# Breast Microcalcification Detection Algorithm Based on Contourlet and ASVM
## 3 Method
### Preprocessing  
In the process of shooting, transmission, and digitization, mammograms are inevitably doped with noise, especially they are doped with salt and pepper noise. If the corresponding inhibition is not given in advance, it will often lead to a large number of false positive areas, which has an adverse impact on the test. Image enhancement is widely used in image processing to improve image quality. The purpose of image enhancement is to enhance weak edges or weak features in images. Recently, many methods are based on wavelet transform, because wavelet transform has multi-scale structure and good results can be achieved. However, all existing methods are unable to obtain geometric information in the image for image enhancement.  
In 2002, [PERSON] (2002) proposed a tower-shaped directional filter bank, which is an analysis method superior to the wavelet transform and is a new extension of the multi-resolution and multi-directional wavelet transform. Firstly, the image is multiscale scaled by the Laplacian pyramid transform to capture singular points. Directional filters are applied to synthesize singular points into coefficients, where points are distributed in the same direction. It should be indicated that the base support space is a rectangle that varies in length and [PERSON] with scale. Therefore, not only the multi-resolution and time-frequency local characteristics of the wavelet transform are obtained, basic functions are  
Figure 1: Flow chart of the computer-aided detection algorithm for breast calcification.  
distributed in multiple scales and multiple directions. However, only a small number of coefficients can be effectively captured. Because the noise is mainly in the high-frequency subband, I mainly deal with the bandpass image (see Figure 2).  
Mathematical morphology is a commonly used nonlinear filtering method, based on the dilatation and erosion. They are often used to solve problems, such as feature extraction, image segmentation and the edge detection of binary images. The theory of mathematical morphology is very complicated, but its basic idea is simple and perfect. It regards the image as a set of points and uses the structure matrix to shift, intersect, and combine operations to form various algorithms of morphology. Since noises are mostly located in the high-frequency subband, the bandpass sub-image is filtered by the median, which is beneficial to remove the high-frequency noise and perform the mathematical morphology calculation. Nonlinear mapping function [21; 22] removes isolated dots and burrs and preserves the overall shape of the image. Formula (1) express the nonlinear mapping function. Figure 2 introduces the specific process of the algorithm.  
\[F=\left\{\begin{array}{ll}P(\mathrm{i},\mathrm{j})&\text{Low frequency coefficient}\\ \text{median}(P(\mathrm{i},\mathrm{j}))&\text{High frequency coefficient}\\ 0&\text{Noise}\end{array}\right. \tag{1}\]  
Our image enhancement algorithm is based on Contourlet transform and mathematical morphology, which makes full use of the multi-resolution analysis of Contourlet transform and the characteristics of image edge information processing and mathematical morphology. The algorithm proposed in this paper effectively solves the contradiction between suppressing noise and retaining edges.