陷阱英语Robust and Rapid Matching of Oblique UAV Images of Urban Area Xiongwu Xiao a, Bingxuan Guo*b, Yueru Shi b, Weishu Gong c, Jian Li b, Chunn Zhang a
a College of Geomatics, Xi’an University of Science and Technology, Xi’an 710054, China;
b State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing,
Wuhan University, Wuhan 430079, China;
c The Ohio State University at Columbus, Columbus, Ohio State, USA
ABSTRACT
The robust and rapid matching of oblique UAV images of urban area remains a challenge until today. The method propod in this paper, Nicer Affine Invariant Feature (NAIF), calculates the image view of an oblique image by making full u of the rough Exterior Orientation (EO) elements of the image, then recovers the oblique image to a rectified image by doing the inver affine transform, and left over by the SIFT method. The significance test and the left-right validation have applied to the matching process to reduce the rate of mismatching. Experiments conducted on oblique UAV images of urban area demonstrate that NAIF takes about the same time as SIFT to match a pair of oblique images with
a plenty of corresponding points and an extremely low mismatching rate. The new algorithm is a good choice for oblique UAV images considering the efficiency and effectiveness.
Keywords: matching, inver affine transform, oblique image, rectified image, Unmanned Aerial Vehicle (UAV), Nicer Affine Invariant Feature (NAIF), SIFT, ASIFT
1.INTRODUCTION
The affine deformation of the oblique images is so big that has brought a huge challenge to the image matching. At prent, veral popular ud affine invariant algorithms, such as MSER[1], LLD[2][3], Hessian-affine and Harris-
Affine[4][5], etc, are not fully affine invariant. The algorithms may result in a poor corresponding result for the matching of oblique images. While ASIFT[6] is fully affine invariant, which has normalized all six affine parameters -- ASIFT simulates two camera axis orientation parameters, then applies SIFT[7] to simulate scale and normalize the translation and rotation. It significantly outperforms the state-of-the-art methods SIFT, MSER, Harris-affine, and Hessian-affine[6]. However, ASIFT us too many times to simulate the camera axis parameters, the area of the simulated images is more than 13 times as the area of the original images and it significantly increas
es the computational complexity of the algorithm[8]. Although ASIFT performs well for oblique images with a high correct matching rate, its low efficiency can not meet the demand of practical applications. Therefore, in order to improve the efficiency of ASIFT, a new matching algorithm NAIF is propod in this paper. We get the two camera axis parameters directly with the rough exterior orientation elements of the image, which has greatly reduced the simulation and matching time of ASIFT. The experimental results have proved that the propod algorithm is significantly more efficient than ASIFT with a higher correct matching rate.
2.NICER AFFINE INVARIANT FEATURE (NAIF) ALGORITHM
Digital image acquisition of a flat object can be described as
110 (1)
u S G ATμ
=
Where u is a digital image and u0 is an (ideal) infinite resolution frontal view of the flat object. T and A are a plane translation and a planar projective map due to the camera motion. G1 is a Gaussian c
onvolution modeling the optical blur, and S1 is the standard sampling operator on a regular grid with mesh 1. The Gaussian kernel is assumed to be broad enough to ensure no aliasing by the 1-sampling, namely, IS1G1AT u0 = G1AT u0, where I denotes the Shannon-Whittaker interpolation operator. A major difficulty of the recognition problem is that the Gaussian convolution G1, which becomes a broad convolution kernel when the image is zoomed out, does not commute with the planar projective map A.
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2.1 The affine camera model [6]
The local tangency of perspective deformations reduces to affine maps. Indeed, by the first order Taylor formula, any planar smooth deformation can be approximated around each point by an affine map. The apparent deformation of a plane object induced by a camera motion is a planar homographic transform, which is smooth and therefore locally tangent to affine transforms. More generally, a solid object's apparent deformation arising from a change in the camera position can be locally modeled by affine planar transforms, provided that the object's facets are smooth. In short, all
local perspective effects can be modeled by local affine transforms u(x, y) → u(ax+by +e, cx+dy +f) in each image region.
Any affine map a b A c d ⎡⎤=⎢⎥⎣⎦
with strictly positive determinant which is not a similarity has a unique decomposition 12cos sin 0cos sin ()() (2)sin cos 01sin cos t t A H R T R λφφφλφφΨ−Ψ−⎡⎤⎡⎤⎡⎤=Ψ=⎢⎥⎢⎥⎢⎥ΨΨ⎣⎦⎣⎦⎣⎦
where λ > 0, t λ is the determinant of A , R i are rotations,[0,180)φ∈o , and T t is a tilt, namely, a diagonal matrix with first eigenvalue t > 1 and cond eigenvalue equal to 1.
Figure 1. Geometric interpretation of the decomposition (2). The image u is a flat physical object. Th
e small
parallelogram at the top right reprents a camera looking at u . The angles φ and θ are the camera optical axis
longitude and latitude. A third angle Ψ parameterizes the camera spin, and λ is a zoom parameter.
Figure 1 shows a camera motion interpretation of the affine decomposition (2): φ and ()arccos 1/t θ= are the viewpoint angles, Ψ parameterizes the camera spin, and λ corresponds to the zoom. The camera is assumed to stay far away from the image and starts from a frontal view u , i.e., λ = 1, t = 1, φ = Ψ = 0. The camera can first move parallel to the object’s plane: This motion induces a translation T that is eliminated by assuming (without loss of generality) that the camera axis meets the image plane at a fixed point. The plane containing the normal and the optical axis makes an angle φ with a fixed vertical plane. This angle is called longitude. Its optical axis then makes a θ angle with the normal to the image plane u . This parameter is called latitude. Both parameters are classical coordinates on the obrvation hemisphere. The camera can rotate around its optical axis (rotation parameter Ψ). Last but not least, the camera can move forward or backward, as measured by the zoom parameter λ.
In (2) the tilt parameter, which has a one-to-one relation to the latitude angle 1/cos t θ=, entails a strong image deformation. It caus a directional subsample of the frontal image in the direction given by the longitude φ.
under怎么读
2.2 NAIF Algorithm
NAIF proceeds by the following steps.
四级作文题
Step1: According to the rough exterior orientation elements (angle elements: ϕωκ、、) of images to calculate the two
axis camera parameters: the latitude ,
[0, 90) θθ∈o o and longitude , [0, 180) φφ∈o o . Using the rough exterior orientation elements (Angular elements: ϕωκ、、) of a image, we can obtain the Rotation Matrix R of the image as
托福学习方法123123123 (3)a a a R b b b c c c ⎛⎞⎜⎟=⎜⎟⎜⎟⎝⎠ where 123123123cos cos sin sin sin cos sin sin sin cos sin cos cos sin cos cos sin sin cos cos sin sin sin sin cos sin cos cos cos a a a b b b c c c ϕκϕωκ
ϕκϕωκϕωωκωκωϕκϕωκϕκϕωκϕω=−⎫⎪=−−⎪⎪=−⎪=⎪⎪=⎬⎪=−⎪=+=−+=⎭ (4)⎪⎪⎪⎪ Then, we can calculate the three angles of the tilt-swing-azimuth ()t s α−− system as [9]
()13133112cos tan (5)tan t c a s b c c α−−−⎫⎪=⎪⎪
⎛⎞−⎪=⎜⎟⎬−⎝⎠⎪⎪
⎛⎞−⎪=⎜⎟⎪−⎝⎠⎭ It does require the u of an inver tangent function which computes the full-circle range from 180−o to 180o , such as the “atan2” function in C or FORTRAN.
Thus,
The latitude angle ： (6)t θ=
The longitude angle ： (7)φα=
So we can directly compute the latitude θ and longitude φ.
As the affine matrix
(8)f f a b e A A T c d f ⎡⎤⎡⎤==⎢⎥⎣⎦⎣⎦
Where
cos sin 0cos sin 1, = (9)sin cos 01sin cos cos t a b A t c d φφλφφθΨ−Ψ−⎡⎤⎡⎤⎡⎤⎡⎤==⎢⎥⎢⎥⎢⎥⎢⎥ΨΨ⎣⎦⎣⎦⎣⎦⎣⎦
and (10)f e T f ⎡⎤=⎢⎥⎣⎦ Becau of SIFT algorithm is full scale and rotation invariance, therefore the scaling parameter λ is t to 1 and rotation parameter Ψis t to 0. And we can randomly give a coordinate value of (, f )e first, and calculate the translation matrix m T to move the rectified image to a suitable place later. In this paper, e and f are both t to 0.
Step2: Compute the rectified image.
Affine transformation f a b e A c d f ⎡⎤=⎢⎥⎣⎦
can be expresd by 0000** (11)**x a x b y e y c x d y f
=++⎧⎨=++⎩ or 00 (12)x x a b e y y c d f ⎛⎞⎛⎞⎛⎞⎛⎞=+⎜⎟⎜⎟⎜⎟⎜⎟⎝⎠⎝⎠⎝⎠⎝⎠ Then,
00** (13)**d b bf de x x y ad bc ad bc ad bc c a ce af y x y ad bc ad bc ad bc −−⎧=++⎪⎪−−−⎨−−⎪=++⎪−−−⎩ or 00 (14)d b bf de x x ad bc ad bc ad bc y c a y ce af ad bc ad bc ad bc −−⎛⎞⎛⎞⎜⎟⎜⎟⎛⎞⎛⎞−−−⎜⎟⎜⎟=+⎜⎟⎜⎟−−⎜⎟⎜⎟⎝⎠⎝⎠⎜⎟⎜⎟−−−⎝⎠⎝⎠
Thus,
1'* (15)f I A I −= where 1 (16)f d b b f d e a d b c
a d
b
c a
d b c A c a c
e a
f a d b c a d b c a d b c −−⋅−⋅⎡⎤⎢⎥⋅−⋅⋅−⋅⋅−⋅=⎢⎥−⋅−⋅⎢⎥⎢⎥⋅−⋅⋅−⋅⋅−⋅⎣⎦
In formula (15), I is the input image ，'I is the rectified image.
dream什么意思And we should calculate the size of the rectified image and the translation matrix m T to move the rectified image to aleke
图钉英文
suitable place.
We can u the four corners of the input image I and the Matrix 1f A −to calculate the four corners of the rectified image
'I as
1'* i=0,1,2,3 (17)'1i i f i i x x A y y −⎛⎞⎛⎞⎜⎟=⎜⎟⎜⎟⎝⎠⎜⎟⎝⎠ where ()()()()()()()()001102203300, y 0, 0, y - 1, 0 (18), y 0, - 1, y - 1, - 1x x W x H x W H ⎫=⎪=⎪⎬=⎪⎪=⎭
In formula (18), 0W is the width of the input image I and 0H is the height of the input image I .
Then, we calculate the maximum value and the minimum value of 'i x and ()' 0,1,2,3i y i = as
max min max min max{'}min{'} (19)max{'}min{'}i i i i X x X x Y y Y y =⎫⎪=⎪⎬=⎪
⎪=⎭
In formula (19), max X and min X , respectively, are the maximum value and the minimum value of 'i x , max Y and min Y , respectively, are the maximum value and the minimum value of ()' 0,1,2,3i y i = .
So we can calculate the size of the rectified image 'I and the translation matrix m T as
冬季安全小常识1max min 1max min 1 (20)1W X X H Y Y =−+⎫⎬=−+⎭
min m min 1001 (21)001X T Y −⎡⎤⎢⎥=−⎢⎥⎢⎥⎣⎦
In formula (20), 1W is the width of the rectified image 'I and 1H is the height of the rectified image 'I .
Then, we calculate the affine matrix ft A , which is the affine matrix f A after doing a translation.
1'''*= (22)'''ft f m a b e A A T c d f −⎡⎤=⎢⎥⎣⎦
And the pudo-inver matrix of ft A can be calculated as
英语四六级官网打印准考证入口1'''''''''''''''''' (23)''''''''''''''''''ft d b b f d e a d b c a d b c a d b c A c a c e a f a d b c a d b c a d b c −−⋅−⋅⎡⎤⎢⎥⋅−⋅⋅−⋅⋅−⋅=⎢⎥−⋅−⋅⎢⎥⎢⎥⋅−⋅⋅−⋅⋅−⋅⎣⎦
Thus,corning
10'* (24)ft I A I −=
Where I is the input image ，0'I is the rectified image after translation to the suitable place, that is to say, the coordinate value min min (,
Y )X in 'I is moved to the coordinate value (0, 0) in 0'I .
In our paper, we do affine transform only once to each of images.
Step3: The two rectified images are compared by a scale invariant matching algorithm (SIFT).
We extract SIFT interest points from the rectified images, then we compare the descriptors of interest points by using some uful matching strategies, including the significance test and the left-right validation, and we get the matches on the rectified images. Finally, we can calculate the corresponding matches on the original images by using the affine matrix ft A .
Suppo there are two oblique images: a side-view image and a bottom-view image. The specific process of NAIF as shown in figure 2.
Figure 2. The flow chart of NAIF algorithm
