CN105160686B - A kind of low latitude various visual angles Remote Sensing Images Matching Method based on improvement SIFT operators - Google Patents
A kind of low latitude various visual angles Remote Sensing Images Matching Method based on improvement SIFT operators Download PDFInfo
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Abstract
The invention discloses a kind of based on the low latitude various visual angles Remote Sensing Images Matching Method for improving SIFT operators, feature point detection is carried out to the first image and the second image using the DoG operators of optimization first, then utilize SIFT description simulated of being sampled based on regional area that characteristic point is described to form characteristic vector, initial matching characteristic point is finally formed using NNDR strategies, and match point purified using the RANSAC algorithms based on Epipolar geometric constraint.The problems such as present invention can efficiently solve various visual angles present in low altitude remote sensing image matching and weak texture.
Description
Technical field
The invention belongs to Remote Sensing Image Processing Technology field, it is related to a kind of Remote Sensing Images Matching Method, is related to one kind and is based on
Improve the low latitude various visual angles Remote Sensing Images Matching Method of SIFT operators.
Background technology
Image Matching is always photogrammetric and research emphasis and focus in remote sensing fields, is image orientation, orthogonal projection
As making, image autoregistration and one of splicing, the committed step of three-dimensional reconstruction directly influence the essence of subsequent product making
Degree and effect.Compared with traditional remote sensing image, the acquisition environment of low altitude remote sensing image is more complicated, particularly obtains with different view
The image taken, there are problems that serious geometric distortion, similar grain, texture fracture, shade, substantially reduce same
Similitude of one target on the different images with overlapping region, the matching strip to low latitude image comes great difficult.Therefore,
How reliable and stable match point is obtained from the low latitude various visual angles image with serious geometric distortion to be significant.
Image Matching Algorithm is broadly divided into two classes：Matching based on image greyscale and the matching based on image feature.It is based on
The matching process of image greyscale is directly operated to the pixel on image in certain window ranges, passes through pixel in window ranges
Gray Correlation carry out homotopy mapping, although such method can be obtained in the case where image radiation and geometric form diminish
Higher matching precision, but its grey scale change to image is more sensitive, is not suitable for the geometry in the various visual angles image of low latitude
Distortion, similar grain, texture fracture, shade, the problems such as block.Matching process based on image feature is by extracting in image
The geometric properties such as point, line, surface are matched, and can preferably supplement the deficiency of the matching process based on gray scale.
At present, in feature-based matching method, most widely used is the SIFT (Scale that Lowe is proposed
Invariant Feature Transformation) algorithm, it can preferably handle rotation, the yardstick contracting in image geometry deformation
Put and translate change the problem of, but big perspective images to the problem of on, still can not obtain gratifying effect.In order to
Improve the matching effect for different visual angles image, scholars carry out a variety of researchs and improvement to SIFT operators, it is proposed that ASIFT
(Affine-SITT), ISIFT (Iterative-SITT) and MM-SIFT (Multi-resolution MSER based
The various visual angles image matching method such as SIFT).ASIFT is carried out according to camera affine model to longitude, three parameters of latitude and yardstick
Sampling, with analog image view transformation, so that affine space image is set up, it is then special in the upper carry out SIFT of all analog images
Levy a detection and match, thus this method has complete affine-invariant features, in the case of larger visual angle change, can also obtain
Preferable matching result is obtained, at the same time, its time complexity increases therewith, limits its application.In order to balance matching
As a result and time efficiency, ISIFT methods utilize a geometric transformation modeling wherein width image for iterative estimate, then using only
The width analog image having carries out SIFT with another width image and matched, and substantially increases matching efficiency.But when geometry between image
When distorting larger, the algorithm can be because geometrical model solves failure and fails.MM-SIFT is met according to correspondence regional area in image
The theory of same affine model, carries out circle normalization, then normalized to the locally ellipticity region in two width images
SIFT matchings are carried out in elliptic region.This method substantially increases time efficiency, and there is between image big visual angle change
In the case of, remain able to obtain some correct match points, but its regional area dependence to extraction is big, it uses MSER
During operator extraction regional area, not optimal threshold, and existing Region Segmentation Algorithm is still immature for various visual angles image.
The content of the invention
The deficiency existed for existing Image Matching technology is high it is an object of the invention to provide a kind of time efficiency and right
Image geometry distortion is compared with stable based on the improved low latitude various visual angles image matching methods of SIFT.
The technical solution adopted in the present invention is：A kind of low latitude various visual angles Remote Sensing Images Matching based on improvement SIFT operators
Method, it is characterised in that comprise the following steps：
Step 1：The characteristic point in the first image and the second image is detected using the DoG operators of adaptive threshold；
Step 2：Son is described based on improved SIFT description is clicked through to feature；
For the characteristic point extracted on the first image and the second image, it is respectively adopted and is adopted based on border circular areas in its neighborhood
Sample and based on elliptic region sample gray value characteristic point is described, ultimately form 128 dimensional feature vectors；
Step 3：Nearest neighbor distance and the ratio of time nearest neighbor distance between the corresponding characteristic vector of distinguished point based
(NNDR, Nearest Neighbor Distance Ratio) this strategy obtains initial matching point set；
Step 4：RANSAC algorithms based on Epipolar geometric constraint are purified to initial matching point set, are finally matched
Point.
Preferably, the DoG operators of the use adaptive threshold described in step 1 are detected in the first image and the second image
Characteristic point, be according to the adaptive threshold value T_ of half-tone information in certain window ranges centered on characteristic point
Contrast, its expression formula is：
Wherein, (m, n) is coordinate of the characteristic point in image, and N is window size, xklIt is pixel in DoG metric spaces
Gray value,It is the average gray of pixel in window ranges, r is determined by the yardstick of image, can be calculated as follows：
Wherein, SiFor the yardstick where current signature point, MIRepresent the quantity of image in DoG metric spaces, σ0Represent image
Smooth degree.
Preferably, characteristic point is described based on the gray value that border circular areas is sampled for the use described in step 2, it is right
In the arbitrary characteristics point (x of the first imagei,yi), the border circular areas sampled point in its neighborhoodExpression formula be：
Wherein, rijFor sample radius, θkFor sampling angle.
Preferably, characteristic point is described based on the gray value that elliptic region is sampled for the use described in step 2, it is right
In the arbitrary characteristics point (x ' of the second imagei,y′i), the elliptic region sampled point (x ' in its neighborhoodi jk,y′i jk) expression formula be：
x′i jk=x 'i+aij cos(θk)cos(θ0)+bij cos(θk)sin(θ0)；
y′i jk=y 'i+aij sin(θk)sin(θ0)-bij cos(θk)cos(θ0)；
Wherein, aijFor ellipse sampling major axis, bijFor ellipse sampling short axle, bij=aij/ γ, γ >=1, θ0For oval direction,
θkFor sampling angle.
Preferably, the gradient calculation expression formula of sampled point is as follows：
Wherein, d.() represents the point θ and the Grad in γ directions, and m () represents the gradient direction of the point, sampled point
Gray value then asked for by the way of bilinear interpolation, be designated as
Preferably, determining elliptic parameter γ and θ using the strategy of iterative0, comprise the following steps that：
Step 2.1：M characteristic point is randomly selected from the first image, its characteristic vector is designated as
Step 2.2：When carrying out oval sampling in the second image, if γ=γs, θ0=0, obtain all feature point features
Vector, is designated asThe first image and the second image, the correct matching of note are matched using closest minimum distance method
Number is n；
Step 2.3：Change γ and θ0Value, wherein γ ∈ [γs,γe], θ0In the case of ∈ [0 °, 90 °], acquisition multiple analog
D ' and corresponding correct match point ni；
Step 2.4：Compare it is a variety of in the case of matching result, when obtain max (ni) when, corresponding γ*And θ*It is as optimal
Solution；
Step 2.5：Max (n are selected in the first imagei) when characteristic point as initial point, re-start step 2.1-
Step 2.5, until γ*And θ*Value tend towards stability.
Preferably, being completed in step 2 after neighbouring point sampling, the gray value of sampled point is asked for by bilinear interpolation method.
Compared with prior art, the present invention has following features and beneficial effect,
1st, adaptive threshold is used in the feature point extraction stage so that DoG operators can adapt to the image of different texture, from
And ensure that subsequent match result；
2nd, the stage is described in feature, goes to simulate visual angle change by the way of ellipse sampling, add same target not
With the similitude on perspective images, the matching effect of various visual angles and weak texture region is substantially improved；
3rd, simulated using localized region rather than view picture image is handled, improving the same of matching precision
When, take into account time efficiency.
Brief description of the drawings
Fig. 1：For the flow chart of the embodiment of the present invention；
Fig. 2：For the border circular areas sampling schematic diagram in the embodiment of the present invention；
Fig. 3：For the elliptic region sampling schematic diagram in the embodiment of the present invention.
Embodiment
Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with the accompanying drawings and embodiment is to this hair
It is bright to be described in further detail, it will be appreciated that implementation example described herein is merely to illustrate and explain the present invention, not
For limiting the present invention.
It is proposed by the present invention a kind of based on the low latitude various visual angles Remote Sensing Images Matching Method for improving SIFT operators, use first
The DoG operators of optimization extract characteristic point respectively on reference to image and image to be matched；Secondly using based on local area simulation
SIFT description son carry out feature description；Minimum distance is then based on the ratio strategy of time adjacency to characteristic point progress
Match somebody with somebody, and initial matching result is purified using the RANSAC based on pole geometry, obtain final match point.
When it is implemented, the present invention can realize automatic running flow using computer software technology.To describe this hair in detail
Bright technical scheme, see Fig. 1, it is a kind of based on the low latitude various visual angles Remote Sensing Images Matching side for improving SIFT operators that the present invention is provided
Method, comprises the following steps：
Step 1：The characteristic point in the first image and the second image is detected using the DoG operators of adaptive threshold；
In order to adapt to the image of different details, the present invention does not use the fixed threshold in original DoG, but according to feature
The adaptive threshold value T_contrast of half-tone information in certain window ranges centered on point, its expression formula is：
Wherein, (m, n) is coordinate of the characteristic point in image, and N is window size, xklIt is pixel in DoG metric spaces
Gray value,It is the average gray of pixel in window ranges, r is determined by the yardstick of image, can be calculated as follows：
Wherein, SiFor the yardstick where current signature point, MIRepresent the quantity of image in DoG metric spaces, σ0Represent image
Smooth degree.
Step 2：Son is described based on improved SIFT description is clicked through to feature；
For the characteristic point extracted on the first image and the second image, it is respectively adopted and is adopted based on border circular areas in its neighborhood
Sample and based on elliptic region sample gray value characteristic point is described, ultimately form 128 dimensional feature vectors；
The research object of the present invention is low latitude various visual angles remote sensing image, due to the complexity of image-forming condition, different visual angles shadow
Serious geometric distortion is there is as between so that overall image is unsatisfactory for same affine transformation, but, with overlapping region
The corresponding part plan region of various visual angles image can be represented with same affine transformation.In image geometry, circle and ellipse
Between relation can be for portraying an affine transformation, therefore, feature of the present invention in feature describes stage, a width image
Point description scope uses the description scope in border circular areas, another width image using the elliptic region of simulation, it is therefore an objective to simulate shadow
The similitude of half-tone information in the view transformation of picture, increase feature vertex neighborhood, so as to improve the matching effect of various visual angles image.
When to the characteristic point of a wherein width image with border circular areas to describe when, to each characteristic point (xi,yi), its office
The size available radius in portion circle description region represents that its expression formula is as follows.
Wherein, σiIt is characterized a place yardstick.
Different directly using the gray value in adjacent integers coordinate from original SIFT, the present invention uses sampling and the side of interpolation
Formula obtains the half-tone information in neighborhood, and sample mode is as shown in Figure 2.Radius in region and angle are described to part-circular
Sampling expression formula be respectively：
rij=jwi/s；
θk=k π/180；
Wherein, s is total radius sampling number, and j=1 ..., s, k are sampling angle, k=1 ..., 360 °/n ...,
360°。
According to sample radius and sampling angle, sampled point can be calculatedCoordinate：
Wherein, rijFor sample radius, θkFor sampling angle.
The gray value of sampled point is then asked for by the way of bilinear interpolation, is designated asBilinear interpolation is one
Common method is planted, is repeated no more herein.
When using elliptic region Expressive Features point to other width image, the content that characteristic point elliptic region is included should
It is as far as possible identical with the content that same place border circular areas is included to ensure matching effect.For each characteristic point (x 'i,y′i), root
According to major axis aij, short axle bijAnd ellipse direction θ0Three elliptic parameters, you can determine the sample range of elliptic region.aijMeter
Calculation mode and rijIt is identical, if bij=aij/ γ, the then parameter for controlling elliptic region to change is γ and θ0.Ellipse is sampled
When, sample mode is as shown in figure 3, each sampled point (x 'i jk,y′i jk) coordinate can be calculated according to equation below：
x′i jk=x 'i+aij cos(θk)cos(θ0)+bij cos(θk)sin(θ0)；
y′i jk=y 'i+aij sin(θk)sin(θ0)-bij cos(θk)cos(θ0)；
Wherein j=1 ..., s, θ0∈ [0 °, 180 °], θk=k π/180, k=1 ..., 360 °/n ..., 360 °.
Complete after neighbouring point sampling, the gray value of elliptic region sampled point is equally obtained by the way of bilinear interpolation.
It is different from original SIFT when calculating gradient, without using adjacent feature point, such as (xi,yi), (xi,yi- 1), (xi-1,
yi) etc., but above-mentioned neighbouring sample point is used, such as Deng being retouched with circle
State exemplified by region, the specific calculation expression of gradient is as follows：
Wherein, d.() represents the point θ and the Grad in γ directions, and m () represents the gradient direction of the point.
The shade of gray obtained according to above formula, can calculate gradient direction Nogata according to original SIFT calculation
Figure, and then obtain the characteristic vector of each characteristic point.
Can above-mentioned SIFT description based on local area simulation sampling effectively solve the geometric deformation under big visual angle and ask
Topic, key is simulation degree of the elliptic region to border circular areas, that is, the parameter for controlling elliptic region to change is γ and θ0.This hair
Bright use iterative strategy solves γ and θ0Value, to ensure matching effect, comprise the following steps that：
Step 2.1：M characteristic point is randomly selected from the first image, its characteristic vector is designated as
Step 2.2：When carrying out oval sampling in the second image, if γ=γs, θ0=0, obtain all feature point features
Vector, is designated asThe first image and the second image, the correct matching of note are matched using closest minimum distance method
Number is n；
Step 2.3：Change γ and θ0Value, wherein γ ∈ [γs,γe], θ0In the case of ∈ [0 °, 90 °], acquisition multiple analog
D ' and corresponding correct match point ni；
Step 2.4：Compare it is a variety of in the case of matching result, when obtain max (ni) when, corresponding γ*And θ*It is as optimal
Solution；
Step 2.5：Max (n are selected in the first imagei) when characteristic point as initial point, re-start step 2.1-
Step 2.5, until γ*And θ*Value tend towards stability.
Step 3：Using NNDR matching strategies matching characteristic point
Strategy using arest neighbors and time neighbour's ratio (NNDR, Nearest Neighbor Distance Ratio) enters
Row matching, when it is implemented, calculate the Euclidean distance between each feature descriptor, for each feature, if with its most phase
The distance of two near features meets minimum range and the ratio of time small distance is less than certain threshold value △, then it is assumed that the matching pair
It is a pair of correct matchings pair；
Step 4：Error matching points are rejected using the RANSAC based on Epipolar geometric constraint
Complete after Feature Points Matching, in initial matching result, there can be some erroneous matchings.Conventional method is to utilize
Affine transformation matrix between RANSAC (Random Sample Consensus) estimation image rejects erroneous matching, but right
For big perspective images, view picture image is not particularly suited for same affine transformation, therefore, in the specific implementation, using extremely several
The method of what constraint, erroneous matching is rejected by estimating the fundamental matrix between image picture pair.
It should be appreciated that the part that this specification is not elaborated belongs to prior art.
It should be appreciated that the above-mentioned description for preferred embodiment is more detailed, therefore it can not be considered to this
The limitation of invention patent protection scope, one of ordinary skill in the art is not departing from power of the present invention under the enlightenment of the present invention
Profit is required under protected ambit, can also be made replacement or be deformed, each fall within protection scope of the present invention, this hair
It is bright scope is claimed to be determined by the appended claims.
Claims (5)
1. it is a kind of based on the low latitude various visual angles Remote Sensing Images Matching Method for improving SIFT operators, it is characterised in that including following step
Suddenly：
Step 1：The characteristic point in the first image and the second image is detected using the DoG operators of adaptive threshold；
Step 2：Son is described based on improved SIFT description is clicked through to feature；
For the characteristic point extracted on the first image and the second image, it is respectively adopted what is sampled based on border circular areas in its neighborhood
Gray value and based on elliptic region sample gray value characteristic point is described, ultimately form 128 dimensional feature vectors；
Characteristic point is described based on the gray value that elliptic region is sampled for wherein described use, for any of the second image
Characteristic point (x 'i,y′i), the elliptic region sampled point in its neighborhoodExpression formula be：
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Wherein, aijFor ellipse sampling major axis, bijFor ellipse sampling short axle, bij=aij/ γ, γ >=1, θ0For oval direction, θkFor
Sampling angle；
Elliptic parameter γ and θ are determined using the strategy of iterative0, comprise the following steps that：
Step 2.1：M characteristic point is randomly selected from the first image, its characteristic vector is designated as
Step 2.2：When carrying out oval sampling in the second image, if γ=γs, θ0=0, all characteristic point characteristic vectors are obtained,
It is designated asThe first image and the second image are matched using closest distance method, the correct matching number of note is n；
Step 2.3：Change γ and θ0Value, wherein γ ∈ [γs,γe], θ0∈ [0 °, 90 °], obtains the D ' in the case of multiple analog
With corresponding correct match point ni；
Step 2.4：Compare it is a variety of in the case of matching result, when obtain max (ni) when, corresponding γ*And θ*As optimal solution,
Wherein * is general symbol；
Step 2.5：Max (n are selected in the first imagei) when characteristic point as initial point, re-start step 2.1- steps
2.5, until γ*And θ*Value tend towards stability；
Step 3：Nearest neighbor distance and this strategy of the ratio of time nearest neighbor distance between the corresponding characteristic vector of distinguished point based
Obtain initial matching point set；
Step 4：RANSAC algorithms based on Epipolar geometric constraint are purified to initial matching point set, obtain final match point.
2. it is according to claim 1 based on the low latitude various visual angles Remote Sensing Images Matching Method for improving SIFT operators, its feature
It is：The DoG operators of use adaptive threshold described in step 1 detect the characteristic point in the first image and the second image, are
According to the adaptive threshold value T_contrast of half-tone information in certain window ranges centered on characteristic point, its expression formula
For：
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Wherein, SiFor the yardstick where current signature point, MIRepresent the quantity of image in DoG metric spaces, σ0Represent that image is smooth
Degree.
3. it is according to claim 1 based on the low latitude various visual angles Remote Sensing Images Matching Method for improving SIFT operators, its feature
It is：Characteristic point is described based on the gray value that border circular areas is sampled for use described in step 2, for the first image
Arbitrary characteristics point (xi,yi), the border circular areas sampled point in its neighborhoodExpression formula be：
<mrow>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
<mrow>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>=</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>&theta;</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
Wherein, rijFor sample radius, θkFor sampling angle.
4. it is according to claim 1 based on the low latitude various visual angles Remote Sensing Images Matching Method for improving SIFT operators, its feature
It is：The characteristic point gradient calculation expression formula based on area sampling described in step 2 is as follows：
<mrow>
<msub>
<mi>d</mi>
<mi>&theta;</mi>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>I</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>I</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mrow>
<mo>(</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>d</mi>
<mi>&gamma;</mi>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>I</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>I</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>;</mo>
</mrow>
<mrow>
<mi>m</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msqrt>
<mrow>
<msubsup>
<mi>d</mi>
<mi>&theta;</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>d</mi>
<mi>&gamma;</mi>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>,</mo>
<msubsup>
<mi>y</mi>
<mi>i</mi>
<mrow>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
</msqrt>
<mo>;</mo>
</mrow>
Wherein,Represent characteristic pointGrad in θ directions,Represent characteristic pointGrad in γ directions,Represent characteristic pointGradient direction, the gray value of sampled point
Then asked for, be designated as by the way of bilinear interpolationWherein * is general symbol.
5. it is according to claim 1 based on the low latitude various visual angles Remote Sensing Images Matching Method for improving SIFT operators, its feature
It is：Completed in step 2 after neighbouring point sampling, the gray value of sampled point is asked for by bilinear interpolation method.
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| CN107909094A (en) * | 2017-10-31 | 2018-04-13 | 天津大学 | A kind of adaptive threshold multiple target SIFT matching algorithm implementation methods |
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