A Novel Global Energy and Local Energy-Based Legendre Polynomial Approximation for Image Segmentation

Feng Hu,Mengyun Zhang,Bo Chen,Chuanjun Chen

doi:10.1155/2020/2061841

Abstract

Active contour model (ACM) is a powerful segmentation method based on differential equation. This paper proposes a novel adaptive ACM to segment those intensity inhomogeneity images. Firstly, a novel signed pressure force function is presented with Legendre polynomials to control curve contraction. Legendre polynomials can approximate regional intensities corresponding to evolving curve. Secondly, global term of our model characterizes difference of Legendre coefficients, and local energy term characterizes fitting evolution curve of interested region. Final contour evolution will minimize the energy function. Thirdly, a correction term is employed to improve the performance of curve evolution according to the initial contour position, so wherever the initial contour being in the image, the object boundaries can be detected. Fourthly, our model combines the advantages of two classical models such as good topological changes and computational simplicity. The new model can classify regions with similar intensity values. Compared with traditional models, experimental results show effectiveness and efficiently of the new model.

Highlights

Image segmentation [1], image denoising [2, 3], and image reconstruction [4] are all basic tasks in image processing field
Many segmentation methods based on partial differential equation (PDE) model [1] have been proposed with the development of PDE [5,6,7,8,9,10] and stochastic theory [11, 12]
We give a comparison of the Dice value in Table 1; it can be seen from Figure 3 and Table 1 that our proposed model is proved to be more efficient in segmenting images with intensity inhomogeneity and more accurate in terms of segmentation accuracy than the other four methods

Summary

Introduction

Image segmentation [1], image denoising [2, 3], and image reconstruction [4] are all basic tasks in image processing field. Zhou et al introduce a global and local intensity information (LGIF) [17] model, which can achieve high segmentation accuracy while with heavy computational complexity. LCV model cannot perform well on intensity inhomogeneous images and sometimes leads to edge leakage because the average convolution operator is employed in local region. Shi and Pan [22] present a LGBF to deal with intensity inhomogeneous image segmentation problem. This paper proposes a novel Legendre polynomial approximation with adaptive global energy based on our previous model [23]. Experimental results show that our model is robust and efficient to segment intensity inhomogeneity images. This rest of this paper is organized as follows.

The Related Works

A Novel Adaptive Segmentation Model

Algorithm Procedure

Experimental Results

Conclusion

Coefficient Vectors are Invertible and Existing