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[[Image:Pavlovsk Railing of bridge Yellow palace Winter.jpg|thumb|250px|Original image.]][[Image:Pavlovsk Railing of bridge Yellow palace Winter bw threshold.jpg|thumb|250px|The binary image resulting from a thresholding of the original image.]]
In [[digital image processing]], '''thresholding''' is the simplest method of [[image segmentation|segmenting images]]. From a [[grayscale]] image, thresholding can be used to create [[binary image]]s.<ref>
==Definition==
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While in some cases, the threshold <math>T</math> can be selected manually by the user, there are many cases where the user wants the threshold to be automatically set by an algorithm. In those cases, the threshold should be the "best" threshold in the sense that the partition of the pixels above and below the threshold should match as closely as possible the actual partition between the two classes of objects represented by those pixels (e.g., pixels below the threshold should correspond to the background and those above to some objects of interest in the image).
Many types of automatic thresholding methods exist, the most famous and widely used being [[Otsu's method]].
* '''[[Histogram]] shape'''-based methods, where, for example, the peaks, valleys and curvatures of the smoothed histogram are analyzed.<ref>{{Cite journal |last1=Zack |first1=G W |last2=Rogers |first2=W E |last3=Latt |first3=S A |date=July 1977 |title=Automatic measurement of sister chromatid exchange frequency |journal=Journal of Histochemistry & Cytochemistry |language=en |volume=25 |issue=7 |pages=741–753 |doi=10.1177/25.7.70454 |pmid=70454 |s2cid=15339151 |doi-access=free }}</ref> Note that these methods, more than others, make certain assumptions about the image intensity probability distribution (i.e., the shape of the histogram),
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=== Global vs local thresholding ===
In most methods, the same threshold is applied to all pixels of an image. However, in some cases, it can be advantageous to apply a different threshold to different parts of the image, based on the local value of the pixels. This category of methods is called local or adaptive thresholding. They are particularly adapted to cases where images have inhomogeneous lighting, such as in the sudoku image on the right. In those cases, a neighborhood is defined and a threshold is computed for each pixel and its neighborhood. Many global thresholding methods can be adapted to work in a local way, but there are also methods developed specifically for local thresholding, such as the Niblack<ref>{{Cite book |title=An introduction to digital image processing |date=1986 |publisher=Prentice-Hall International |isbn=0-13-480600-X |oclc=1244113797 }}{{pn|date=April 2024}}</ref> or the Bernsen algorithms.
Software such as [[ImageJ]] propose a wide range of automatic threshold methods, both
=== Benefits of Local Thresholding Over Global Thresholding<ref>Zhou, Huiyu., Wu, Jiahua., Zhang, Jianguo. Digital Image Processing: Part II. United States: Ventus Publishing, 2010.{{pn|date=April 2024}}</ref> === ▼
▲=== Benefits of Local Thresholding Over Global Thresholding<ref>Zhou, Huiyu., Wu, Jiahua., Zhang, Jianguo. Digital Image Processing: Part II. United States: Ventus Publishing, 2010.{{pn}}</ref> ===
* Adaptability to Local Image Characteristics: Local thresholding can adapt to variations in illumination, contrast, and texture within different parts of the image. This adaptability helps in handling images with non-uniform lighting conditions or complex textures.
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=== Examples of Algorithms for Local Thresholding ===
* Niblack's Method:<ref>{{Cite book |first=Wayne |last=Niblack |title=An introduction to digital image processing |date=1986 |publisher=Prentice-Hall International |isbn=0-13-480600-X |oclc=1244113797
* Bernsen's Method:<ref>Chaki, Nabendu., Shaikh, Soharab Hossain., Saeed, Khalid. Exploring Image Binarization Techniques. Germany: Springer India, 2014.{{pn|date=April 2024}}</ref> Bernsen's algorithm calculates the threshold for each pixel by considering the local contrast within a neighborhood. It uses a fixed window size and is robust to noise and variations in background intensity.
* Sauvola's Method:<ref>{{cite journal |last1=Sauvola |first1=J. |last2=Pietikäinen |first2=M. |title=Adaptive document image binarization |journal=Pattern Recognition |date=February 2000 |volume=33 |issue=2 |pages=225–236 |doi=10.1016/S0031-3203(99)00055-2 |bibcode=2000PatRe..33..225S }}</ref> Sauvola's algorithm extends Niblack's method by incorporating a dynamic factor that adapts the threshold based on the local contrast and mean intensity. This adaptive factor improves the binarization results, particularly in regions with varying contrasts.
==Extensions of binary thresholding==
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==References==
{{Reflist}}
==Further reading==
*Gonzalez, Rafael C. & Woods, Richard E. (2002). Thresholding. In Digital Image Processing, pp. 595–611. Pearson Education. {{ISBN|81-7808-629-8}}
* {{cite journal |last1=Eichmann |first1=Marco |title=Framework for efficient optimal multilevel image thresholding |journal=Journal of Electronic Imaging |date=2009 |volume=18 |issue=1 |pages=
* {{cite journal |last1=Rosin |first1=Paul L. |title=Efficient Circular Thresholding |journal=IEEE Transactions on Image Processing |date=March 2014 |volume=23 |issue=3 |pages=992–1001 |doi=10.1109/TIP.2013.2297014 |pmid=24464614 |bibcode=2014ITIP...23..992Y |url=https://orca.cardiff.ac.uk/id/eprint/61181/ }}
*Scott E. Umbaugh (2018). Digital Image Processing and Analysis, pp 93–96. CRC Press. {{ISBN|978-1-4987-6602-9}}
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