CN102968780B - A kind of remote sensing images joining method based on human-eye visual characteristic - Google Patents

Abstract

The invention discloses a kind of remote sensing images joining method based on human-eye visual characteristic, comprise the following steps: 1) extract the unique point on reference picture and image to be spliced, set up matching characteristic point pair; 2) reject the matching characteristic point pair of mistake, obtain transformation matrix H initial between reference picture and image to be spliced; 3) be divided into interested region and common region with reference to image, utilize the ratio of the average gradient value in two regions to obtain weight factor α; 4) the optimization increment of Increment Matrix P as initial transformation matrix H is set, utilize step 2) in the right coordinate information of matching characteristic point and step 3) in weight factor α iterative Increment Matrix P, and utilize the Increment Matrix P obtained each time in iterative process can calculate corresponding transformation matrix H, until convergence finishing iteration process; 5) apply final transformation matrix H to treat stitching image and carry out projective transformation, and carry out splicing with reference picture and merge, complete the splicing of image.

Description

A kind of remote sensing images joining method based on human-eye visual characteristic

Technical field

The present invention relates to computer image processing technology field, particularly relate to a kind of remote sensing images joining method based on human-eye visual characteristic.

Background technology

Remote sensing images are the images obtained by the platform of the high-altitude flights such as satellite, aircraft or hot air balloon, having very important effect in fields such as disaster alarm, resource detection, military surveillance, ground mappings, is the important channel that the mankind understand the information change such as terrestrial climate, resource.

In the process obtaining remote sensing images, always wish the high-definition picture obtaining enough visual fields, like this can so that people extract useful information rapidly.But under existing technical conditions, visual field and resolution are two contradictions being difficult to be in harmonious proportion.

Existing solution is continue to increase the resolution of sensor on the one hand, on the one hand by a certain large regions repeatedly imaging obtain several there are high-resolution superimposed images, be reduced into the high-resolution remote sensing images of a width large coverage by follow-up image processing techniques.

Remote sensing images splicing can two parts: image registration and image co-registration.

Image registration is the core link of image mosaic technology, is the means of the transformation relation of acquisition two width superimposed images.

In order to obtain the relation more accurately between image, usually can be optimized in image registration, the method for optimization has a variety of.

But optimized algorithm is in the past all the optimization of unitarity, importance namely not between differentiate between images content, actual result likely reaches higher splicing precision at some to actual production otiose region of living, but in some very important contents, obtain the result of non-constant on the contrary, be unfavorable for follow-up application.

Summary of the invention

The object of the invention is to provide a kind of for the difference of remote sensing images scenery importance can, for the optimization method of different applied environments, make the result optimized meet the visual determination characteristic of human eye.

To achieve these goals, the invention provides a kind of remote sensing images joining method based on human-eye visual characteristic, comprise the following steps:

1) extract the unique point on reference picture and image to be spliced, set up matching characteristic point pair, obtain the initial matching relationship between two width image characteristic points;

2) reject the matching relationship of mistake, obtain the matching characteristic point pair that matching relationship is correct, and obtain transformation matrix H initial between reference picture and image to be spliced;

3) described reference picture is divided into interested region and common region, calculates the average gradient value S in two regions respectively _interestand S (G) _normal(G) ratio of average gradient value, is utilized to obtain weight factor α;

4) the optimization increment of Increment Matrix P as initial transformation matrix H is set, utilize step 2) in the right coordinate information of matching characteristic point and step 3) in weight factor α iterative Increment Matrix P, and utilize the Increment Matrix P obtained each time in iterative process can calculate corresponding transformation matrix H, until convergence finishing iteration process;

5) apply final transformation matrix H to treat stitching image and carry out projective transformation, and carry out splicing with reference picture and merge, complete the splicing of image.

The unique point of reference picture and image to be spliced is chosen and is adopted SIFT algorithm, and the initial matching relationship utilizing European geometric distance principle to obtain between unique point; And utilize RANSAC method to reject the matching relationship of mistake, namely the matching characteristic point pair that matching relationship is correct is obtained, the transformation matrix obtained by correct matching relationship can make that two width stitching images are reasonable to overlap, and the coupling of mistake then can produce splicing by mistake.

Make described step 2) in the homogeneous coordinates of reference picture unique point be X ₁=(x ₁, y ₁, 1), the homogeneous coordinates of image characteristic point to be spliced are X ₂=(x ₂, y ₂, 1), and initial transformation matrix H is:

$H=\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]$

In formula, h ₁~ h ₈be the element in transformation matrix H, characterize the Transformation Relation of Projection between reference picture and image to be spliced, the coordinate conversion relation between reference picture and image to be spliced corresponds to following formula:

$\left[\begin{array}{c}{x}_1\\ y_1\\ 1\end{array}\right]~\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ 1\end{array}\right]$

In image, the Grad G (x, y) of pixel is expressed from the next:

$G(x,y)=\sqrt{I_x^2(x,y)+I_y^2(x,y)}$

$I_x=\frac{\∂I(x,y)}{\∂x},$ $I_y=\frac{\∂I(x,y)}{\∂y}$

In formula, (x, y) is the coordinate of pixel in image, I _xrepresent the gradient of image in x direction, I _yrepresent image gradient in y-direction, I (x, y) represents the gray-scale value of image.

Described weight factor α is expressed as:

$\mathrm{\β}=\frac{S_{\mathrm{interest}}\left(G\right)}{S_{\mathrm{normal}}\left(G\right)}$

$\mathrm{\α}=\frac{1}{\mathrm{\β}+1}$

In formula: S _interest(G) be the mean value of all pixel gradient values of area-of-interest, S _normal(G) be the mean value of all pixel gradient values of normal areas.

Described Increment Matrix P is expressed as:

$P=\left[\begin{array}{ccc}{p}_1& p_2& p_3\\ p_4& p_5& p_6\\ p_7& p_8& 1\end{array}\right]$

In formula, the element p in Increment Matrix P ₁~ p ₈the fractional increments of respective element in difference correspondent transform matrix H.

Arrange middle coordinate variable X ' ₂=(x ' ₂, y ' ₂, 1) and be convenient to mathematical expression calculating:

$\left[\begin{array}{c}{x}_2^{\′}\\ y_2^{\′}\\ 1\end{array}\right]~\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ 1\end{array}\right]$

Increment Matrix P characterizes the fractional increments of projective transformation matrix H in iterative process each time, and its effect is constantly optimized H to approach, and its expression formula is:

(I+P)H→H

In formula, I is unit matrix, utilize middle coordinate variable X ' ₂=(x ' ₂, y ' ₂, 1) and formula:

(I+P)HX ₂＝(I+P)X′ ₂＝X3＝(x ₃，y ₃，1)

Computational short cut can be made, X ₃=(x ₃, y ₃, 1) and represent the coordinate of unique point coordinate after projective transformation of image to be spliced.

Introduce weight factor α, image be divided into two parts:

$E\left(p\right)=\underset{n\∈S_1}{\mathrm{\Σ}}\mathrm{\α}\left|\right|X_1^{\left(n\right)}-X_3^{\left(n\right)}\left|\right|+\underset{m\∈S_2}{\mathrm{\Σ}}(1-\mathrm{\α})\left|\right|X_1^{\left(m\right)}-X_3^{\left(m\right)}\left|\right|$

In formula, represent coordinate and the coordinate of image to be spliced n-th unique point coordinate after projective transformation of reference picture n-th unique point respectively, represent coordinate and the coordinate of image to be spliced m unique point coordinate after projective transformation of reference picture m unique point respectively, α is weight factor, S ₁, S ₂represent interested region and common region respectively.

The Increment Matrix P obtained in iterative process each time, obtains the transformation matrix H in the iterative process of next time according to (I+P) H → H, the end condition of iteration is for convergence or exceed iterations restriction, and obtains final transformation matrix H.

Reference picture described in final transformation matrix H is substituted into and the coordinate conversion relation formula between image to be spliced:

$\left[\begin{array}{c}{x}_1\\ y_1\\ 1\end{array}\right]~\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ 1\end{array}\right]$

Complete image to be spliced and carry out projective transformation, and obtain stitching image.

The present invention has following advantage:

In the process that the present invention optimizes at remote sensing image registration, introduce the theory of weight optimization.According to the significance level of remote sensing images content, give different weighted values, make the result of remote sensing image registration optimization more meet human eye vision and judge.In important remote sensing region, the error of image registration can be little as much as possible, and registration accuracy reaches a higher level, and last stitching image can be applied in wider actual demand.

Accompanying drawing explanation

Fig. 1 is the operational flowchart of the remote sensing images joining method that the present invention is based on human-eye visual characteristic;

Fig. 2 a, Fig. 2 b, Fig. 2 c and Fig. 2 d are the process that the present invention sets up Image Feature Point Matching relation;

Fig. 2 a is reference picture;

Fig. 2 b is image to be spliced;

Fig. 2 c is the initial matching relationships of two width image characteristic points;

Fig. 2 d is the correct matching relationship obtained after RANSAC method;

Fig. 3 a is the splicing result after common Levenberg-Marquardt algorithm optimization;

Fig. 3 b, Fig. 3 c are marked region corresponding in Fig. 3 a;

Fig. 4 a is the splicing result after joining method of the present invention is optimized;

Fig. 4 b, Fig. 4 c are marked region corresponding in Fig. 4 a;

Fig. 5 a is the reference picture of emulation;

Fig. 5 b is the image to be spliced of emulation;

Fig. 6 a is the splicing result after common LM algorithm optimization;

Fig. 6 b, Fig. 6 c and Fig. 6 d are marked region corresponding in Fig. 6 a;

Fig. 7 a is the splicing result after joining method of the present invention is optimized;

Fig. 7 b, Fig. 7 c and Fig. 7 d are marked region corresponding in Fig. 7 a;

Fig. 8 a is the reference picture of remote sensing images;

Fig. 8 b is the image to be spliced of remote sensing images;

Fig. 8 c is the splicing result after joining method of the present invention is optimized.

Embodiment

As shown in Figure 1, the present invention is the remote sensing images joining method based on human-eye visual characteristic, by following two concrete examples, concrete embodiment is described.

Example one: the process that whole joining method is described with Fig. 2 a, Fig. 2 b, Fig. 2 c and Fig. 2 d.

(1) Fig. 2 a and Fig. 2 b is reference picture and image to be spliced respectively, utilizes SIFT technology to extract the unique point of reference picture and image to be spliced, and Fig. 2 c shows the initial matching relationship of the two width image characteristic points that obtain.

(2) transformation relation between two width images is characterized with projective transformation model, namely transformation matrix contains 8 parametric variables, then adopt RANSAC technology to reject the match point of mistake, obtain the feature point pairs that matching relationship is correct, obtain initial transformation matrix H simultaneously.The homogeneous coordinates of reference picture unique point are made to be X ₁=(x ₁, y ₁, 1), the homogeneous coordinates of image characteristic point to be spliced are X ₂=(x ₂, y ₂, 1), matrix H is the projective transformation matrix of 3x3, and wherein transformation matrix H is:

$H=\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]$

In formula, h ₁~ h ₈be the element in projective transformation matrix H, characterize the Transformation Relation of Projection between reference picture and image to be spliced, its coordinate conversion relation corresponds to following formula:

$\left[\begin{array}{c}{x}_1\\ y_1\\ 1\end{array}\right]~\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ 1\end{array}\right]$

(3) the weight optimization algorithm considering content significance level is adopted.The quantification of the significance level of remote sensing images content, can be set to two kinds of methods: subjective method and objective method.Subjective algorithm is user's additional weight value artificial to the various content of remote sensing images, and such as airfield runway, military target can add higher weight, and the span of weighted value be interval [0,1].For the optimized algorithm demand of robotization, design and utilize the gradient information of image to characterize the information importance level in certain region.The gradient of image slices vegetarian refreshments is determined by following formula:

$G(x,y)=\sqrt{I_x^2(x,y)+I_y^2(x,y)}$

$I_x=\frac{\∂I(x,y)}{\∂x},$ $I_y=\frac{\∂I(x,y)}{\∂y}$

In formula, (x, y) is the coordinate of pixel in image, I _xrepresent the gradient of image in x direction, I _yrepresent image gradient in y-direction, I (x, y) represents the gray-scale value of image.

Weight factor α is expressed as:

$\mathrm{\β}=\frac{S_{\mathrm{interest}}\left(G\right)}{S_{\mathrm{normal}}\left(G\right)}$

$\mathrm{\α}=\frac{1}{\mathrm{\β}+1}$

In formula: S _interest(G) be the mean value of all pixel gradient values of area-of-interest, S _normal(G) be the mean value of all pixel gradient values of normal areas.

(4) the optimization increment of Increment Matrix P as initial transformation matrix H is set, exploitation right repeated factor α and the right coordinate position iterative Increment Matrix P of matching characteristic point.The Increment Matrix P obtained each time in iterative process and initial transformation matrix H forms the initial transformation matrix H of next iteration, until convergence finishing iteration process.

Increment Matrix P is expressed as:

$P=\left[\begin{array}{ccc}{p}_1& p_2& p_3\\ p_4& p_5& p_6\\ p_7& p_8& 1\end{array}\right]$

Arrange middle coordinate variable X ' ₂=(x ' ₂, y ' ₂, 1) and be convenient to mathematical expression calculating:

$\left[\begin{array}{c}{x}_2^{\′}\\ y_2^{\′}\\ 1\end{array}\right]~\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ 1\end{array}\right]$

Increment Matrix P characterizes the fractional increments of projective transformation matrix H in iterative process each time, and its effect is constantly optimized H to approach, and its expression formula is:

(I+P)H→H

I is unit matrix, utilize middle coordinate variable X ' ₂(I+P) HX ₂=(I+P) X ' ₂=X ₃=(x ₃, y ₃, 1) and can computational short cut be made.

In order to obtain Increment Matrix P, we require to separate following formula:

$E\left(p\right)=\underset{n}{\mathrm{\Σ}}\left|\right|X_1^{\left(n\right)}-X_3^{\left(n\right)}\left|\right|$

In formula, represent coordinate and the coordinate of image to be spliced n-th unique point coordinate after projective transformation of reference picture n-th unique point respectively.

Introduce weight factor α, image be divided into two parts:

$E\left(p\right)=\underset{n\∈S_1}{\mathrm{\Σ}}\mathrm{\α}\left|\right|X_1^{\left(n\right)}-X_3^{\left(n\right)}\left|\right|+\underset{m\∈S_2}{\mathrm{\Σ}}(1-\mathrm{\α})\left|\right|X_1^{\left(m\right)}-X_3^{\left(m\right)}\left|\right|$

In formula, represent coordinate and the coordinate of image to be spliced n-th unique point coordinate after projective transformation of reference picture n-th unique point respectively, represent coordinate and the coordinate of image to be spliced m unique point coordinate after projective transformation of reference picture m unique point respectively, α is weight factor, S ₁, S ₂represent interested region and common region respectively.

Levenberg-Marquardt Algorithm for Solving is utilized to go out Increment Matrix P.The Increment Matrix P obtained in iterative process each time, obtains the transformation matrix H in the iterative process of next time according to (I+P) H → H, the end condition of iteration is for convergence or exceed iterations restriction.The standard of convergence is that ε is less than 1 pixel:

$\mathrm{\ϵ}=\left(\underset{n\∈S_1}{\mathrm{\Σ}}\sqrt{{(x_3^n-x_1^n)}^2+{(y_3^n-y_1^n)}^2}\right)/n$

In formula, represent the coordinate of reference picture in area-of-interest unique point, represent the coordinate of image characteristic point to be spliced after conversion.Preferably, maximum iteration time is set as 100, and in some cases, the situation more complicated of two width images of acquisition, within the average error of area-of-interest cannot be reduced to a pixel, is just the end condition of iteration with iterations.

Utilize Increment Matrix P and transformation matrix H can obtain final transformation matrix H, then according to the Transformation Relation of Projection formula between reference picture and image to be spliced by (I+P) H → H iterative:

$\left[\begin{array}{c}{x}_1\\ y_1\\ 1\end{array}\right]~\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ 1\end{array}\right]$

Image to be spliced is carried out projective transformation, and obtains final optimization stitching image.

Splicing result after the splicing result of optimization method of the present invention and common LM algorithm optimization compared, can obtain: Fig. 3 a is the splicing result after common Levenberg-Marquardt algorithm optimization, Fig. 4 a is the splicing result adopting optimization method of the present invention.Fig. 3 b and Fig. 3 c is respectively the enlarged image in corresponding region in Fig. 3 a, and wherein Fig. 3 b comes as normal areas, and Fig. 3 c comes as area-of-interest, and it is good that we can find that the optimum results of Fig. 3 b compares, but the difference that the optimum results of Fig. 3 c compares.But in Fig. 4 b and Fig. 4 c, we just can find that the image optimization effectiveness comparison of area-of-interest Fig. 4 c is good, but the effect of optimization of Fig. 4 b is relatively poor.

Example two: the characteristic of the inventive method on human eye vision is described by the optimization splicing result of contrast simulation image and remote sensing images.

(1) Fig. 5 a and Fig. 5 b is the reference picture of input and image to be spliced.

(2) Fig. 6 a is the optimization splicing construction not having weighted value.Fig. 6 b and Fig. 6 c carrys out the area-of-interest as our definition, and it is optimized spliced result and has occurred larger error.Fig. 6 d carrys out the normal areas as our definition.

(3) Fig. 7 a is for adopting optimization of the present invention splicing result.Compared to optimization error very little of Fig. 6 b and Fig. 6 c, Fig. 7 b and Fig. 7 c, substantially eliminate the difference in vision aspect, and Fig. 7 d visually relative to Fig. 6 d substantially without large difference.

(4) Fig. 8 a and Fig. 8 b is the reference picture of remote sensing images and image to be spliced, and Fig. 8 c is for adopting splicing result of the present invention, and wherein the unique point optimization error of area-of-interest reaches sub-pix rank.

Claims (8)

1., based on a remote sensing images joining method for human-eye visual characteristic, it is characterized in that, comprise the following steps:

1) extract the unique point on reference picture and image to be spliced, set up matching characteristic point pair, obtain the initial matching relationship between two width image characteristic points;

2) reject the matching relationship of mistake, obtain the matching characteristic point pair that matching relationship is correct, and obtain transformation matrix H initial between reference picture and image to be spliced;

3) described reference picture is divided into interested region and common region, calculates the average gradient value S in two regions respectively _interestand S (G) _normal(G) ratio of average gradient value, is utilized to obtain weight factor α;

Described weight factor α is expressed as: $\mathrm{\α}=\frac{1}{\mathrm{\β}+1},\mathrm{\β}=\frac{S_{interest}\left(G\right)}{S_{normal}\left(G\right)};$

4) the optimization increment of Increment Matrix P as initial transformation matrix H is set, utilize step 2) in the right coordinate information of matching characteristic point and step 3) in weight factor α iterative Increment Matrix P, and utilize the Increment Matrix P obtained each time in iterative process can calculate corresponding transformation matrix H, until convergence finishing iteration process;

The standard of convergence is that ε is less than 1 pixel:

$\mathrm{\ϵ}=\left(\underset{n\∈S_1}{\Σ}\sqrt{{(x_3^n-x_1^n)}^2+{(y_3^n-y_1^n)}^2}\right)/n$

In formula, represent the coordinate of reference picture in area-of-interest unique point, represent the coordinate of image characteristic point to be spliced after conversion;

Introduce formula:

$E\left(p\right)=\underset{n\∈S_1}{\Σ}\mathrm{\α}\left|\right|X_1^{\left(n\right)}-X_3^{\left(n\right)}\left|\right|+\underset{m\∈S_2}{\Σ}(1-\mathrm{\α})\left|\right|X_1^{\left(m\right)}-X_3^{\left(m\right)}\left|\right|$

In formula, represent coordinate and the coordinate of image to be spliced n-th unique point coordinate after projective transformation of reference picture n-th unique point respectively, represent coordinate and the coordinate of image to be spliced m unique point coordinate after projective transformation of reference picture m unique point respectively, α is weight factor, S ₁, S ₂represent interested region and common region respectively; And utilize Levenberg-Marquardt algorithm iteration to solve Increment Matrix P;

5) apply final transformation matrix H to treat stitching image and carry out projective transformation, and carry out splicing with reference picture and merge, complete the splicing of image.

2., as claimed in claim 1 based on the remote sensing images joining method of human-eye visual characteristic, it is characterized in that, make described step 2) in the homogeneous coordinates of reference picture unique point be X ₁=(x ₁, y ₁, 1), the homogeneous coordinates of image characteristic point to be spliced are X ₂=(x ₂, y ₂, 1), and described initial transformation matrix H is:

$H=\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]$

In formula, h ₁~ h ₈be the element in transformation matrix H, characterize the Transformation Relation of Projection between reference picture and image to be spliced.

3., as claimed in claim 2 based on the remote sensing images joining method of human-eye visual characteristic, it is characterized in that, in image, the Grad G (x, y) of pixel is expressed from the next:

$G(x,y)=\sqrt{I_x^2(x,y)+I_y^2(x,y)}$

$I_x=\frac{\∂I(x,y)}{\∂x},I_y=\frac{\∂I(x,y)}{\∂y}$

In formula, (x, y) is the coordinate of pixel in image, I _xrepresent the gradient of image in x direction, I _yrepresent image gradient in y-direction, I (x, y) represents the gray-scale value of image.

4., as claimed in claim 3 based on the remote sensing images joining method of human-eye visual characteristic, it is characterized in that, described Increment Matrix P is expressed as:

$P=\left[\begin{array}{ccc}{p}_1& p_2& p_3\\ p_4& p_5& p_6\\ p_7& p_8& 1\end{array}\right]$

In formula, the element p in Increment Matrix P ₁~ p ₈the fractional increments of respective element in difference correspondent transform matrix H.

5., as claimed in claim 4 based on the remote sensing images joining method of human-eye visual characteristic, it is characterized in that, the relational expression of Increment Matrix P and transformation matrix H is:

(I+P)H→H

In formula, I is unit matrix.

6., as claimed in claim 5 based on the remote sensing images joining method of human-eye visual characteristic, it is characterized in that, the coordinate of unique point coordinate after projective transformation of described image to be spliced is:

X ₃＝(x _3,y ₃,1)＝(I+P)HX ₂＝(I+P)X' ₂

In formula, I is unit matrix, X' ₂for middle coordinate variable, and X' ₂=(x' ₂, y' ₂, 1).

7. as claimed in claim 6 based on the remote sensing images joining method of human-eye visual characteristic, it is characterized in that, utilize the Increment Matrix P obtained in each iterative process, obtain the transformation matrix H in the iterative process of next time according to (I+P) H → H, and substitute into formula (I+P) H → H iterative and obtain final transformation matrix H.

8., as claimed in claim 7 based on the remote sensing images joining method of human-eye visual characteristic, it is characterized in that, the coordinate conversion relation formula between described reference picture and image to be spliced is:

$\left[\begin{array}{c}{x}_1\\ y_1\\ 1\end{array}\right]~\left[\begin{array}{ccc}{h}_1& h_2& h_3\\ h_4& h_5& h_6\\ h_7& h_8& 1\end{array}\right]\left[\begin{array}{c}{x}_2\\ y_2\\ 1\end{array}\right]$

Utilize final transformation matrix H to substitute in above formula, image to be spliced is carried out projective transformation, and obtains stitching image.