Tb. Nguyen et Bj. Oommen, MOMENT-PRESERVING PIECEWISE-LINEAR APPROXIMATIONS OF SIGNALS AND IMAGES, IEEE transactions on pattern analysis and machine intelligence, 19(1), 1997, pp. 84-91
Approximation techniques are an important aspect of digital signal and
image processing. Many lossy signal compression procedures such as th
e Fourier transform and discrete cosine transform are based on the ide
a that a signal can be represented by a small number of transformed co
efficients which are an approximation of the original. Existing approx
imation techniques approach this problem in either a time/spatial doma
in or transform domain, but not both. This paper briefly reviews vario
us existing approximation techniques. Subsequently, we present a new s
trategy to obtain an approximation (f) over cap(x) of f(x) in such a w
ay that it is reasonably close to the original function in the domain
of the variable x, and exactly preserves some properties of the transf
ormed domain. In this particular case, the properties of the transform
ed values that are preserved are geometric moments of the original fun
ction. The proposed technique has been applied to single-variable func
tions, two-dimensional planar curves, and two-dimensional images, and
the results obtained are demonstrative.