INTEGRAL PROJECTIONS
An integral projection is a one-dimensional pattern, or signal, obtained through the sum of a given set of pixels along a given direction. Horizontal and vertical integral projections are most commonly used, although they can be applied on any direction.
Let i(x,y)
be an image (greyscale or color) and R(i) a
region in it (i.e., a set of pixels in i(x,y)),
the Vertical Integral Projection of R(i),
denoted by PVR(i), is a
discrete function:
PVR(i) : {ymin,
..., ymax} ® R
Defined by:
PVR(i) (y) = Mean(i(x,y));
" (x,y) Î R(i)
The Horizontal
Integral Projection of R(i), denoted by
PHR(i), is defined in a
similar way:
PHR(i) : {xmin,
..., xmax} ® R
PHR(i) (x)
= Mean(i(x,y)), " (x,y) Î R(i)
The Integral
Projection Along an Arbitrary Angle a,
denoted by PaR(i), is
defined as the vertical integral projection of R(i),
after applying to the image a rotation of a.
Sample image, with vertical
(right) and horizontal (down) integral projections.
Projection Models
Rapid Alignment of Integral Projections
Facultad de Informática. Despacho 2.34
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