For example, contours of zero Gaussian or mean curvature on a 3-D surface are space curves invariant under similarity transforms of the surface. Intuitively, torsion is a local measure of how non-planar a space curve is. This involves sampling the contour at equal intervals and recording the 3-D coordinates of each sampled point.
Next step is to compute torsion on each smoothed space curve.
The features recovered from a TSS image for matching are the maxima and minima of its zero-crossing contours. The matching of two TSS images consists of finding the optimal horizontal shift of the extrema in one of the TSS images that would yield the best possible overlap with the extrema of the other TSS image. The left figure above shows a space curve depicting a chair with red points showing the locations of its torsion zero-crossing points during evolution, and the right figure shows the construction of its TSS image.