Solving Small-Piece Jigsaw Puzzles by Growing Consensus

In this paper, we present a novel computational puzzle solver for square-piece image jigsaw puzzles with no prior information such as piece orientation, anchor pieces or resulting dimension of the puzzle. By "piece" we mean a square dxd block of pixels, where we investigate pieces as small as 7x7 pixels. To reconstruct such challenging puzzles, we aim to search for piece configurations which maximize the size of consensus (i.e. grid or loop) configurations which represent a geometric consensus or agreement among pieces. Pieces are considered for addition to the existing assemblies if these pieces increase the size of the consensus configurations. In contrast to previous puzzle solvers which goal for assemblies maximizing compatibility measures between all pairs of pieces and thus depend heavily on the pairwise compatibility measure used, our new approach reduces the dependency on the pairwise compatibility measures which become increasingly uninformative at small scales and instead exploits geometric agreement among pieces. Our contribution also includes an improved pairwise compatibility measure which exploits directional derivative information along adjoining boundaries of the pieces. For the challenging unknown orientation piece puzzles where the size of pieces is small, we reduce assembly error by up to 75% compared with previous algorithms for standard datasets.