In computer vision

Computer vision

Computer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...

 and image processing

Image processing

In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...

, Otsu's method is used to automatically perform histogram shape-based image thresholding

Thresholding (image processing)

Thresholding is the simplest method of image segmentation. From a grayscale image, thresholding can be used to create binary images Thresholding is the simplest method of image segmentation. From a grayscale image, thresholding can be used to create binary images Thresholding is the simplest method...

, or, the reduction of a graylevel image to a binary image. The algorithm assumes that
the image to be thresholded contains two classes of pixels or bi-modal histogram (e.g. foreground and background) then calculates the optimum threshold separating those two classes so that their combined spread (intra-class variance

Variance

In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...

) is minimal.
The extension of the original method to multi-level thresholding is referred to as the Multi Otsu method.
Otsu's method is named after .

Method

In Otsu's method we exhaustively search for the threshold that minimizes the
intra-class variance, defined as a weighted sum of variances of the two
classes:


Weights are the probabilities of the two classes separated
by a threshold and variances of these classes.

Otsu shows that minimizing the intra-class variance is the same as maximizing
inter-class variance:


which is expressed in terms of class probabilities and
class means .

The class probability is computed from the histogram as :

while the class mean is:

where is the value at the center of the th histogram bin.
Similarly, you can compute and on the right-hand side
of the histogram for bins greater than .

The class probabilities and class means can be computed iteratively. This idea
yields an effective algorithm.

Algorithm

1. Compute histogram and probabilities of each intensity level
2. Set up initial and
3. Step through all possible thresholds maximum intensity
   1. Update and
   2. Compute
4. Desired threshold corresponds to the maximum

External links

• Lecture notes on thresholding - covers the Otsu method.
• A plugin for ImageJ using Otsu's method to do the threshold.
• A full explanation of Otsu's method with a worked example and Java implementation.
• Implementation of Otsu's method in ITK
  Insight Segmentation and Registration Toolkit
  ITK is a cross-platform, open-source application development framework widely used for the development of image segmentation and image registration programs. Segmentation is the process of identifying and classifying data found in a digitally sampled representation. Typically the sampled...
  
  
• Otsu Thresholding in C# A straightforward C# implementation with explanation.