Measurement of the lengths of digitized curved lines

A comparative evaluation of length estimators of digital curves

“…This method was originally proposed by Ellis et al in [4]. We present here both a linear time algorithm and a multigrid convergence proof of such an estimator.…”

Quantitative perimeter and area measurements of digital images

“…Mendelbrot (1977) and others (Rigaut et al, 1984) have noted that the perimeter of a digitized region often grows exponentially as the digitalization becomes finer, whereas the area tends towards a finite limit. Consequently, area estimators are generally more stable than perimeter estimators, as noted by several researchers (Freeman, 1978;Ellis et al, 1979). In this paper, we discuss aspects of data extraction, interactive devices for manual tracings, and the relationship between the two-dimensional area and its perimeter length to three-dimensional features.…”

Laplace–Beltrami Operator on Digital Surfaces

“…4), which has been used for a long time [20,40]. Normal vectors are estimated using the estimator presented in [11,41], which has the multigrid convergence property.…”

“…In a classical interpolating triangular mesh, a good approximation of the underlying smooth structure area is simply given by triangle areas whereas for digital surfaces naive measures (such as the quadrangular face area for 2D surface in 3D) give poor approximations. Although multigrid-convergent estimators of object global volume and area/perimeter have existed for a long time [20,40], local measure estimators (length of a 1-cell, area of a 2-cell, etc) have seen advances only in the past ten years. Parameter-free tangent and normal estimation along 2D digital curves were established by Lachaud et al [36,62], using properties of maximal digital straight segments.…”