# Thresholding (image processing)

Original image
Example of a threshold effect used on an image

Thresholding is the simplest method of image segmentation. From a grayscale image, thresholding can be used to create binary images (Shapiro, et al. 2001:83).

## Definition

The simplest thresholding methods replace in an image with a black pixel if the image intensity ${\displaystyle I_{i,j}}$ is less than some fixed constant T (that is, ${\displaystyle I_{i,j}), or a white pixel if the image intensity is greater than that constant. In the example image on the right, this results in the dark tree becoming completely black, and the white snow becoming completely white.

## Categorizing thresholding Methods

To make thresholding completely automated, it is necessary for the computer to automatically select the threshold T. Sezgin and Sankur (2004) categorize thresholding methods into the following six groups based on the information the algorithm manipulates (Sezgin et al., 2004):

• Histogram shape-based methods, where, for example, the peaks, valleys and curvatures of the smoothed histogram are analyzed
• Clustering-based methods, where the gray-level samples are clustered in two parts as background and foreground (object), or alternately are modeled as a mixture of two Gaussians
• Entropy-based methods result in algorithms that use the entropy of the foreground and background regions, the cross-entropy between the original and binarized image, etc.[1]
• Object Attribute-based methods search a measure of similarity between the gray-level and the binarized images, such as fuzzy shape similarity, edge coincidence, etc.
• Spatial methods [that] use higher-order probability distribution and/or correlation between pixels
• Local methods adapt the threshold value on each pixel to the local image characteristics. In these methods, a different T is selected for each pixel in the image.

## Multiband thresholding

Colour images can also be thresholded. One approach is to designate a separate threshold for each of the RGB components of the image and then combine them with an AND operation. This reflects the way the camera works and how the data is stored in the computer, but it does not correspond to the way that people recognize colour. Therefore, the HSL and HSV colour models are more often used; note that since hue is a circular quantity it requires circular thresholding. It is also possible to use the CMYK colour model (Pham et al., 2007).

## Probability distributions

Histogram shape-based methods in particular, but also many other thresholding algorithms, make certain assumptions about the image intensity probability distribution. The most common thresholding methods work on bimodal distributions, but algorithms have also been developed for unimodal distributions, multimodal distributions, and circular distributions.

## Citations

• Pham N, Morrison A, Schwock J et al. (2007). Quantitative image analysis of immunohistochemical stains using a CMYK color model. Diagn Pathol. 2:8.
• Shapiro, Linda G. & Stockman, George C. (2002). "Computer Vision". Prentice Hall. ISBN 0-13-030796-3
• Mehmet Sezgin and Bulent Sankur, Survey over image thresholding techniques and quantitative performance evaluation, Journal of Electronic Imaging 13(1), 146–165 (January 2004). doi:10.1117/1.1631315

## References and further reading

• Gonzalez, Rafael C. & Woods, Richard E. (2002). Thresholding. In Digital Image Processing, pp. 595–611. Pearson Education. ISBN 81-7808-629-8
• M. Luessi, M. Eichmann, G. M. Schuster, and A. K. Katsaggelos, Framework for efficient optimal multilevel image thresholding, Journal of Electronic Imaging, vol. 18, pp. 013004+, 2009. doi:10.1117/1.3073891
• Y.K. Lai, P.L. Rosin, Efficient Circular Thresholding, IEEE Trans. on Image Processing 23(3), pp. 992–1001 (2014). doi:10.1109/TIP.2013.2297014