Automatic image registration by using multi-variate spline functions
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Abstract
Image registration is an image processing to transform different sets of data in which one has an overlap with another into one coordinate system. Usually, the data is multiple photographs such as the data from different sensors, times, depths, or viewpoints. Image registration is a very important and popular research field in image processing, not only because the requirement of the medical image processing such as Computational Anatomy(CA) which is applied to study health, disease and epidemiology and uses deformable mappings between images as a basic technique, but also because it is the basis for the application of the meteorological satellite spectral image data[1]. There are various methods for image registration, such as affine, deformable Directly Manipulated Free-Form Deformation(DMFFD), diffeomorphic transformation method with mutual information(MI), mean squared difference(MSQ) or fast cross correlation(CC) as its similarity measure, thin spline method, landmark method and so on. In this paper, an new automatic image registration will be given and discussed. This method has three parts which are edge searching, image registration method by using multivariate spline function and automatic image registration with satellite images. That is, we will introduce a new image registration method by using multivariate spline functions. To facilitate the application with some previous results, we generalized them by using matrix variable. The basic idea of our method is as follows: we had already found the image registration method by using multivariate spline function, now we try to update it as an automatic image registration method, so, firstly, we need find a suitable edge searching method for this method, secondly, we need a method which can make those two parts which are edge searching and image registration method by using multivariate spline function works automatically. The summary of this paper as follows:
Chapter 1 includes the introduction and the preliminaries. The first section includes the background of image registration and the recent progress of Spline Methods. The second section provides definitions and theorems which will be used in this paper.
Chapter 2 describes the boundary selection method for multivariate spline method. There are four sections in this chapter: In section 1, the Pre-boundary Selection Method 1 will be introduce, this method is based on using Otsu's method. In section 2, the Pre-boundary Selection Method 2 will be introduce, this method is based on using sobel operator. In section 3, the Boundary Selection Method will be given
by using Pre-boundary Selection Method 1 and Pre-boundary Selection Method 2. Section 4 introduces Object Recognition Method which is based on the Boundary Selection Method.
Chapter 3 describes the multivariate Spline Method. There are four sections in this chapter: In section 1, the feature point is introduced. In this section, feature points are chosen as the interpolation points for multivariate spline functions. Section 2 is affine transformation. In this section, we will demonstrate the way to calculate the affine transformation by using the feature points. Section 3 introduces the Delaunay triangulation. By using the corresponding interpolation points in output image, we will perform the corresponding Delaunay triangulations in this section. Section 4 shows the application of multivariate spline interpolation. In this section, the barycentric coordinates are used to evaluate the expression of multivariate spline functions. Section 5 describes size determination. In this section, the size of the output image is determined. Section 6 is the valuation scheme. In this section, two valuation schemes can be used for output image.
Chapter 4 describes the Automatic Image Registration by using Multivariate Spline Method. In this chapter, there are 2 sections. Section 1 is Pre-Selection Method for Automatic Image Registration, the basic idea of the Pre-Selection Method is tried to find the first three corresponding feature points automatically, then tried to find more corresponding feature points as much as possible so that we can use the Multivariate Spline Method. Section 2 is Adding point Method for Automatic Image Registration,
the basic idea of Adding point Method is that try to match the number of points for the pair of corresponding feature points, we add enough points so that the number of the points is equal to the least common multiple(LCM) of the number of the points in corresponding feature points, then tried to find more corresponding feature points as much as possible so that we can use the Multivariate Spline Method.
Chapter 5 includes results and experimental procedures. We will show some results
by using both satellite image and MRI.
Chapter 6 includes the conclusion and future work. Some conclusion and future work
will be given in this chapter.