A Novel Scheme Based on the Diffusion to Edge Detection

A Novel Scheme Based on the Diffusion to Edge Detection

Abstract: A novel scheme of edge detection based on the physical law of diffusion is presented in this paper. Though the most current researches are using data based methods such as Deep Neural Networks, these methods on machine learning need big data of labeled ground truth as well as a large amount of resources for training.

On the other hand, the widely used traditional methods are based on the gradient of the grayscale or color of images with using different sorts of mathematical tools to accomplish the mission. Instead of treating the outline of an object in an image as a kind of gradient of grayscale or color, our scheme deals with the edge detection as a character of an energy diffusing in the space of media such as Charge-coupled Device (CCD). By using the characteristic function of diffusion, the information of the energy will be extracted. The scheme preserves the structural information of images very well. Because it comes from the inhere law of images’ physical property, it has a unified mathematical framework for images’ edge detection under different conditions, for example, multiscales, diferent light conditions and so on. Moreover, it has low computational complexity.

Existing system:

On the other hand, in some applications of images such as enhancement, denoising and compression applications, the diffusion method has various different uses. It is reasonable to ask the following questions: 1) Since some applications of image processing can be accomplished by using diffusion rule, is it one of the basic rules to form images 2) Does a characteristic function exist for mapping physical properties of diffusion to the information of edges or the outlines in an image Based on the researching work in the physics, Ralf Widenhorn and et al. find out how the charge spreading into a CCD that depends on the location of the light spot and measure the energy of diffusion by experiment. Therefore, most likely, we can answer “Yes� to the two questions above . Whereas, in this paper, we present a novel scheme.

Proposed system: In Section 3, the mathematical description of global function of diffusion on forming images is proposed. In Section, the characteristic function of diffusion is presented and analyzed. In Section , the scheme to measure and calculate the characteristic of diffusion based on the principles which have been given is presented. In Section, the experiments results are presented and analyzed. Finally, in Section , the conclusion is drawn and discussion is given. Canny not only presented the algorithm in the paper, also proposed the criteria for judging the quality of edge detections. He suggested three criteria : Signal-to-noise ratio(SNR) criterion, localization precision criterion and single edge response criterion Another roadmap of this area is based on the Partial Differentia Equation. The representative one is the nonlinear diffusion approach that is called P M model proposed by Perona and Malik. They propose a nonlinear equation to replace the general heat equation by of the porous medium type.

Advantages: The advantages of our scheme are simple for using because of the unified framework, high efficiency for computing and reserving the structure of the original image well.

Moreover, our scheme has the advantages of handling images only by diffusion.

For example, in this scheme, we do not need to concern the scales of the filters or the masks for doing convolution.

Because the running time of Canny and Sobel are determined by the scale of the filter times the size of the image, both of them declare themselves as ‘linear’ method. At the same time, our scheme .

Disadvantages: However, in this paper, the C is the value which represents record of light energy such as grayscale. Meanwhile, the D is the conductivity of light energy.

In this problem, we use the Sobolev space that yields gradient flows which are well-posed in this problem , to solve the diffusion equation thereby it provide us a tool to extract features from images.

To accomplish our work, we solve the diffusion equation. We use Sobolev space to deal with images’ function. Then, because the problem is on property of energy function the operator based on Fourier transform is designed. We analyze the relationship between parameters of our operator and characteristics of images.

Furthermore, we present the experimental results of our scheme in edge detection of images.

Modules: Image processing: EDGE detection is an important work in image processing. It is one of the essential steps for image segmentation , object recognition and computer vision . Traditional schemes of edge detection are mainly depend on calculating the gradient of the value of greyscale or color. By using the threshold, the boundaries may be filtered out. For instance, it is a traditional way of handling images, that Marr and Hildreth approximated the receptive fields as Laplacian of Gaussian (LoG), which in turn can be closely approximated by Difference of Gaussians (DOG). The other method of detecting boundaries comes from Witkin who noticed that the solutions of the low pass filters which use the convolution of the signal with Gaussians in different scales have the same mathematical form of heat equation. By using the diffusion equation, the effect of smoothing or edge detection for images can be obtained.

One of the important progresses in this area comes from Malik and Perona . They proposed the Anisotropic Diffusion equation to replace the heat equation. By using

the a nonlinear equation of the porous medium type, the conditions of equation can be adjusted to fit the different images.

Diffusion: Therefore, in the first time, a unified framework to extract the information of diffusion in images is presented. Under this mathematical framework, we are going to accomplish the edge detection based on the mapping relation. By this scheme, an image is treated as a whole space and the characteristic of diffusion of the light energy has been analyzed. We present the scheme to measure and extract the features in the images and use them to accomplish work of edge detection shows the example of result that is obtained based on the scheme. Since images have two dimensions, in our scheme, the diffusion of light energy in an two-dimensional space has been analyzed. The Sobolev gradient flows are well-posed in both the forward and backward directions. Therefore, to achieve the goal of extracting the diffusion information, the media of recording (e.g. CCD) is being treated as a space for recording the information of light energy diffusing in it and the theory of Sobolev Space is used to analyze this kind of procedure .

Recent works of edge detection combine the features of the each pixel location using local brightness, texture and color gradient together such as probability of boundary. Many researches use Machine learning algorithm, for instance, the Deep learning to extract the features to locate the outlines in the images. Whereas, in this paper, we present a novel scheme of edge detection base on the idea that associates the properties of signal with the characteristic function of diffusion of light energy for forming an image in the media. Therefore, in the first time, a unified framework to extract the information of diffusion in images is presented. Under this mathematical framework, we are going to accomplish the edge detection based on the mapping relation.

Sobolove space : Therefore, to achieve the goal of extracting the diffusion information, the media of recording (e.g. CCD) is being treated as a space for recording the information of

light energy diffusing in it and the theory of Sobolev Space is used to analyze this kind of procedure. According to the diffusion theory , partial derivative equation(PDE) is used to describe the process. Whereas, the Riesz and Bessel potentials are used to compute the second derivative operator to solve the PDE. Physical principle of the diffusion of light energy in the media; 2) A appropriate measure of image function space, Bessel potential and Sobolev space theory are used to describe the phenomenon of forming images; Algorithms based on the diffusion theory is used to obtain the features of images.