Abstract
Image segmentation technology is dedicated to the segmentation of intensity inhomogeneous at present. In this paper, we propose a new method that incorporates fractional varying-order differential and local fitting energy to construct a new variational level set active contour model. The energy functions in this paper mainly include three parts: the local term, the regular term and the penalty term. The local term combined with fractional varying-order differential can obtain more details of the image. The regular term is used to regularize the image contour length. The penalty term is used to keep the evolution curve smooth. True positive (TP) rate, false positive (FP) rate, precision (P) rate, Jaccard similarity coefficient (JSC), and Dice similarity coefficient (DSC) are employed as the comparative measures for the segmentation results. Experimental results for both synthetic and real images show that our method has more accurate segmentation results than other models, and it is robust to intensity inhomogeneous or noises.
Highlights
The fractional-order PDE is an important branch of mathematical analysis, but it is little known by engineering scholars
The fractional order differential has the characteristics of increasing the high frequency component of the signal while preserving the low frequency component of the signal nonlinearly
Li et al proposed a novel active contour model based on an adaptive fractional order differential to solve the impact of noise on the image in the process of segmentation [1]
Summary
The fractional-order PDE (partial differential equation) is an important branch of mathematical analysis, but it is little known by engineering scholars. Traditional integer-order differential operations have overall properties to matrix functions such as images. We think that the fractional order differential can be used to enhance the detailed features of complex texture in two-dimensional image signals. Some scholars have started the application of fractional order differential in image segmentation. Li et al proposed a novel active contour model based on an adaptive fractional order differential to solve the impact of noise on the image in the process of segmentation [1]. Ren presented a new adaptive active contour model based on fractional order differential [2]. Chen et al proposed an adaptive-weighting active contour model, which incorporates image gradient, local environment and global information into a framework [3]. On the basis of fractional order differential and our application to other image processing algorithms [5,6,7], we proposed a fractional varying-order differential, which can simultaneously perform different fractional orders differential operations on each element function of a matrix function, i.e., the differential orders of different parts of the image can
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