thresholding

Thresholding is a processing operation that assigns values based on a comparison with a threshold. It is widely used to simplify data, reduce noise, or categorize values. In statistics, it can set values below or above a cutoff to fixed values; in image and signal processing, it often performs segmentation or denoising.

In image processing, thresholding transforms a grayscale image into a binary image by comparing pixel values against a chosen threshold. Global thresholding uses a single threshold; adaptive (local) thresholding computes thresholds from local neighborhoods to handle illumination variation; multilevel thresholding uses several thresholds to partition into multiple classes. Otsu's method is a popular automatic threshold selection technique that maximizes between-class variance.

In signal processing and data analysis, thresholding includes hard thresholding (setting coefficients below threshold to zero) and soft thresholding (shrinking coefficients toward zero). It is used in denoising, sparse representation, and wavelet transforms. In statistics, thresholding supports variable selection and regularization; L1 minimization leads to soft-thresholding as a proximal operator.

Applications and limitations: thresholding is used in OCR, medical imaging, and texture analysis. The choice of threshold is data-dependent and sensitive to noise; improper thresholds can erase detail or misclassify signals. Variants such as hysteresis thresholding or probabilistic thresholding address some edge cases and provide smoother transitions in certain tasks.