Freeman chain codes - PDF document

Freeman [9] Freeman chain codes clc2 . . c, Figure 1: object is is equal considerable error many types [8]. presented more area and citing an unpublished Duda 8-connected Freeman chain coding [9] uses a 0 5 c 5 boundary point. l(a). 8-connected Freeman chain coding l(b). Freeman chain generalized chain [lo]. mid-crack chain [ll] points. Assume square with a pixel is given in I some special [ll, 121. chain codes can be determined [a], binary object. O(N). where n is the length of the chain, ci, and ciy are the x and y components of the ith chain element cj (ci,, ciy E (1, 0, -1) indicating the change of the x- and y-coordinates), and y;-1 chain element c, coordinate system. ci,, c,, and yj-1 be computed [9] computed the perimeter as the length of the chain. The formula for the perimeter is where n, chain elements no chain element horizontal connection between two boundary element indicates diagonal connection, a. improved Freeman's estimating lengths by us- ing a corner count n,, chain elements Freeman chain code by P = 0.980ne + 1.406n0 - O.O9lnC (7) where the weights were found by a least-square fitting for all straight lines with n, +no mid-crack chain used, Eq. can still cj, and cjy since more possible values i.e., cj,, ci, E (-1, -112, 0, 112, background-tc-object transi- tions can cj, and cjY perimeter, Eq. (6) fact determine without generating chain codes. n,, no and n, result. Kulpa Kulpa derived a compensation factor this factor, (6) becomes From Fig. 2(b) Kulpa's compensation factor which gave an overestimation. Gray's method was very a relative error Duda and mid- these two methods are if we 2(c). Kulpa's perimeter together with slightly larger than the with Duda's Gray's area. Kulpa's perimeter and Gray's area are both combinations do give good an example areas and perimeters are the spread large resolution (We assume area can pk- can be a polygon, object. This be multiplied a compensation a bet- ter estimation. above can be generalized as linear model as the and odd weights. Nonlinear also been developed [6]. area and ter estimators approximately a a good a bad been improved area and perimeter estima- still a large bias and Duda's ter compared Freeman's method method, but order from Kulpa's method better than the other a small may have different assump- Freeman's method boundaries are a distance compute the best result computed simultaneously. Gray's area can be a discrete Green's theo- discrete Green's [13, 141 a contour evaluates a a discrete [15], be extended 3D object. useful for perimeter esti- therefore interesting a faithful be made. made. believed that it was very difficult, and was even circular arcs. a method analyze a characterization, they (one dimensional regions each discrete characterization given value Eq. a characterization a least-square fitting. suggests a a linear linear model pixels perimeter is problem, since all having lengths, correspond alzzation. Thus, to 0 other shapes. (e.g. in medical applica- tions [I]). features from discrete binary image. can often be accurately estimated [7] proposed a systematic approach to com- puting the area and the perimeter. The method is also presented in the book of Pratt [a].