Curvature estimation in oriented patterns using curvilinear models applied to gradient vector fields

Abstract

AbstractÐCurved oriented patterns are dominated by high frequencies and exhibit zero gradients on ridges and valleys. Existing curvature estimators fail here. The characterization of curved oriented patterns based on translation invariance lacks an estimation of local curvature and yields a biased curvaturedependent confidence measure. Using parameterized curvilinear models we measure the amount of local gradient energy along the model gradient as a function of model curvature. Minimizing the residual energy yields a closed-form solution for the local curvature estimate and the corresponding confidence measure. We show that simple curvilinear models are applicable in the analysis of a wide variety of curved oriented patterns.

Curvature of n-dimensional space curves in grey-value images

“…For the smallest eigenvalue, has to be inverted, which becomes time consuming for large . In the 2-D or 3-D case analytic solutions are possible and much faster [9], [19]. For line like structures the tangent orientation is given by the "smallest" eigenvector .…”

“…In order to obtain the orientation field along a space curve embedded in a -D image we use the gradient structure tensor (GST) [3], [9], [17]- [20]. For any image , we can always compute the GST:…”

“…Isophote curvature [6]- [8] can successfully be applied to edges in 2-D and three-dimensional (3-D) grey-value images, but it fails when applied to lines (space curves) [9]. To overcome the problems associated with isophote curvature, one transforms the grey-value image into an orientation map from which the curvature can be derived after solving the discontinuity problem [1].…”

Localization of corresponding points in fingerprints by complex filtering

“…The orientation tensor field is often used to represent the global structure in a fingerprint [3,1,4]. Also when estimating curvature in oriented patterns the orientation field is used [5,6]. An original fingerprint and its estimated orientation field are shown in Figure 1 as illustration.…”

Complex Filters Applied to Fingerprint Images Detecting Prominent Symmetry Points Used for Alignment

“…The orientation tensor field is often used to represent the global structure in a fingerprint [1,3]. Also when estimating curvature in oriented patterns the orientation field is used [4,5]. An original fingerprint and its estimated orientation field are shown in Fig.…”