Logo SATIEImage-based reconstruction consists in determining the optimal organization between the parts of an object of interest characterized by structured visual information. Such a general problem includes reconstruction of frescoes / paintings or mosaics from their fragments. It has thus straightforward applications in heritage restoration and archeology. In the case of heritage restoration, it mainly deals with the reconstruction of frescoes destroyed during earthquakes or wars, and for which having a model (picture before destruction according to documentary source) appears likely. In this context, the DAFNE challenge [Dondi et al., 2020] proposed simulated data sets for the evaluation of algorithms knowing the fresco model. In the case of applications in archeology, the problem is much more complex since there is no model and the support can be 3D (case of anastylosis, e.g. objects found during excavations or monuments). Compared to a classic “puzzle” or jigsaw problem, the targeted reconstruction presents several additional difficulties: (i) the gigantic number of pieces (fragments), (ii) the variable characteristics of the latter, whether in size or image content, (iii) the irregular shape of the pieces and the deterioration of their edges (erosion of the latter inducing discontinuities between the pieces), (iv) the presence of pieces not belonging to the puzzle, (v) the loss of some pieces preventing the complete reconstruction. the objective of this thesis is to develop approaches taking into account binary terms (or even more) to model the interactions between the fragments and to assess the relevance of their placement side by side. We will compare so-called classical approaches and learning approaches. In the first case, the problem is reformulated through a functional to be optimized, functional which potentially includes some data attachment terms (corresponding to unary terms), but also some interaction terms between the fragments (corresponding to binary terms), and possibly some terms corresponding to geometric priors such as the non-overlapping of fragments, the minimization of the area occupied by a given set of fragments. The algorithm for optimizing this functional will be defined jointly with the latter to ensure the possibility of obtaining solutions in a reasonable time. Specifically, for an optimization using graph cuts, the properties of the sub-modularity of the functional must be verified. We also may take inspiration from proposes a Mahalanobis-like distance for color images while compares five consistency measures between adjacent fragments and describes how to optimize the “best” one chosen.

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