• Christoph Blankenburg University of Applied Sciences Darmstadt, Germany CNRS, CRAN, UMR 7039, 54516 Vand{\oe}uvre-l\`es-Nancy, France Universit{\'e} de Lorraine, CRAN, UMR 7039, 2 avenue de la For{\^e}t de Haye
  • Christian Daul CNRS, CRAN, UMR 7039, 54516 Vand{\oe}uvre-l\`es-Nancy, France Universit{\'e} de Lorraine, CRAN, UMR 7039, 2 avenue de la For{\^e}t de Haye
  • Joachim Ohser University of Applied Sciences Darmstadt



discrete geometry, integral of torsion, skeleton line


Curvature and torsion of three-dimensional curves are important quantities in fields like material science or biomedical engineering. Torsion has an exact definition in the continuous domain. However, in the discrete case most of the existing torsion evaluation methods lead to inaccurate values, especially for low resolution data. In this contribution we use the discrete points of space curves to determine the Fourier series coefficients which allow for representing the underlying continuous curve with Cesàro’s mean. This representation of the curve suits for the estimation of curvature and torsion values with their classical continuous definition. In comparison with the literature, one major advantage of this approach is that no a priori knowledge about the shape of the cyclic curve parts approximating the discrete curves is required. Synthetic data, i.e. curves with known curvature and torsion, are used to quantify the inherent algorithm accuracy for torsion and curvature estimation. The algorithm is also tested on tomographic data of fiber structures and open foams, where discrete curves are extracted from the pore spaces.


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How to Cite

Blankenburg, C., Daul, C., & Ohser, J. (2016). ESTIMATING TORSION OF DIGITAL CURVES USING 3D IMAGE ANALYSIS. Image Analysis and Stereology, 35(2), 81–91.



Original Research Paper