A Comprehensive Survey on Two and Three-Dimensional Fourier Shape Descriptors: Biomedical Applications

Medical image analysis plays an essential role in the diagnosis, management, and treatment of various diseases. Today, due to the capacity for fast and accurate access to high-quality images of the anatomical structures using modern medical imaging scanners, the opportunity to study and assess the shape with a wide range of medical applications is provided. One of the efficient and conscientious representation techniques to model and analyze the shape data is Fourier-based descriptors. Different studies addressed these descriptors with various clinical applications and contributed a lot in this area. This review gives a comprehensive overview of the theories and methodologies of the Fourier descriptors approaches involving 2D contours and 3D surfaces for shape modeling and analysis. This article collected studies that have employed Fourier-based descriptors in different organs with a wide range of clinical applications and placed them in five different groups, including "Segmentation," "Classification," "Modeling," "Shape analysis," and "others" from 1994 to 2021. To clarify several aspects of the research, we have summarized both the opportunities and challenges of the considered studies. In addition, we have introduced three novel subject evaluation metrics to analyze the influence and concentration of the collected studies on these five various topics. These metrics suggest a new insight into different researches usage and impact, which can be extended simply to the other works. This review is recommended for researchers working in various fields of medical image analysis using shapes containing two-dimensional contours and three-dimensional surfaces.