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Three-dimensional surface meshes are the most common discrete representation of the exterior of a virtual shape. Extracting relevant geometric or topological features from them can simplify the way objects are looked at, help with their recognition, and facilitate description and categorization according to specific criteria. This book adopts the point of view of discrete mathematics, the aim of which is to propose discrete counterparts to concepts mathematically defined in continuous terms. It explains how standard geometric and topological notions of surfaces can be calculated and computed on a 3D surface mesh, as well as their use for shape analysis. Several applications are also detailed, demonstrating that each of them requires specific adjustments to fit with generic approaches. The book is intended not only for students, researchers and engineers in computer science and shape analysis, but also numerical geologists, anthropologists, biologists and other scientists looking for practical solutions to their shape analysis, understanding or recognition problems.

The challenges of Reproducibility and Replicability (R & R) in computer science experiments have become a focus of attention in the last decade, as efforts to adhere to good research practices have increased. However, experiments using Deep Learning (DL) remain difficult to reproduce due to the complexity of the techniques used. Challenges such as estimating poverty indicators (e.g., wealth index levels) from remote sensing imagery, requiring the use of huge volumes of data across different geographic locations, would be impossible without the use of DL technology. To test the reproducibility of DL experiments, we report a review of the reproducibility of three DL experiments which analyze visual indicators from satellite and street imagery. For each experiment, we identify the challenges found in the data sets, methods and workflows used. As a result of this assessment we propose a checklist incorporating relevant FAIR principles to screen an experiment for its reproducibility. Based on the lessons learned from this study, we recommend a set of actions aimed to improve the reproducibility of such experiments and reduce the likelihood of wasted effort. We believe that the target audience is broad, from researchers seeking to reproduce an experiment, authors reporting an experiment, or reviewers seeking to assess the work of others. Plain Language Summary This paper aims to help researchers understand the challenges of reproducing Deep Learning (DL) publications, mitigate reproducibility gaps, and make their own work more reproducible. We build on the work of others and add recommendations organized by (a) the quality of the data set (and associated metadata), (b) the DL methodology, (c) the implementation methodology, and the infrastructure used. To our knowledge, this is the first initiative of its kind to address the problem of reproducibility in remote sensing imagery and DL problems for real‐world tasks. We hope this paper lowers the barrier to entry for the DL community to improve research. Following the lifecycle mantra: reproduce!, then replicate! With the goal of improving reproducibility! Key Points We discuss the reproducibility challenges faced in research by Deep Learning approaches using Big Data We provide advice for pre‐screening papers (before experiments) to avoid poorly invested effort We present a recipe with a set of mitigation strategies to address common errors users (researchers, authors, reviewers) may encounter

PurposePancreatic cancer is the fourth cause of death by cancer worldwide. Lymph node (LN) involvement is known to be the main prognostic factor. However, lymphatic anatomy is complex and only partially characterized. The aim of the study was to study the pancreatic lymphatic system using computer-assisted anatomic dissection (CAAD) technique and also to update CAAD technique by automatizing slice alignment.MethodsWe dissected three human fetuses aged from 18 to 34 WA. 5-µm serial sections of duodeno-pancreas and spleen blocks were stained (hematoxylin–eosin, hematoxylin of Mayer and Masson trichrome), scanned, aligned and modeled in three dimensions.ResultsWe observed a rich, diffuse but not systematized lymphatic network in the peri-pancreatic region. There was an equal distribution of LNs between the cephalic and body–tail portions. The lymphatic vascularization appeared in continuity from the celiac trunk to the distal ends of its hepatic and splenic arterial branches parallel to the nerve ramifications of the celiac plexus. We also observed a continuity between the drainage of the pancreatic head and the para-aortic region posteriorly.ConclusionIn view of the wealth of peri-pancreatic LNs, the number of LNs to harvest could be increased to improve nodal staging and prognostic evaluation. Pancreatic anatomy as described does not seem to be compatible with the sentinel LN procedure in pancreatic surgery. Finally, we are now able to offer an alternative to manual alignment with a semi-automated alignment.

Background and AimsAnalysis of anatomical sections of wood provides important information for understanding the secondary growth and development of plants. This study reports on a new method for the automatic detection and characterization of cell files in wood images obtained by light microscopy. To facilitate interpretation of the results, reliability coefficients have been determined, which characterize the files, their cells and their respective measurements.MethodsHistological sections and blocks of the gymnosperms Pinus canariensis, P. nigra and Abies alba were used, together with histological sections of the angiosperm mahogany (Swietenia spp.). Samples were scanned microscopically and mosaic images were built up. After initial processing to reduce noise and enhance contrast, cells were identified using a ‘watershed’ algorithm and then cell files were built up by the successive aggregation of cells taken from progressively enlarged neighbouring regions. Cell characteristics such as thickness and size were calculated, and a method was developed to determine the reliability of the measurements relative to manual methods.Key ResultsImage analysis using this method can be performed in less than 20 s, which compares with a time of approx. 40 min to produce the same results manually. The results are accompanied by a reliability indicator that can highlight specific configurations of cells and also potentially erroneous data.ConclusionsThe method provides a fast, economical and reliable tool for the identification of cell files. The reliability indicator characterizing the files permits quick filtering of data for statistical analysis while also highlighting particular biological configurations present in the wood sections.

Metric comparison of human fossils has long relied on more or less sophisticated statistical analysis of distance and angle measurements between anatomical landmarks. Recently, geometric morphometry has enabled a more global approach to the analysis of shape differences using techniques such as the Procrustes projection and \"thin-plate splines.\"32 However, the use of these methodologies is often limited to 2D analysis of CT images or to a variable number of points extracted from 3D images.26,33-36 New techniques are now being investigated to evaluate integration of the entire 3D surface of the skull into phylogenic analysis.37-39 This process is expected to be challenging. Technical image analysis will require highly reliable automatic point extraction. Morphometric analysis will require development of computer codes to align homologous cranial structures and quantify their variations and defects in terms of a reduced number of parameters (Fig. 7, Fig. 8). Analysis of paleoanthropological statistics will require new mathematical tools to model the evolution of anatomical structures and to assist in the differentiation of intraspecies variations from interspecies variations that have significant evolutionary implication. Because of these problems, morphometric analysis of 3D CT images in a global mode, namely, the surface and internal morphology of fossils, is still out of reach. However, it should be emphasized that 3D CT imaging has already allowed comparison of skull ontogenesis between current primates,40 Neanderthal remains and Homo sapiens.41 Dissemination of knowledge to the public is an important responsibility of the scientific community. The study of human evolution lends itself well to scientific popularization, and 3D imaging technology is particularly attractive for the purpose of illustrating the main morphological changes in primates that led to modern humans. Reconstructions using 3D CT images are powerful tools for communication and education (Fig. 9).42 As this teaching tool is likely to become more popular, 3D imaging will continue to broaden its scope of application from laboratory analysis to other computer-assisted techniques such as 3D display of archeological sites, paleoclimates, extinct wildlife and the paleoenvironment of prehistoric communities. The development of imaging technology has facilitated virtual reproduction of fossil specimens using computer-assisted 3D reconstruction. Some investigators have advocated free access to the databases of CT imaging of hominid fossils.46-48 The Institute for Anthropology of the University of Vienna has made 3D CT data from 4 hominoid fossilized skull specimens available to all researchers. This universal access is beneficial to the entire paleoanthropology community but raises the issue of intellectual property rights. Until recently, imaging studies have been carried out on either cast models or, more rarely, on original specimens stored in museums or scientific institutions, located mainly in Africa in the case of the oldest specimens. Local researchers have been granted exclusive study rights within the framework of scientific partnership programs. Because there is a considerable time lag between the discovery of the fossils and the publication of the specimen, there has been a call for a \"glasnost in paleoanthropology.\"47 Gerhard Weber has suggested that funding agencies should require open access to fossils after a certain period, either in the form of images on the Web or on CD-ROM.46

We present a scalable encoding strategy for the 3D facial data in various bandwidth scenarios. The scalability, needed to cater diverse clients, is achieved through the multiresolution characteristic of JPEG2000. The disparate 3D facial data is synchronously unified by the application of data hiding wherein the 2.5D facial model is embedded in the corresponding 2D texture in the discrete wavelet transform (DWT) domain. The unified file conforms to the JPEG2000 standard and thus no novel format is introduced. The method is effective and has the potential to be applied in videosurveillance and videoconference applications.