Thresholding (image processing)

In digital image processing, thresholding is the simplest method of segmenting images. From a grayscale image, thresholding can be used to create binary images.

Definition

The simplest thresholding methods replace each pixel in an image with a black pixel if the image intensity

I

i

,

j

{\displaystyle I_{i,j}}

is less than a fixed value called the threshold

T

{\displaystyle T}

, or a white pixel if the pixel intensity is greater than that threshold. In the example image on the right, this results in the dark tree becoming completely black, and the bright snow becoming completely white.

Automatic thresholding

While in some cases, the threshold

T

{\displaystyle T}

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. Sezgin et al 2004 categorized thresholding methods into broad groups based on the information the algorithm manipulates. Note however that such a categorization is necessarily fuzzy as some methods can fall in several categories (for example, Otsu's method can be both considered a histogram-shape and a clustering algorithm)

Histogram shape-based methods, where, for example, the peaks, valleys and curvatures of the smoothed histogram are analyzed. Note that these methods, more than others, make certain assumptions about the image intensity probability distribution (i.e., the shape of the histogram),

Clustering-based methods, where the gray-level samples are clustered in two parts as background and foreground,

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.,

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 use higher-order probability distribution and/or correlation between pixels.