外文翻譯-機(jī)械模具自動(dòng)化【期刊】在圖像中基于偽極坐標(biāo)的大尺度變換、旋轉(zhuǎn)和平移的估算-外文文獻(xiàn)

1、Pseudo-polar based estimation of large translations rotations and scalings in imagesYosi Keller Amir Averbuch Moshe IsraeliDepartment of Mathematics Department of Computer Science Department of Computer Science Yale Univ

2、rsity Tel-Aviv University Technion Institute of Technology New Haven, CT, USA Tel-Aviv, Israel Haifa, Israel yosi.keller@yale.eduAbstractOne of the major challenges related to image registration is the estimation of larg

3、e motions without prior knowledge. This paper presents a Fourier based approach that estimates large translation, scale and rotation motions. The algorithm uses the pseudo-polar transform to achieve substantial im- prove

4、d approximations of the polar and log-polar Fourier transforms of an image. Thus, rotation and scale changes are reduced to translations which are estimated using phase correlation. By utilizing the pseudo-polar grid we

5、increase the performance (accuracy, speed, robustness) of the reg- istration algorithms. Scales up to 4 and arbitrary rotation angles can be robustly recovered, compared to a maximum scaling of 2 recovered by the current

6、 state-of-the-art algo- rithms. The algorithm utilizes only 1D FFT calculations whose overall complexity is significantly lower than prior works. Experimental results demonstrate the applicability of these algorithms.1 I

7、ntroductionImage registration plays a vital role in many image pro- cessing applications such as video compression [1], video enhancement [2] and scene representation [3] to name a few. This problem was analyzed using va

8、rious computa- tional techniques, such as pixel domain Gradient methods [2], correlation techniques [15] and discrete Fourier (DFT) domain algorithms [6, 11]. Gradient methods based image registration algorithms are cons

9、idered to be the state-of-the- art. They may fail unless the two images are misaligned by only a moderate motion. Fourier based schemes, which are able to estimate relatively large rotation, scaling and transla- tion, ar

10、e often used as bootstrap for more accurate gradient methods. The basic notion related to Fourier based schemes is the shift property [18] of the Fourier transform which allows robust estimation of translations using the

11、 normal- ized phase-correlation algorithm [6, 9, 10]. Hence, in or-der to account for rotations and scaling, the image is trans- formed into a polar or log-polar Fourier grid (referred to as the Fourier-Mellin transform)

12、. Rotations and scaling are reduced to translations in these representations and can be estimated using phase-correlation. In this paper we propose to iteratively estimate the po- lar and log-polar DFT using the pseudo-p

13、olar FFT (PPFFT) [19]. The resulting algorithm is able to robustly register im- ages rotated by arbitrary angles and scaled up to a factor of 4. It should be noted that the maximum scale factor re- covered in [11] and [1

14、6] was 2.0 and 1.8, respectively. In particular, the proposed algorithm does not result to inter- polation in either spatial or Fourier domain. Only 1D FFT operations are used, making it much faster and especially suited

15、 for real-time applications. The rest of paper is organized as follows: Prior results related to FFT based image registration are given in Section 2, while the proposed algorithm, is presented in Section 3. Experimental

16、results are discussed in Section 4 and final conclusions are given in Section 5.2 Previous related work2.1 Translation estimationThe basis of the Fourier based motion estimation is the shift property [18] of the Fourier

17、transform. Denote byF ff (x, y)g , b f (ωx, ωy) (1)the Fourier transform of f (x, y). Then,F ff (x + ¢x, y + ¢y)g = b f (ωx, ωy) ej(ωx¢x+ωy¢y). (2) Equation 2 can be used for the estimation of image t

18、ransla- tion [6, 10]. Assume the images I1 (x, y) and I2 (x, y) have some overlap thatI1 (x + ¢x, y + ¢y) = I2 (x, y) . (3)Proceedings of the IEEE Workshop on Motion and Video Computing (WACV/MOTION’05) 0-7695

19、-2271-8/05 $ 20.00 IEEE rotation and translation estimation algorithm operates as follows:1. Let (m1, l1) and (m2, l2) be the sizes of I1 (i, j) and I2 (i, j) , respectively. Then, at iteration n = 0, I1 (i, j) and I2 (i

20、, j) are zero padded such thatm1 = l1 = m2 = l2 = 2k, k 2 Z. (12)2. The magnitudes MP P 1 ¡ θi, rj ¢ and MP P 2 ¡ θi, rj ¢ ofthe PPFFTs of I(n) 1 (i, j) and I2 (i, j) are calculated, respectively.3. T

21、he polar DFTs ,magnitudes c MPolar 1 ¡ θi, rj ¢ and c MPolar 2 ¡ θi, rj ¢ of I(n) 1 (i, j) and I2 (i, j) are substi-tuted by MPP 1 ¡θi, rj ¢ and MP P 2 ¡θi, rj ¢ respectively.4. Th

22、e translation along the ?! θ axis of MPP 1 ¡ θi, rj ¢and MP P 2 ¡θi, rj ¢ is estimated using phase correla- tion. The result is denoted by ¢θn.5. Let θn be the accumulated rotation angle estimate

23、d at iteration nθn ,n Xi=0 ¢θi = θn? 1 + ¢θn.Then, the input image I1 (i, j) is rotated by θn (around the center of the image) using the FFT based image ro- tation algorithm described in [4]. This rotation sche

24、me is accurate and fast since only 1D FFT operations are usedI(n+1) 1 (θ, r) = I(0) 1 (θ + θn, r) , n = 1, . . .The rotation can be conducted around any pixel. We recommend to use the central pixel of I1 (i, j) such that

25、 the bounding rectangular of the rotated image will be as small as possible.6. Steps 2-5 are reiterated until the angular refinement term ¢θn is smaller than a predefined threshold εθ, i.e. j¢θnj 0). The polar

26、 axis is approximated using the same procedure as in section 3.1, while the radial axis is approximated using nearest-neighbor interpolation.4. The relative translation between c MLog? Polar 1 (i,j) and c MLog? P olar 2

27、(i,j) is recovered by a 2D phase correla-tion on the ?! θ and ?! r axes.5. Let ¢θn and ¢rn be the rotation angle and the scaling value estimated at iteration n, respectively. Then, the input image I1 (x, y) is

28、rotated (around the center of the image) [4] and then scaled using DFT domain zero paddingI(n+1) 1 (θ, r) = I(0) 1 (θ + θn, r ¢ rn) (16)whereθn =n Xi=0 ¢θi = θn? 1 + ¢θnrn =n Yi=0 ¢ri = rn? 1 ¢ &