The second derivatives of a 2D or 3D signal is claimed to be of fundamental value for image analysis, segmentation, visualization and many other tasks. But to serve this purpose, the derivative responses at each point must be converted to three features: magnitude, shape, and orientation. This paper presents a recently developed derotation algorithm for this task based on eigenvalues analysis of the Hessian matrix and spherical harmonics. Scale invariance is achieved by combining results from different scale detectors. The algorithm has been successfully implemented and applied to magnetic resonance volume data to segment string-like cerebral vessels, for which case some preliminary experimental results are presented.

Rotation-invariant operators of order 0 and 2 are used first to detect and then to enhance lines. The enhancement procedure, suitable for fingerprints, is based on suppression of line responses with an orientation that creates a mismatch with the locally dominating direction of the fingerprint. The rotation-invariant operators also serve as basis functions. By construction they are mutually orthogonal and by proper normalization they form an orthonormal set. At the origin any pattern a(r, phi ) can be expanded or at least approximated by such a set of basis functions.>

Two algorithms for visual inspection of printed-circuit boards are presented that perform width checking of conductors and insulators. The first detects the difference between the results of shrinking and connectivity-preserving shrinking (CPS). The second algorithm produces a difference between the original and the shrunk picture. This result is subject to a number of CPS-operations after which errors are easily detected. Both algorithms can be adapted to a suitable level of sensitivity to sharp corners and edge irregularities. A sequential version of CPS is also described which is well suited for hardware implementation in a pipelined structure.>