Description: Wavelets are mathematical functions that allow the decomposition of a signal or function into different scale components. Unlike traditional transformations, such as the Fourier transform, which break down a signal into sine and cosine frequencies, wavelets provide a more flexible and localized representation. This means they can capture both high-frequency information (fine details) and low-frequency information (general trends) of a signal, making them particularly useful in the analysis of non-stationary data. Wavelets are characterized by their ability to adapt to different scales and positions, allowing for a more accurate representation of the signal’s features. In computer graphics and computer vision, wavelets are used for image compression, signal processing, and feature detection, among other applications. Their versatility and efficiency have made them a fundamental tool in data analysis and in enhancing visual quality across various domains.
History: The concept of wavelets was developed in the 1980s, although its roots trace back to earlier work in signal analysis. The wavelet transform was formally introduced by mathematician Yves Meyer in 1986, who laid the theoretical foundations for its use. Since then, wavelet theory has evolved and expanded, with significant contributions from researchers like Ingrid Daubechies, who developed orthogonal wavelets that are widely used in practice. Over the years, wavelets have found applications in various fields, from image compression to real-time data analysis.
Uses: Wavelets are used in a variety of applications, including image compression (such as in JPEG 2000), signal processing, noise reduction, and feature detection in images. They are also useful in time series analysis and in representing data at multiple scales, allowing for better interpretation of complex phenomena. In computer vision, wavelets assist in tasks such as image segmentation and pattern recognition.
Examples: A practical example of wavelet use is in image compression, where they are used to reduce file sizes while maintaining visual quality. JPEG 2000, an image compression standard, employs wavelet transforms for efficient compression. Another example is in edge detection in images, where wavelets can identify abrupt changes in pixel intensity, facilitating object segmentation in a scene.
