Application of Radon Transform in Ct Image Matching

When Industrial Computerized Tomography (CT) techniques are adopted to inspect quality of industrial products, we lay emphases on their installation validity or inner defects. In order to do so, we always try to perform matching operation between reference object and test objects. However, conventional image matching methods can’t meet on-line detection demand because of their slow recognition speed and low throughput rate. In this paper, we attempt to directly use CT projection data or object’s Radon transform to solve matching parameters. Firstly we discuss some properties of Radon transform invariant to geometric distortion such as translation, rotation and uniform scaling, and then discuss recognition methods of matching parameters. Experimental results confirm that this scheme is robust to geometric distortions and greatly improve matching speed and precision. Introduction: X-ray Computed Tomography enjoys rapidly growing interest in industrial quality inspection. However, to take advantage of this technique in the automated manufacturing process, one has to employ robust image processing algorithms that perform inspection tasks without human interaction. Image matching method is one of basic image processing algorithms and is a technique of estimating the similarity of different images. It is fundamental in image analysis and pattern recognition, and has a wide variety of application, such as detecting changes in a scene, estimating object motion, locating targets, identifying objects, integrating information from different types of image, etc. Among those applications considered most frequently are geometrical transformation such as translation, uniform scaling and rotations. The early interest in this problem comes from computer vision, which requires transformation from one coordinate space to another. Target recognition in remote sensing is another field of practical application. Recently with the advent of multimodality images in medical diagnosis, this problem becomes more and more important in studies and implementations. The fundamental operation for image matching is to compare various correlations under different names and guises depending on specific implementations. Basically, there are three categories of algorithm in the existing literatures. They are (i) techniques based on image intensities, such as moments [1-3], correlations [4-5], integral kernel technique, and Fourier methods. (ii) Featured-based methods and (iii) elastic model-based methods [6]. A general review was given in [7,8]. In the recent applications of medical diagnosis and therapy treatment planning, many combined methods appeared. However, conventional image matching methods can’t meet the on-line detection need because of their slow recognition speed and low throughput rate. We attempt to directly use CT projection data or object’s Radon transform (RT), to solve matching parameters. Generally geometric distortion, only referring to rigid distortion, such as translation, rotation and uniform scaling is the key problem of image matching, therefore, we focus on how to solve geometric deformation parameters by RT. In Section 2 we’ll introduce some properties of RT invariant to geometric distortion and describe methods for determining the transform parameters in section 3. Many simulative experiments and results are shown in section 4. 2 Radon Transform and Its Prosperities: In recent years, Hough transform, Trace transform and the related Radon transform have received much attention. In the view of mathematics, Hough transform is a derivative of RT and RT is a special case of Trace transform [9]. These three transforms are able to transform two dimensional images with lines into a domain of possible line parameters, where each line in the image will give a peak positioned at the corresponding line parameters. These have lead to many line, circle and curves detection applications within image processing, computer vision, etc. The following will only describe RT and its properties. Though several definitions of the RT are existed, they are related. A very popular form express is as what discussed in [10]. In computed tomography (CT) when a bundle of x-ray goes through an object, its attenuation depends on content of object, distance and direction or angle of this projection. This set of projections is called RT. In two dimensions, let f (x, y) be a 2D image, its RT denoted as is the 2D function of the real variable t and angle f R θ , defined by: