A new active contour model driven by pre-fitting bias field estimation and clustering technique for image segmentation

Highlights

• A new function for computing bias field is proposed.

• The computation of the bias field is completed before the iteration and there is no more time-consuming convolutions in iterations.

• The computing of clustering center points takes into account the average value of the grayscale within and without the contour of the bias field.

• The variational level set function is optimized with an adaptive function to limit the magnitude of the data driven term.

• The proposed model shows better segmentation accuracy and robustness.

Abstract

Due to uneven illumination or limitations of imaging devices, intensity inhomogeneities are more or less present in images obtained by different imaging modes. This ubiquitous intensity inhomogeneity makes image segmentation more difficult. This paper proposes a new bias field model (KPBFE) based on pre-fitting bias field estimation to deal with intensity inhomogeneity in the image segmentation. A new function for computing bias field $b$ is proposed with K-means++ clustering algorithm. The computation method of clustering center points takes into account the average value of the grayscale within the contour of the bias field estimation and outside the contour. Meanwhile, we use a variational level set function with arctan function and a new adaptive function $\tau$ to limit the magnitude of the data driver term. Since the computation of bias field estimation is completed before the iteration and there is no convolution operation in the process, the computing speed of the proposed model is greatly increased. Experiments results show that our model can effectively segment the images with intensity inhomogeneity. Compared with some classical models, our method also has faster computation speed, higher segmentation accuracy and better initial robustness.

Introduction

Image segmentation is an important part in the field of image processing and computer vision. It is widely used in many fields, including industrial automation production, medical image analysis, intelligent monitoring and traffic management. In the past decades, various image segmentation methods were proposed (Wu and Kang, 2021, Mousavirad et al., 2020, Sarkar et al., 2016, Çataloluk and Çelebi, 2018, Li et al., 2006, Gamino-Sánchez et al., 2018, Demirhan and Güler, 2011, Jin and Weng, 2019, Cai et al., 2018, Chan et al., 2018, Banerjee and Maji, 2019). Active contour model (ACM) is one of the most representative image segmentation methods since Kass et al. (2011) proposed. Active contour model can obtain subpixel level accuracy of the target boundary and provide a smooth closed contour as the segmentation result (Miao et al., 2018). Therefore, it is suitable for scenes requiring high segmentation accuracy, such as detecting the shape and size of lesions, locating damaged areas of industrial machines, automatic segmentation and identification of vehicle license plates, etc (Pham et al., 2016, Comelli et al., 2019). In addition, the introduction of level set method (Li et al., 2010) promotes the development of active contour model. Nowadays it is also a research hotspot in image segmentation. Traditional active contour models can be classified as: edge-based models (Li et al., 2010, Li et al., 2016, Liu et al., 2017, Zhou et al., 2015) and region-based models (Wang et al., 2009, Zhang et al., 2010, Chan and Vese, 1977, Li et al., 2008).

The most widely used active contour model is region-based models. There are usually some interferences in image segmentation, such as uneven illumination, noise, shadow and intensity inhomogeneity. These disturbances bring great difficulties to image segmentation. Traditional region-based models are not ideal enough to guarantee segmentation accuracy and speed simultaneously for intensity inhomogeneity image. Another kind of region-based segmentation method is called bias field model. The bias correction (BC) model (Li et al., 2011) and the LSACM model (Zhang et al., 2016) are two classical bias field models. The BC model has strong robustness to the initial contour. Nevertheless, too much convolution computation in iteration results in slow segmentation speed. The LSACM model has a good segmentation effect for images with intensity inhomogeneity. However, it still fails to solve the problems of initial contour sensitivity and slow segmentation speed. The CLSM model proposed by Zhou et al. (Zhou et al., 2017) in 2017 allows flexible initializations and can segment images effectively with both noise and intensity inhomogeneity. Its defect is a kernel function leads to long segmentation time. Wang et al. proposed the EFI model (Wang et al., 2018) to deal with images with intensities inhomogeneous and estimate their bias fields with a high performance. However, the convolution computation in this model still increases the iteration time. Table 1 briefly summarizes the characteristics of the above four bias field models.

In this paper, we propose a new active contour model (KPBFE) to compute the estimation of bias field and overcome the shortcomings of the BC model and the LSACM model. Firstly, we use K-means++ clustering algorithm to cluster multivariable data and take the clustering center point as bias field $b$. The computation method of clustering center points takes the average value of the grayscale within and outside the contour into account. The function of clustering center can be regarded as a special case of the CV model. Then we minimize the energy function. We optimize a variational level set function with different data driven term. A new adaptive function $\tau$ is used to limit the magnitude of the data driver term. Finally, we compute gradient flow function and complete the computation. The computation of bias field value $b$ is completed before the iteration. There is no convolution operation in the computing process, so the computation speed is greatly increased. Experiments results show that our model has faster segmentation speed and better robustness on the images with intensity inhomogeneity.

The rest of this paper is organized as follows. We introduce the research background in Section 2. The proposed model is shown in Section 3. Section 4 is experiments. Section 5 includes several discussions. The conclusion is in Section 6.