SIAM J.I MAGING S CIENCES c
2013Society for Industrial and Applied Mathematics Vol.6,No.3,pp.1345–1366
A Variational Approach for Image Stitching II:Using Image Gradients ∗
Michael K.Ng †and Wei Wang ‡
Abstract.In [W.Wang and M.K.Ng,SIAM J.Imaging Sci.,6(2013),pp.1318–1344],we proposed and developed an image stitching algorithm by studying a variational model for automatically computing weighting mask functions on input images and stitching them together.The main aim of this paper is to further develop an image stitching algorithm using the gradients of input images.Our idea is to study a variational method for computing a stitched image by using an energy functional containing the data-fitting term based on the difference between the gradients of the stitched image and the input images,and the Laplacian regularization term based on the smoothness of weighting mask functions.The use of image gradient information allows us to automatically adjust the stitched image to handle color inconsistency across input images.In the model,we incorporate both boundary conditions of the stitched image and the weighting mask functions.The existence of a solution of the proposed energy functional is shown.We also present an alternating minimizing algorithm for solving
the variational model numerically,and we show the convergence of this algorithm.Experimental results show that the performance of the proposed method is better than the other testing methods proposed in the literature for input images with color inconsistency.Key words.image stitching,variational model,image gradients,algorithm,weighting mask functions AMS subject classifications.65K10,68U10,91-08DOI.10.1137/rge objects often cannot be captured in a single picture under the view of camera phones or Planetary Data System cameras.Image stitching is a process that combines two or more images and blends them into one.It is the main step in the generation of panoramic images,and it is widely used in remote sensing [1,2],superresolution [3],and
texture synthesis [4].The main aim of image stitching is to find a visually acceptable or
seamless blending from the input images with overlapping regions.Stitching problems usually contains two steps:image alignment and image blending.The goal of image alignment is to find corresponding point pairs in the overlapping region of two images;see,for instance,[5,6,7,8,9].Image blending combines the two aligned images seamlessly.There are two main approaches for image stitching in the literature.Optimal seam meth-ods [4,10,11,12,13,14]search for a curve in the overlapping region on which the differences
between two original images are minimal.Then each image is copied to the corresponding side of the curve.When the difference between two input images is zero on the curve,there will
∗
Received by the editors April 2,2012;accepted for publication April 10,2013;published electronically July 11,2013./journals/siims/6-3/87214.html †
Centre for Mathematical Imaging and Vision and Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong (mng@.hk ).This author’s research was supported in part by an HKRGC grant and HKBU FRG grant.
‡
Corresponding author.Department of Mathematics,Tongji University,Shanghai 200442,China (weiwamng@
).This author’s research was supported by National Natural Science Foundation of China grant 11201341and China Postdoctoral Science Foundation grants 2012M511126and 2013T60459.
1345D o w n l o a d e d 10/31/13 t o 218.201.115.245. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h p
