Minimal test patterns for connectivity preservation in parallel thinning algorithms for binary digital images

AbstractIn successive deletion stages of parallel thinning algorithms for binary digital images, one usually checks the preservation of connectivity by verifying that: (a) every removed pixel is individually deletable without modifying connectivity (well-known criteria, such as those of Rosenfeld and Yokoi, exist for that purpose); (b) every pair of 8-adjacent removed pixels is deletable without connectivity modification. In the case of the 8-connectivity for the figure (and the 4-connectivity for the background), two more patterns must be tested for connectivity preservation: an isolated triple or quadruple of mutually 8-adjacent pixels.In this paper we give a formal characterization of these patterns for testing connectivity preservation by what we call minimal non-x-deletable sets (x-MND sets), where x=4, 8 or {4,8} (the type of connectivity considered for the figure). A parallel thinning algorithm whose deletion stage cannot remove an x-MND set is guaranteed to preserve the connectivity properties of any figure. We show that an x-MND set consists in either (1) a single pixel; or (2) a pair of 8-adjacent pixels; or (3) an isolated triple or quadruple of mutually 8-adjacent pixels (for x=8 only)

An improved rotation-invariant thinning algorithm

Ahmed & Ward have recently presented an elegant, rule-based rotation-invariant thinning algorithm to produce a single-pixel wide skeleton from a binary image. We show examples where this algorithm fails on two-pixel wide lines and propose a modified method which corrects this shortcoming based on graph connectivity

Improved 3D thinning algorithms for skeleton extraction

In this study, we focused on developing a novel 3D Thinning algorithm to extract one-voxel wide skeleton from various 3D objects aiming at preserving the topological information. The 3D Thinning algorithm was testified on computer-generated and real 3D reconstructed image sets acquired from TEMT and compared with other existing 3D Thinning algorithms. It is found that the algorithm has conserved medial axes and simultaneously topologies very well, demonstrating many advantages over the existing technologies. They are versatile, rigorous, efficient and rotation invariant.<br /

Correcting curvature-density effects in the Hamilton-Jacobi skeleton

The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method

An automatic correction of Ma's thinning algorithm based on P -simple points

International audienceThe notion of P -simple points has been introduced by Bertrand to conceive parallel thinning algorithms. In 'A 3D fully parallel thinning algorithm for generating medial faces', Ma has proposed an algorithm for which there exists objects whose topology is not preserved. In this paper, we propose a new application of P -simple points: to automatically correct Ma's algorithm