On the accuracy of point curvature estimators in a discrete environment

Boundary-based corner detection using eigenvalues of covariance matrices

“…Many discrete algorithms have been developed to compute the curvature of boundary points lying on a digital curve (Worring and Smeulders, 1993;Fairney and Fairney, 1994;Tsai and Chen, 1994). Tsai (1997) measures the curvature by using neural networks to recognize the included angles at boundary points.…”

Towards computerized typology and classification of ceramics

“…͗mԽA i ͘ ͗mԽm͘ (11) are small. Clearly, m vanishes if m (s) is indeed in the space spanned by the prototypes, and it equals one (which is its maximal value) if m (s) is orthogonal to all the prototypes.…”

“…The extraction of the curvature function from numerical data poses a few problems which are discussed in the literature (see [11,30]). The main problem stems from the fact that the curvature involves the second derivative of the contour, and numerical differentiation introduces large errors.…”

“…Together with the computation of the coordinates and the extrapolation parameters, we computed the 'quality factors' m defined in equation (11). For each period its mean value is less than 0.25 which supports the use of two prototypes in the analysis.…”

K-Cosine Corner Detection

“…Liu and Srinath evaluated the curvature by convolving the edge direction function with the first derivative of a Gaussian function at each pixel [16]. Fairney et al experimented with several different measures of digital curvature and found them to be unreliable in the presence of noise [5]. Tsai and Chen computed directly the curvature by measuring the first-and second-order derivatives of the continuous functions [33].…”