular area, the calculation process of I _∑ (x) is ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ The calculation expression of the sum of pixel values I _∑ (reg _ABCD ) of a certain rectangular area ABCD corresponding to the input image I is I _∑ (reg _ABCD )＝I _∑ (A)-I _∑ (B)+I _∑ (C)-I _∑ (D), Wherein I _∑ (A), I _∑ (B), I _∑ (C), and I _∑ (D) represent the integral image I _∑ (x) values corresponding to points A, B, C, and D, respectively. 3. the method for feature point in the improved extraction image according to claim 1, is characterized in that: Hessian matrix is expressed as $\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left[\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; xy</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; xy</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>& {\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; yy</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; ,</span>$ L _xx (x, σ) represents the value of the convolution of the second-order partial derivative of the Gaussian function about x and the image I at x, and L _xy (x, σ) represents the second-order partial derivative of the Gaussian function about x and about y and The value of the convolution of the image I at x, L _yy (x, σ) represents the value of the convolution of the second-order partial derivative of the Gaussian function with respect to y and the convolution of the image I at x, where σ is the variance of the Gaussian function; approximate Hessian The determinant det(H _approx ) is expressed as det(H _approx )=D _xx D _yy -(wD _xy ) ² , Among them, D _xx , D _xy , D _yy represent L _xx , L _xy , L _yy obtained through the corresponding calculation of the second-order partial derivative of x, the second-order partial derivative of x and y, and the second-order partial derivative of y, respectively. The approximate value of , where the weight w=0.9. 4. the method for feature point in the improved extraction image according to claim 1, is characterized in that: filter is a side length and is the square of the product size of an odd number and 3, is expressed as 3 (2k-1), wherein k is an integer not less than 2, which corresponds to different layers in different layers in the scale space, and the sequence of k values corresponding to the layers in the nth layer is: the tolerance of not less than 2 ^n-1 +1 is 2 ^n-1 Integer sequence; different k values correspond to different filter sizes, so that the corresponding Hessian determinant value is calculated at each position in the scale space. 5. the method for feature point in the improved extraction image according to claim 3, is characterized in that: the computing method of D _yy is, filter is divided into 9 squares that the side length of equal size is (2k-1) Regions, in order from left to right and from top to bottom, are called upper left region reg _{lt_sq} , upper middle region reg _{ct_sq} , upper right region reg _{rt_sq} , left middle region reg _{lc_sq} , central region reg _{cc_sq} , and right middle region reg _{rc_sq} , lower left area reg _{lb_sq} , lower middle area reg _{cb_sq} , lower right area reg _{rb_sq} ; the four areas with only one common vertex with the central area are upper left area, upper right area, lower left area, and lower right area; among these four areas, Respectively take a square area with a common vertex and a side length of k with the central area, called reg _{lt_sq_sub} , reg _{rt_sq_sub} , reg _{lb_sq_sub} and reg _{rb_sq_sub} respectively; When k is an odd number, square areas reg _{lc_sq_sub} and reg _{rc_sq_sub} with a side length of k are respectively taken in the left middle area reg _{lc_sq} and the right middle area reg _{lc_sq} , and these two square areas are respectively adjacent to the left and right sides of the central area reg _{cc_sq} , Their centers are on the same horizontal line as the center of the central area reg _{cc_sq} ; when k is an even number, two square areas reg _{lc_sq_sub_1} and reg _{lc_sq_sub_2} with a side length of k are taken in the left middle area reg _{lc_sq} , and they are all adjacent to the central area On the left side of reg _{cc_sq} , two symmetrical square areas reg _{rc_sq_sub_1} and reg _{rc_sq_sub_2} are taken in the right middle area reg _{rc_sq} , they are all close to the right side of the central area reg _{cc_sq} , the vertical positions of the upper ends of reg _{lc_sq_sub_1} and reg _{rc_sq_sub_1} are both Located at the first counting from the upper end of the central area reg _{cc_sq}

position, the vertical position of the upper end of reg _{lc_sq_sub_2} and reg _{rc_sq_sub_2} is located at the first counting from the upper end of the central area

location; The calculation formula of D _yy is

D _xx is calculated as

6. the method for feature point in the improved extraction image according to claim 3, it is characterized in that: the calculation method of _Dxy is, take the central position of filter as the center of circle, take 2k+1 as diameter, make a circle Area; remove the horizontal symmetry axis and vertical symmetry axis of the filter, the circular area is divided into four fan-shaped areas of π/2 size; the upper left, upper right, lower left, and lower right areas are called reg _{lt_fan} , reg _{rt_fan} respectively , reg _{lb_fan} , reg _{rb_fan} ; mark the circumscribed square area of the upper left fan-shaped area reg _{lt_fan} with a side length of k as reg _{lt_fan_sq} , that is, there is a vertex coincident with the center of the fan-shaped area, and there are two sides and the outermost side of the fan-shaped area The two radii coincide; the circumscribed square area reg _{lt_fan_sq} points to the intersection of the diagonal line of the center of the fan-shaped area reg _{lt_fan} and the arc of the fan-shaped area reg _{lt_fan} , and the endpoint of the diagonal line outside the fan-shaped area. The square area formed is called reg _{lt_fan_sq_1} ; inscribed with the region reg _{lt_fan_sq} , circumscribed with reg _{lt_fan_sq_1} and have a vertex located on the arc of the fan-shaped region reg _{lt_fan} , two square regions symmetrical to the diagonal of reg _{lt_fan_sq} are called reg _{lt_fan_sq_2_l} , reg _{lt_fan_sq_2_r} ; and the region reg _{lt_fan_sq} is inscribed, and reg _{lt_fan_sq_2_l} is circumscribed and has a vertex and the square area above the fan-shaped area reg _{lt_fan} arc is called reg _{lt_fan_sq_3_l} ; similarly can get reg _{lt_fan_sq_3_r} , reg _{lt_fan_sq_4_l} , reg _{lt_fan_sq_4_r} a series of square areas; then reg The calculation expression of the approximate area sum of _{lt_fan} is I _∑ (reg _{lt_fan_approx} )≈I _∑ (reg _{lt_fan_sq} )-[I _∑ (reg _{lt_fan_sq_1} )+ I _∑ (reg _{lt_fan_sq_2_l} )+I _∑ (reg _{lt_fan_sq_2_r} )+I _∑ (reg _{lt_fan_sq_3_l} )+I _∑ (reg _{lt_fan_sq_3_r} )+...] In the same way, the expressions of the approximate areas of other sectors are obtained; the final calculation expression of D _xy is D _xy =I _∑ (reg _{lt_fan_approx} )−I _∑ (reg _{rt_fan_approx} )+I _∑ (reg _{rb_fan_approx} )−I _∑ (reg _{lb_fan_approx} ). 7. The improved method for extracting feature points in an image according to claim 1, characterized in that: for a series of Hessian determinant values calculated on the scale space, in each layer, for a certain position, check Whether this position is the extreme point in the 3×3×3 area in the adjacent upper and lower levels, if it is the extreme point of the area, then it will be selected as the feature point detected in the corresponding scale space, corresponding to The feature point information includes the position information of the extreme point, the layer number and the layer number corresponding to the extreme point in the scale space.

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