# Active Contours in the Complex Domain for Salient Object Detection
## 1 Introduction
The model deals well with the inhomogeneity issue, but wastes time in iteration. [PERSON] [38] constructed a local binary fitting model by introducing a local kernel function into the Chan and Vese (CV) model. The model utilizes spatial connections among pixels and extracts local information using a Gaussian function. However, it fails when improper initialization is performed. A new level set introduced by [PERSON] [39] successfully reduces reinitialization and avoids numerical error. [PERSON] [40] suggests using local fitting energy to extract local image information. Local binary fitting decreases the dissimilarity of the image. [PERSON] [41] introduced an active contour model with selective local or global segmentation (ACSLGS). The ACSLGS model combines the ideas of the Chan-Vese and geodesic active contour (GAC) models and utilizes statistical information. A region-based function is used to control the direction of evolution. The signed pressure function creates pressure to shrink the contour when it is outside the object or expand it when the contour is inside the object, but this model fails on intensity inhomogeneity images. The previous algorithms discussed have severe drawbacks. The novel active contours in the complex domain for salient object detection (ACCD_SOD) eliminates the drawbacks of existing state-of-the-art models, including initialization and parameter setting. * An important consideration is that the proposed algorithm can assist as a smooth-edge detector that draws strong edges and helps to preserve edges. This is beneficial in the implementation of the edge sensitivity contour method. * Initialization is a critical step that significantly influences the final performance. In a complex domain, the initialization process is seamlessly carried out, which is most suitable for salient object detection. * In practice, the reinitialization process can be quite complex and costly and have side effects. Our algorithm eliminates reinitialization. * The proposed ACCD_SOD algorithm has been applied to both simulated and real images and outputs precise results. In particular, it appears to perform robustly when there are weak boundaries. * The complex force function has a relatively extensive capture range and accommodates small concavities. * The parameter setting process plays an important role in the ultimate result of ACMs and it can produce a great performance improvement if the proper parameters are given to an active contour model. Our model uses a fixed parameter and it shows good performance when compared to state-of-the-art models. Salience detection can automatically discover salient regions, but it relies on post-processing for accurate boundary detection. The active contour model performs well at localizing boundaries, but it suffers from poor initialization. It requires extra effort to discover the significant regions in the image. The proposed method integrates the salience discovery unit into the active model and uses an active contour model in the complex domain for salient object detection, which eliminates the reinitialization of classic active contour models. We propose a novel active contour model in the complex domain for salient object detection to address the limitations of the existing models. Our proposed model improves detection accuracy with low computational cost. The main contributions of the proposed algorithm are as follows:  
* First, we convert the image to the complex domain. The complex transformation provides salience cues. Salience detection serves as the initialization for our active contour model, which quickly converges to the edge structure of the input image. * We then use a low-pass filter in the complex domain to discover the objects of interest, which serves as the initialization step and eliminates reinitialization. * Subsequently, we define a force function in the complex domain, resulting in a complex-force function, which is used to distinguish the object from the background for the active contour.