Abstract

We present an approach to solving the problem of “physical match,” i.e., reconnecting back together broken or ripped pieces of material. Our method involves correlating the jagged edges of the pieces, using a modified version of the longest common subsequence algorithm.

Highlights

  • The problem of “physical match” spans many different applications, from whimsical puzzle solving [9, 19, 20], to 3-D archeology [17, 14, 7, 6], to the forensic sciences [15, 16]

  • We use a nonlinear least squares (LSQ) solver to find the triad of values which minimizes the sum of the square distances between our remaining longest common subsequence (LCS) matches

  • Starting from the LCS center, the algorithm proceeds in both directions along the seam, by adding the closest pixels from the two pieces, as long as their distance is 0.4 of the average mean distance

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Summary

Introduction

The problem of “physical match” spans many different applications, from whimsical (jigsaw) puzzle solving [9, 19, 20], to 3-D archeology [17, 14, 7, 6] (sometimes utilizing a priori shape knowledge, or rotational symmetry), to the forensic sciences [15, 16]. In the present paper we restrict ourselves to the 2-D problem, and the particular aspects of one-dimensional border which one can take advantage of, for this flat case, but not resorting to the rich information of 3-D surface-to-surface matching. We are making none of these assumptions, and matching via shape alone. Some approach this problem with gross polygon approximations of the pieces [1], whereas others solve with a multiscale of resolutions [3]. Our method is based on correlating the changes of direction along the edges of the pieces. Our analysis is for generic materials, and we concentrate more on the algorithms involved

Background and problem
Modeling random-shaped pieces and breaking them
Image scanning and edge pixel ordering
Edge slope calculations
Filtering out straight lines
Relative orientation
Matching edges
Cyclic correlation
Sewing edges
Filtering random matches
Moving and rotating
Micro-stitching
Goodness of fit
More than two pieces
System parameter values
Optimal values
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