Content
Image moments ( English image moments ) in computer vision , image processing and related areas are some partial average weighted (moment) intensities of image pixels , or a function of such moments. As a rule, moments are selected that have useful properties or interpretations.
In the most general sense, the moment of a function is a certain scalar quantity that characterizes this function and can be used to articulate its important properties. From a mathematical point of view, a set of moments is in a sense a “projection” of a function onto a polynomial basis. It is similar to the Fourier transform , which is the projection of a function onto a basis of harmonic functions [1] .
Image moments are useful for describing objects after segmentation . Simple image properties that can be found using moments include area (or total intensity), geometric center, and orientation information. In addition to them, moments of higher orders, for example, the asymmetry coefficient and the excess coefficient [1], have long been used in mathematical statistics.
Calculation
Central moments of the digitized image with sizes M × N can be calculated as sums of the following form [2] :
Where:
- p and q are the orders of the central moment m corresponding to the image coordinates.
- Is the initial moment of the first order in the coordinate i .
- Is the initial moment of the first order in the coordinate j .
- Is the initial moment of the first order in the coordinate i .
See also
- Random moments
Notes
- ↑ 1 2 Flusser, Suk, Zitová, 2009 .
- ↑ Pouli, Reinhard, Cunningham , Image Moments and Moment Invariants, p. 74.
Sources
- J. Flusser, T. Suk, B. Zitová. What are moments? // Moments and Moment Invariants in Pattern Recognition. - John Wiley & Sons Ltd, 2009. - P. 6. - ISBN 978-0-470-69987-4 .
- T. Pouli, E. Reinhard, D. Cunningham. Image Statistics in Visual Computing. - CRC Press, 2014 .-- P. 35. - ISBN 978-1-4665-3982-2 .