CN1841409A - Coarse positioning method for remote sensing image based on Fourier-Mellin transformation - Google Patents
Coarse positioning method for remote sensing image based on Fourier-Mellin transformation Download PDFInfo
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Abstract
The remote sensing image coarse positioning method based on Fourier-Mellin transformation comprises: (1) extracting short curve c and reference curve C for pre-processing before matching; (2) converting c into binary image named a; (3) with given step and rule, selecting all candidate curve ci and corresponding binary image bi from C; (4) matching bi with a in turn to calculate conversion parameters (alphai, si, x0i, and y0i); (5) taking inverse transformation to c by (alphai, si, x0i, and y0i) to obtain c'i, and calculating the Hi as Hausdorff distance between c'i and ci; (6) taking c* that meets Hmin=min{Hi} as the matching segment of c in C.
Description
Technical field
The present invention relates to the remote sensing technology field, particularly a kind of remote sensing images rough localization method based on Fourier-plum forests (Fourier-Mellin) conversion.
Background technology
In many tasks of pattern-recognition, computer vision and image understanding, all can relate to the problem of Curve Matching, as object identification, vision guided navigation, location etc.In view of the importance of Curve Matching and the irreplaceable effect in some concrete application problem, many scholars have carried out a large amount of research to this, and have proposed various methods.Existing Curve Matching method is divided into two classes, and a class is based on the method for rigid body translation (rigid transformation), and a class is based on the method for non-rigid body translation (non-rigid transformation).Based on the method for rigid body translation, generally the coupling by curvilinear characteristic point (as angle point, curvature extreme point etc.) finds transformation parameter (relative rotation angle, translation vector, convergent-divergent yardstick) optimum between curve; Based on the method for non-rigid body translation, the model of setting up deformation between curve earlier that has by minimizing certain and comprise the energy function of " stretching " and " distortion ", is realized the mapping of a curve to another curve then; Matching relationship between the reference mark of passing through certain invariant of maintenance (as affine invariant, projective invariant or square invariant) that also has obtains the non-rigid body translation parameter between the curve.
This method research be the matching problem that exists between the image curve of similarity transformation, below several main method that solve this type of problem are done one and briefly introduce.The set of keypoints that Freeman etc. form with the point of discontinuity of curvature on the curve is described the two-dimensional shapes of object, calculate the local shape feature (concavity and convexity) between the adjacent key point then, and be characterized as with reference to seeking the corresponding relation between the key point between curve, thereby try to achieve the transformation parameter between curve with local shape.Ayache and Faugeras etc. use polygonal approximation respectively with two contour of object curves, thereby then by the matching parameter between definite two curves of the corresponding relation that compares two polygon limits successively.This method can solve the matching relationship that comprises between rotation, following two curves of Pan and Zoom situation, but when curve is used polygonal approximation, the bar number on two polygon limits and the length of corresponding sides is needed more reasonably control.The method of propositions such as Wolfson is used for seeking segment of curve total in two curves.This method is formed two curves with the local anglec of rotation of each point character chain represents, finds at first that all satisfy the counterpart of certain-length in the feature chain; Calculate transformation parameter by these counterparts then and on actual curve, expand, obtain total segment of curve the longest in the actual curve at last with certain fixing threshold value.The method of usefulness Curve Matching such as Schwartz solves the object identification problem that exists under the partial occlusion situation.This method equally with the contour of object curve with the piecewise linear approximation of segment, in model bank, find corresponding object curve with the mode of least square method by global search then, reach the purpose of identification.
Several Curve Matching methods of introducing above have certain value undoubtedly in actual applications, but further analyze these methods, all there are following 2 deficiencies in they: (1) is difficult to accomplish unified yardstick to polygonal approximation (or piecewise linear approximation) degree of two primary curves; (2) local feature of putting on the curve accurately obtain and the foundation of corresponding relation itself also is a difficult problem.
Summary of the invention
For these reasons, we have provided a kind of Curve Matching method based on Fourier-Mellin (Fourier-plum forests) conversion, the advantage of this method is: generally do not need curve carried out relevant treatment such as smothing filtering, polygonal approximation, but directly utilize the whole frequency domain character of curve to realize two couplings between curve.
1, based on the image registration principle of Fourier-Mellin conversion
Chen and Reddy etc. have very at length discussed the image registration principle based on the Fourier-Mellin conversion.Be simple an introduction below about this method.
1.1 Fourier transform displacement theory
Suppose f
2(x y) is f
1(x is y) at x and y direction difference translation x
0And y
0After image, that is:
f
2(x，y)＝f
1(x-x
0，y-y
0) (1)
Note f
1And f
2Corresponding Fourier transform is respectively F
1(u, v) and F
2(u, v), then the Fourier transform displacement of following formula indication is theoretical sets up:
f
1(x, y) and f
2(x, cross-power spectrum y) is
F wherein
2 *Expression F
2Complex conjugate.
By (3) formula is carried out inverse fourier transform, at (x
0, y
0) locate and will obtain an impulse function.Can determine two relative translation amount x between image subject to registration according to this pulse position
0And y
0
1.2 use relative translation, rotation and zoom factor between Fourier-Mellin transformation calculations image
Consider two width of cloth image s subject to registration (x, y) and r (x, y), (x is that (x is y) through translation (x for r y) to s
0, y
0), the image after rotation alpha degree and consistent yardstick σ (the change of scale factor that the is both direction equates) conversion, that is:
s(x，y)＝r[σ(xcosα+ysinα)-x
0，σ(-xsinα+ycosα)-y
0] (4)
So s (x, y) and r (x, y) pass between the Dui Ying Fourier transform is:
Phase place e in the formula (5)
-j φ s (u, v)Depend on translation, rotation and convergent-divergent yardstick, but amplitude and translation are irrelevant.The corresponding amplitude spectrum of formula (5) is
|S(u，v)|＝σ
-2|R[σ
-1(ucosα+vsinα)，σ
-1(-usinα+vcosα)]| (6)
Definition:
r
p1(θ，logρ)＝r
p(θ，ρ) (7)
s
p1(θ，logρ)＝s
p(θ，ρ) (8)
R wherein
pAnd s
pBe respectively that r and s are at polar coordinate system (θ, ρ) amplitude spectrum in.Be easy to so draw:
s
p1(θ，logρ)＝r
p1(θ-α，logρ-logσ) (9)
Perhaps s
P1(θ, λ)=r
P1(θ-α, λ-κ) (10)
λ=log ρ wherein, κ=log σ.Formula (10) is called as the Fourier-Mellin conversion.
As can be seen, by above-mentioned conversion, formula (10) is transformed to and the identical form of formula (1), so just can use Fourier displacement theory at transformation space, according to formula (2) and (3), tries to achieve α and κ.
If the end of logarithm, be taken as e, so
σ＝e
κ (11)
Anglec of rotation α and scale factor σ have so just been obtained.After α and σ obtained, (x y) revised to s to utilize these two parameters earlier; (x, y) (x only differs a translation transformation between y) to revised s, utilizes Fourier transform displacement theory once more, just can obtain translational movement (x with r
0, y
0).
2, based on the Curve Matching method of Fourier-Mellin conversion
Method for registering images based on the Fourier-Mellin conversion has two outstanding features: the first, and what this method was used is the Global Information of image; The second, registration operation is carried out in frequency domain.So this method has random noise and the insensitive advantage of local deformation.Therefore, utilize this two character, we have provided a kind of image curve matching process based on the Fourier-Mellin conversion.Method and thought is as follows: for two given image curves to be matched that have similarity transformation, earlier they are separately converted to bianry image (wherein the point on the curve is 1, and all the other points are 0); Utilize the method for registering images based on the Fourier-Mellin conversion to calculate transformation relation between two width of cloth bianry images then, thereby also just obtained the transformation parameter between two curves indirectly.
It is to be noted: although curve is regarded as bianry image in our Curve Matching, yet compare with common image registration, it is different to carry out the meaning that Curve Matching implied with the Fourier-Mellin conversion.Here because the curve place is " 1 ", and no curve place is " 0 ", so this moment, the coupling based on the Fourier-Mellin conversion was a kind of coupling of geometric configuration, was a kind of tolerance of geometric configuration similarity; And original image matching method more is a kind of tolerance of pixel grey scale similarity.
3, based on the remote sensing images rough localization method of Fourier-Mellin conversion
3.1, the problem description of remote sensing image coarse positioning
The orbit parameter of satellite positioned when generally speaking, the remote sensing image utilization was taken.Therefore, when the orbit parameter of satellite is unknown, also just can not determine the particular geographic location of captured remote sensing image.A kind of feasible localization method is to extract apparent in view feature from remote sensing image, then with the map match that contains individual features, is determined the latitude and longitude coordinates of remote sensing image by their matching result.When containing the marine site in the remote sensing image, shore line wherein can be extracted as principal character, in the layer of the shore line of electronic chart, search for and find the part that is complementary with it with this, obtain the rough geographic coordinate of remote sensing image thus.
When the counterpart in remote sensing image that contains the shore line and the electronic chart shore line layer can think approximate when having certain similarity transformation, then the location of this type of remote sensing image can be described as following Curve Matching problem abstractively: extract shore line (funiclar curve) from remote sensing image, electronic chart shore line layer is reverted to a long curve (funiclar curve wherein is a certain section on the long curve just), determine corresponding section and the transformation relation thereof of funiclar curve on long curve according to certain module, as shown in Figure 1.
3.2, the localization method embodiment
Remote sensing images rough localization method flow process, the laying-out curve method comprises following several steps: as shown in Figure 2:
(1) pre-service before the coupling, pretreatment operation comprises: (a) with the shore line c in certain curve extracting method acquisition remote sensing image, what we used is the thresholding method of Otsu;
(b) shore line layer in the electronic chart is converted into a plane curve C close with the resolution of c (this method does not need resolution to equate accurately), what we used is UTM (the general transverse Mercator projection of Universal Transverse Mercator) method;
(2) funiclar curve c is converted into bianry image, is designated as a, wherein a is that the mid point with curve c is center, the smallest square that can comprise whole curve c;
(3), on long curve C, choose all candidate's curves and (suppose c according to certain step-length
iBe i section candidate curve, total n section), so-called candidate's curve c
iJust be meant with C and go up some p
iFor the center, be included in the onesize square area of a in (this corresponding bianry image in zone is designated as b
i) one section curve, wherein p
iBe on C, to choose according to the step-length of setting (step-length that this paper sets be actual shore line c length 10%).Why c and C can not be converted into the method for registering images that onesize bianry image is directly used the Fourier-Mellin conversion, be to mate because this method is a whole frequency domain character with image.In the ordinary course of things, the length of c and the length of C differ at least one order of magnitude, and this whole frequency domain character major part that just can't guarantee two width of cloth bianry images is similar, so, need to select candidate's curve.
(4) successively with b
iRight with a composition coupling, use image matching method to mate based on the Fourier-Mellin conversion, obtain the estimated value of transformation parameter, α
i, s
i, x
0 i, y
0 i, α wherein
iBe relative rotation angle, s
iBe relative convergent-divergent yardstick, x
0 iAnd y
0 iIt is respectively the relative translation amount of x and y direction;
(5) c is passed through transformation parameter, α
i, s
i, x
0 i, y
0 i, carry out inverse transformation and obtain c
i', calculate c
i' with c
iBetween the Hausdorff distance H
i
(6) H
Min=min{H
iPairing c
*Be exactly the matching section of c on C, also just determined the rough geographic position of remote sensing image simultaneously.
Matching problem between two image curves is converted into registration problems between two width of cloth bianry images, obtains similarity transformation parameter between curve by the registration relation indirect ground between image;
The higher image curve matching process based on the Fourier-Mellin conversion of a kind of robustness has been proposed;
Do not need to extract the local feature of curve, but directly realize coupling, thereby avoided problems such as extract minutiae and Feature Points Matching, also improved the robustness of method simultaneously greatly with the whole frequency domain character of curve.
Description of drawings
Fig. 1 is a Curve Matching problem description synoptic diagram.
Fig. 2 is the remote sensing images rough localization method process flow diagram based on the Fourier-Mellin conversion with higher robustness.
Fig. 3 is first width of cloth remote sensing image positioning result figure.
Fig. 4 is second width of cloth remote sensing image positioning result figure.
Embodiment
Among Fig. 1, (a) funiclar curve.(b) long curve.Through the funiclar curve after one group of similarity transformation.(c) matching result.
Fig. 2 is based on the rough image curve matching method flow process of Fourier-Mellin conversion.(describing 3.2, in the localization method embodiment) in this omission
Among Fig. 3, (a) original remote sensing image.The shore line of (b) from raw video, extracting.(c) matching result of shore line layer counterpart in shore line and the electronic chart, dotted line is represented the shore line in the electronic chart, solid line is represented the shore line of extracting from remote sensing image.(d) in the rectangle frame be the rough position of remote sensing image in electronic chart.
Among Fig. 4, (a) original remote sensing image.The shore line of (b) from raw video, extracting.(c) matching result of shore line layer counterpart in shore line and the electronic chart, dotted line is represented the shore line in the electronic chart, solid line is represented the shore line of extracting from remote sensing image.(d) in the rectangle frame be the rough position of remote sensing image in electronic chart.
For the practicality based on the remote sensing images rough localization method of Fourier-Mellin conversion is described, experimentize with the true remote sensing image data of two width of cloth.Write down the estimation transformation parameter of counterpart in two groups of shore lines of extracting from remote sensing image and the electronic chart shore line layer in the table 1, Fig. 3, Fig. 4 be the actual coarse localization result of two groups of remote sensing images.From the experiment of True Data as can be seen, though there are many deformation in the curve and the curve in the electronic chart that extract from remote sensing image, but our method still can compare accurately, estimate robust matching parameter, realizes the coarse positioning of remote sensing image in map.
The experimental result of table 1 remote sensing image location
| Group | Remote sensing image shore line length (pixel) | The anglec of rotation | Zoom factor | Horizontal shift | Perpendicular displacement | The Hausdorff distance |
| First group (Fig. 3) | 676 | 356 | 1.29 | -68 | -38 | 7.74 |
| Second group (Fig. 4) | 3997 | 5 | 1.33 | 164 | -121 | 31.06 |
Claims (4)
1, a kind of remote sensing images rough localization method based on the Fourier-Mellin conversion with higher robustness, its step comprises:
(1) pre-service before the coupling, pretreatment operation comprises: (a) with the shore line c in certain curve extracting method acquisition remote sensing image; (b) shore line layer in the electronic chart is converted into a plane curve C close with the resolution of c;
(2) funiclar curve c is converted into bianry image, is designated as a;
(3), on long curve C, choose all candidate's curve c according to certain step-length
i, every section c
iCorresponding bianry image is designated as b
l
(4) successively with b
iRight with a composition coupling, use image matching method to mate based on the Fourier-Mellin conversion, obtain the estimated value of transformation parameter, α
l, s
i, x
0 i, y
0 i
(5) c is passed through transformation parameter (α
l, s
i, x
0 i, y
0 i) carry out inverse transformation and obtain c
l', calculate c
i' with c
iBetween the Hausdorff distance H
i
(6) H
Min=min{H
iPairing c
*Be exactly the matching section of c on C, thereby determined the rough geographic position of remote sensing image.
2, according to the described remote sensing images rough localization method of claim 1 based on the Fourier-Mellin conversion, it is characterized in that, matching problem between two image curves is converted into registration problems between two width of cloth bianry images, obtains similarity transformation parameter between curve by the registration relation indirect ground between image.
According to the described remote sensing images rough localization method of claim 1, it is characterized in that 3, proposed a kind of new regulation of selecting the candidate matches segment of curve in long reference curve, this rule has stronger adaptive faculty based on the Fourier-Mellin conversion.
4, according to the described remote sensing images rough localization method of claim 1 based on the Fourier-Mellin conversion, it is characterized in that, do not need to extract the local feature of curve, but directly realize coupling with the whole frequency domain character of curve, thereby avoided extract minutiae and Feature Points Matching problem, also improved the robustness of method simultaneously greatly.
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