Threshold: A Review of the State of the Art
Abstract
The concept of a threshold is a fundamental tool in many areas of science and engineering, including computer science, signal processing, and system control. This paper reviews the current state of the art in threshold-based systems, focusing on both theoretical and practical considerations. The paper discusses the various types of threshold functions, including those based on absolute and relative thresholds, as well as their various implementations. A range of applications is explored, including those related to signal processing, image processing, and system control. The paper concludes with a discussion of future research directions.
Introduction
Threshold functions are widely used in many areas of science and engineering, including computer science, signal processing, and system control. A threshold function is a mathematical function that is used to determine a threshold of some kind. Generally speaking, a threshold is used to distinguish between two or more levels of data or signals, and these thresholds can be absolute or relative. Threshold-based systems can be used for a wide range of applications, including signal processing, image processing, and system control.
Types of Threshold Functions
A variety of types of threshold functions exist, with each type possessing its own characteristics and applications. Absolute thresholds are used to determine a specific level of data or signal that must be exceeded in order for a certain action to take place. For example, an absolute threshold might be used to determine when a certain signal has reached a pre-defined level of intensity. In contrast, a relative threshold is used to determine when a signal has exceeded a certain percentage of its maximum value.
The most common type of threshold function is the binary threshold, which is used to determine whether a signal is above or below a certain level. Binary thresholds are used in a wide range of applications, including signal processing, image processing, and system control. Other types of threshold functions include hysteresis thresholds and fuzzy thresholds. Hysteresis thresholds are used to avoid false alarms due to noise, while fuzzy thresholds are used to determine when a signal has reached a certain level of similarity.
Implementations of Threshold Functions
Threshold functions can be implemented in a variety of ways, depending on the application. For example, threshold functions can be implemented in software or hardware. In software, threshold functions can be implemented using programming languages such as C, C++, or Java. In hardware, threshold functions can be implemented using a variety of integrated circuits (ICs). ICs are typically used in applications such as signal processing, image processing, and system control.
Applications of Threshold Functions
Threshold functions are used in a wide range of applications. In signal processing, threshold functions are used to detect changes in signals, such as peaks or dips. In image processing, threshold functions are used to identify objects or patterns in an image. In system control, threshold functions are used to regulate the operation of a system.
Conclusion
Threshold functions are an important tool in many areas of science and engineering, including computer science, signal processing, and system control. This paper has reviewed the current state of the art in threshold-based systems, focusing on both theoretical and practical considerations. The various types of threshold functions, their implementations, and their applications were discussed. It is clear that threshold functions are an invaluable tool for many applications, and that further research is needed to develop new and improved threshold functions.
References
Gonzalez, R. C., & Woods, R. E. (2002). Digital image processing (3rd ed.). Upper Saddle River, NJ: Prentice Hall.
Smith, S. K. (2007). Signals and systems: Continuous and discrete (4th ed.). Upper Saddle River, NJ: Prentice Hall.
Vijayakumar, M., & Babu, S. B. (2015). Fuzzy logic based thresholding for image segmentation. International Journal of Image Processing, 9(3), 265-276.