Circular Form Detection Based On Generalized Radon Transform

Digital image processing is also known as the computer image processing, it refers to convert the image signals into digital signals and use the computer to deal with them. The formation of Digital Image Processing is inseparable from the productive forces and social needs. Early image processing is to improve the quality of the image, it objects to the improvement of the human visual effects. The main methods of image processing are image enhancement, rehabilitation, coding, compression etc. With the development of computer technology and artificial intelligence, digital image processing is up to a high level. People have studied how to use the computer system to interpret image. Today, the digital image processing techniques applied to a wide range of scientific research, industrial and agricultural production, military technology, government departments, medical and health, and many other fields. This makes digital image processing technology to become a noticeable subject, and the prospects of it are brightening.Radon transform has an important status in many application fields. It is the mathematical foundation of CT (Computer Tomography) technology and Reconstruction (Reconstruction Problem) which are very active. Reconstruction is not damaged, not broken object. It can understand and study the internal structure, density and distribution of the object. For example, geophysics, seismic exploration, non-destructive testing, medical testing or injuries, medical diagnosis, imaging radar, radio astronomy, etc. Special needs to be pointed out that the success of the Radon transform in the medical applications. With the invention of the United Kingdom's first commercial EMI brain scanner and the wide application of computer, CT technology has developed rapidly in many fields. And now it associates with the very popular wavelet transform, for example, use wavelet to inverse Radon transform and high-definition image reconstruction.One of the first stages in image analysis is the extraction, such as lines, edges, curves. In general we are interested in a given family of shapes. Our assumption is that the members of this family can be described by a set of parameters. The method for detecting parameterized shapes is based on a family of transformations, which includes the Radon transform. This paper studies the application of the detection for circles base on generalize Radon transform in multi-dimensional space. And algorithm improvements: the sampling of generalized Radon transform, accuracy of parameter space, memory requirements. Detection by which a group of objects radius of the circle is given, the size of the radius of circular objects unknown in this paper does not involve. The specific of this paper is as follows:Introduce the development of digital image processing, applications, features and content, Image characteristics and the descriptions, and some of the existing extraction methods. Then study of different forms of traditional Radon transform, and the application of images.Introduce the generalized Radon transform, study a particular case of a generalized Radon transform for circles in detail. The constraint functions provide a convenient for the sampling of the generalized Radon transform. The kernel has a shift-invariant structure. So the operator reduces to a set of convolutions. This implies a large speed-up.To allow computer processing, we must work with digital images. Likewise, the transform should be sampled to match digital images. The sampling of the generalized Radon transform is one of the main points of this paper. Discuss the errors produced by discrete versions of these transform, and the relative solution. This paper compares different models. The Gaussian filter makes the kernel C band-limited. This ensures the parameter space samples safely.Improve the accuracy of the parameter is also one of the main points. Due to these lager circles will produce a higher value (higher confidence) than small ones in the parameter space. A few disconnected sections input will be selected as a larger circle with a higher confidence. The radii of circles with thick walls will be over-estimated. To avoid this, this paper converts the algorithm to a normalized version. And correct the normalization. The simulation show that the correction presents an improved of accuracy of parameter space.The parameter space for the Radon transform typically has more dimensions than the input image. This implies that the requirement of the computer memory is very high. This constraint has traditionally prevented wide-spread use of these transforms for 3D images. This paper introduces different methods for reducing the requirement of memory. Such as, partition of the parameter space and dimensionality reduction. Base on these methods, this paper propose an approach to reduce the memory requirement. Circles can be detected efficiently by storing the maximum projection along the r-axis of P. in this method storing the location of the center of the circle and radii in different space. So reduce the requirement of the memory more efficiently.In the practical application, the accuracy of the extraction and the range of the application need to be further improved for this algorithm.