September 2013
Beginner
756 pages
19h 35m
English
Content preview from Introduction to Digital Image Processing
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SPATIAL MOMENTS 575
(17.3-3)
where, with reference to Figure 12.1-1, the scaled coordinates are
(17.3-4a)
.(17.3-4b)
The origin of the coordinate system is the upper left corner of the image. This for-
mulation results in moments that are extremely scale dependent; the ratio of second-
order (m + n = 2) to zero-order (m = n = 0) moments can vary by several orders of
magnitude (25). The spatial moments can be restricted in range by spatially scaling
the image array over a unit range in each dimension. The (m, n)th scaled spatial geo-
metric moment is then defined as
.(17.3-5)
Clearly,
.(17.3-6)
It is instructive to explicitly identify the lower-order spatial moments. The zero-
order moment
(17.3-7)
is the sum of the pixel values of an image. It is called the ...
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