To cite this version:Jean-Philip Royer, Nadège Thirion-Moreau, Pierre Comon. Computing the polyadic decomposition of nonnegative third order tensors. Signal Processing, Elsevier, 2011, 91 (9) AbstractComputing the minimal polyadic decomposition (also often referred to as canonical decomposition, or sometimes Parafac) amounts to finding the global minimum of a coercive polynomial in many variables. In the case of arrays with nonnegative entries, the low-rank approximation problem is well posed. In addition, due to the large dimension of the problem, the decomposition can be rather efficiently calculated with the help of preconditioned nonlinear conjugate gradient algorithms, as subsequently shown, if equipped with an algebraic calculation of the globally optimal stepsize in low dimension. Other algorithms are also studied (gradient and quasi-Newton approaches) for comparisons. Two versions of each algorithm are considered: the Enhanced Line Search version (ELS), and the backtracking version alternating with ELS. Computer simulations are provided and demonstrate the good behavior of these algorithms dedicated to nonnegative arrays, compared to others put forward in the literature. Finally, applications in the context of data analysis illustrate various algorithms. The main advantage of the suggested approach is to explicitly take into account the nonnegative nature of the loading matrices in the problem parameterization, instead of enforcing positive entries by projection. According to the experiments we have run, such an approach also happens to be more robust with respect to possible modeling errors.

This article describes the set of photogrammetric tools developed for the monitoring of Mediterranean red coral Corallium rubrum populations. The description encompasses the full processing chain: from the image acquisition to the information extraction and data interpretation. The methods applied take advantage of existing tools and new, innovative and specific developments in order to acquire data on relevant ecological information concerning the structure and functioning of a red coral population. The tools presented here are based on: (i) automatic orientation using coded quadrats; (ii) use of non-photorealistic rendering (NPR) and 3D skeletonization techniques; (iii) computation of distances between colonies from a same site; and (iv) the use of a plenoptic approach in an underwater environment.

<p><strong>Abstract.</strong> A key challenge in cultural heritage (CH) sites visualization is to provide models and tools that effectively integrate the content of a CH data with domain-specific knowledge so that the users can query, interpret and consume the visualized information. Moreover, it is important that the intelligent visualization systems are interoperable in the semantic web environment and thus, capable of establishing a methodology to acquire, integrate, analyze, generate and share numeric contents and associated knowledge in human and machine-readable Web. In this paper, we present a model, a methodology and a software Web-tools that support the coupling of the 2D/3D Web representation with the knowledge graph database of <i>Xlendi</i> shipwreck. The Web visualization tools and the knowledge-based techniques are married into a photogrammetry driven ontological model while at the same time, user-friendly web tools for querying and semantic consumption of the shipwreck information are introduced.</p>

This chapter introduces several state of the art techniques that could help to make deep underwater archaeological photogrammetric surveys easier, faster, more accurate, and to provide more visually appealing representations in 2D and 3D for both experts and public. We detail how the 3D captured data is analysed and then represented using ontologies, and how this facilitates interdisciplinary interpretation and cooperation. Towards more automation, we present a new method that adopts a deep learning approach for the detection and the recognition of objects of interest, amphorae for example. In order to provide more readable, direct and clearer illustrations, we describe several techniques that generate different styles of sketches out of orthophotos developed using neural networks. In the same direction, we present the Non-Photorealistic Rendering (NPR) technique, which converts a 3D model into a more readable 2D representation that is more useful to communicate and simplifies the identification of objects of interest. Regarding public dissemination, we demonstrate how recent advances in virtual reality to provide an accurate, high resolution, amusing and appropriate visualization tool that offers the public the possibility to 'visit' an unreachable archaeological site. Finally, we conclude by introducing the plenoptic approach, a new promising technology that can change the future of the photogrammetry by making it easier and less time consuming and that allows a user to create a 3D model using only one camera shot. Here, we introduce the concepts, the developing process, and some results, which we obtained with underwater imaging.