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We present visual methods for the analysis and comparison of the results of curved fibre reconstruction algorithms, i.e., of algorithms extracting characteristics of curved fibres from X-ray computed tomography scans. In this work, we extend previous methods for the analysis and comparison of results of different fibre reconstruction algorithms or parametrisations to the analysis of curved fibres. We propose fibre dissimilarity measures for such curved fibres and apply these to compare multiple results to a specified reference. We further propose visualisation methods to analyse differences between multiple results quantitatively and qualitatively. In two case studies, we show that the presented methods provide valuable insights for advancing and parametrising fibre reconstruction algorithms, and support in improving their results in characterising curved fibres.
We present time-space trade-offs for computing the Euclidean minimum spanning tree of a set S of n point-sites in the plane. More precisely, we assume that S resides in a random-access memory that can only be read. The edges of the Euclidean minimum spanning tree EMST(S) have to be reported sequentially, and they cannot be accessed or modified afterwards. There is a parameter s in {1, ..., n} so that the algorithm may use O(s) cells of read-write memory (called the workspace) for its computations. Our goal is to find an algorithm that has the best possible running time for any given s between 1 and n.
We show how to compute EMST(S) in O(((n^3)/(s^2)) log s) time with O(s) cells of workspace, giving a smooth trade-off between the two best-known bounds O(n^3) for s = 1 and O(n log n) for s = n. For this, we run Kruskal's algorithm on the "relative neighborhood graph" (RNG) of S. It is a classic fact that the minimum spanning tree of RNG(S) is exactly EMST(S). To implement Kruskal's algorithm with O(s)
cells of workspace, we define s-nets, a compact representation of planar graphs. This allows us to efficiently maintain and update the components of the current minimum spanning forest as the edges are being inserted.
The historical importance of ancient manuscripts is unique since they provide information about the heritage of ancient cultures. Often texts are hidden in rolled or folded documents. Due to recent impro- vements in sensitivity and resolution, spectacular disclosures of rolled hidden texts were possible by X-ray tomography. However, revealing text on folded manuscripts is even more challenging. Manual unfolding is often too risky in view of the fragile condition of fragments, as it can lead to the total loss of the document. X-ray tomography allows for virtual unfolding and enables non-destructive access to hid- den texts. We have recently demonstrated the procedure and tested unfolding algorithms on a mockup sample. Here, we present results on unfolding ancient papyrus packages from the papyrus collection of the Musée du Louvre, among them objects folded along approximately orthogonal folding lines. In one of the packages, the first identification of a word was achieved, the Coptic word for “Lord”.