Measuring the Information Content of Fracture Lines

Abstract

Reassembling unknown broken objects from a large collection of fragments is a common problem in archaeology and other fields. Computer tools have recently been developed, by the authors and by others, which try to help by identifying pairs of fragments with matching outline shapes. Those tools have been successfully tested on small collections of fragments; here we address the question of whether they can be expected to work also for practical instances of the problem (10 3 to 10 5 fragments). To that end, we describe here a method to measure the average amount of information contained in the shape of a fracture line of given length. This parameter tells us how many false matches we can expect to find for it among a given set of fragments. In particular, the numbers we obtained for ceramic fragments indicate that fragment outline comparison should give useful results even for large instances of the problem.

Archaeological Fragment Reconstruction Using Curve-Matching

“…However, this will not always be the case when the problem is generalized (Figure 2b) [4]. Methods that do not employ boundary segmentation, must consider all possible combinations of sub-boundaries which is a space of complexity search is manageable [7,8,9,10]. From those, only the best matches are kept and matched again at recursively finer scales.…”

“…In a series of papers [7,8,9,10] that also deal with puzzles com-posed of natural materials Leitao and Stolfi perform curve matching using an elastic model somewhat similar to the technique in Sebastian et al [17], but as mentioned above, they utilize a multi-scale technique which begins at a very coarse scale and is then iteratively refined on only the best matches. As a result, "dense" curve-matching is only performed a small number of times, striking a balance between accuracy and computational cost.…”

“…These adjacency candidates can then be evaluated by stan-dard curve-matching techniques. In order to reduce complexity, we employ a multi-scale technique similar to the one described in [7,8,9,10]. This technique is described in Section 3.…”

Analyzing and simulating fracture patterns of theran wall paintings

“…Leitão and Stolfi [2005] studied the information content in fracture contours with the goal of understanding whether reconstruction of artifacts with many fragments is theoretically possible. McBride and Kimia [2003] studied types of edges and joints in fractured frescoes, observing that the vast majority of junctions appear where three fragments join in a "T" junction (70-89%) and that discernable corners in fragment contours usually align in pairwise fragment matches (77-78% have at least one corner aligned).…”

HINDSITE: A user-interactive framework for fragment assembly

“…First, pairs of fragments are examined with the goal of finding those that were most likely to be adjacent in the original structure (local solutions). Clues are found primarily in the similarity of the shape of their outlines, but also potentially in the similarity of their texture, color, markings, etc., which are then translated into a pairwise affinity measure as well as a pairwise pose relation [3,17,25,24,7,8,9,10,21,22,23].…”