1.北京政法職業學院 信息技術系, 北京100024;
2.北京工商大學 計算機學院, 北京100037;
摘 要:在自動圖像拼接中,圖像模型參數的求取和優化是一個最小二乘問題。本文提出基于Levenberg-Marquardt算法的圖像拼接參數求解算法,通過建立適當的圖像相機參數模型,并將圖像模型參數的優化問題轉化為圖像之間映射誤差的最小二乘問題,解決了圖像配準參數的求取問題。通過利用求得的圖像參數把圖像映射到球面上,使用圖像漸進混合和雙線性插值繪制球面,并對球面進行展開,最終生成平面拼接圖像。
關鍵詞:Levenberg-Marquardt, 圖像拼接, 圖像參數模型,最小二乘問題
The Application of Levenberg-Marquardt Algorithm In the Image Stitching
Juan Hu1,Huanchun Li1,Yipeng Zhou2
1 Department of information and technology, Beijing College of Politics and Law, Beijing, China, 100024
2 Computer school, Beijing technology and business university, Beijing, China, 100037
Abstract: In automatic image stitching, the solving of the image model parameters and optimization is a least squares problem. This paper presents the solution algorithm based on Levenberg-Marquardt algorithm for image stitching parameters. Through the establishment of appropriate image camera parameter model, the image model parameter optimization problem becomes a least squares problem for the mapping error between the images and to solve the problem of the image registration parameters. With the images mapped to the sphere through the use of the image parameters obtained, the progressive mixing of the image and bilinear difference to draw the spherical surface, the final plane mosaic image is generated.
Keywords: Levenberg-Marquardt, image stitching, image parameter model, least squares problem
參考文獻
[1] Kenneth Levenberg. "A Method for the Solution of Certain Non-Linear Problems in Least Squares". The Quarterly of Applied Mathematics (1944) 2: 164–168.
[2] Donald Marquardt (1963). "An Algorithm for Least-Squares Estimation of Nonlinear Parameters". SIAM Journal on Applied Mathematics 11: 431–441.
[3] Björck, A. (1996). Numerical methods for least squares problems. SIAM, Philadelphia.
[4] Mordecai Avriel (2003). Nonlinear Programming: Analysis and Methods. Dover Publishing.
[5] D.K. Arrowsmith and C.M. Place, Dynamical Systems, Section 3.3, Chapman & Hall, London, 1992.
[6] http://hugin.sourceforge.net/
[7] C. Harris and M.J. Stephens. A combined corner and edge detector. In Alvey Vision Conference, pages 147–152, 1988.
[8] Lowe, David G. (1999). "Object recognition from local scale-invariant features". Proceedings of the International Conference on Computer Vision 2: 1150–1157.
[9] Watt,A. (1995). 3D Computer Graphics. Addison-Wesley,third edition
[10] 李曉輝,周蔭清,王祖林. 基于曲面拼接的球面全景生成算法. 北京航空航天大學學報, 2007, 33(6): 668-671,681.
[11] 李艷麗,向輝. 穩健的球面全景圖全自動生成算法. 計算機輔助設計與圖形學學報, 2007, 19(11): 1393-1398.
[12] Oliver Faugeras. Three-Dimensional Computer Vision: A Geometric Viewpoint.MIT Press, Cambridge, MA, 1993.
[13] K. Madsen, H.B. Nielsen, O. Tingleff. METHODS FOR NON-LINEAR LEAST SQUARES PROBLEMS.
[14] Martin A. Fischler and Robert C. Bolles (June 1981). "Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography". Comm. of the ACM 24: 381–395.
作者簡介:胡娟,女,碩士,講師,北京政法職業學院教師,研究方向移動商務、圖像處理。