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The temporally and spatially resolved tracking of lithium intercalation and electrode degradation processes are crucial for detecting and understanding performance losses during the operation of lithium-batteries. Here, high-throughput X-ray computed tomography has enabled the identification of mechanical degradation processes in a commercial Li/MnO2 primary battery and the indirect tracking of lithium diffusion; furthermore, complementary neutron computed tomography has identified the direct lithium diffusion process and the electrode wetting by the electrolyte. Virtual electrode unrolling techniques provide a deeper view inside the electrode layers and are used to detect minor fluctuations which are difficult to observe using conventional three dimensional rendering tools. Moreover, the ‘unrolling’ provides a platform for correlating multi-modal image data which is expected to find wider application in battery science and engineering to study diverse effects e.g. electrode degradation or lithium diffusion blocking during battery cycling.
Conflicting hypotheses about the relationships among the major lineages of aculeate Hymenoptera clearly show the necessity of detailed comparative morphological studies. Using micro-computed tomography and 3D reconstructions, the skeletal musculature of the meso- and metathorax and the first and second abdominal segment in Apoidea are described. Females of Sceliphron destillatorium, Sphex (Fernaldina) lucae (both Sphecidae), and Ampulex compressa (Ampulicidae) were examined. The morphological terminology provided by the Hymenoptera Anatomy Ontology is used. Up to 42 muscles were found. The three species differ in certain numerical and structural aspects. Ampulicidae differs significantly from Sphecidae in the metathorax and the anterior abdomen. The metapleural apodeme and paracoxal ridge are weakly developed in Ampulicidae, which affect some muscular structures. Furthermore, the muscles that insert on the coxae and trochanters are broader and longer in Ampulicidae. A conspicuous characteristic of Sphecidae is the absence of the metaphragma. Overall, we identified four hitherto unrecognized muscles. Our work suggests additional investigations on structures discussed in this paper.
We present visual methods for the analysis and comparison of the results of curved fibre reconstruction algorithms, i.e., of algorithms extracting characteristics of curved fibres from X-ray computed tomography scans. In this work, we extend previous methods for the analysis and comparison of results of different fibre reconstruction algorithms or parametrisations to the analysis of curved fibres. We propose fibre dissimilarity measures for such curved fibres and apply these to compare multiple results to a specified reference. We further propose visualisation methods to analyse differences between multiple results quantitatively and qualitatively. In two case studies, we show that the presented methods provide valuable insights for advancing and parametrising fibre reconstruction algorithms, and support in improving their results in characterising curved fibres.
Motivation: The ever-rising volume of patients, high maintenance cost of operating rooms and time consuming analysis of surgical skills are fundamental problems that hamper the practical training of the next generation of surgeons. The hospitals prefer to keep the surgeons busy in real operations over training young surgeons for obvious economic reasons. One fundamental need in surgical training is the reduction of the time needed by the senior surgeon to review the endoscopic procedures performed by the young surgeon while minimizing the subjective bias in evaluation. The unprecedented performance of deep learning ushers the new age of data-driven automatic analysis of surgical skills.
Method: Deep learning is capable of efficiently analyzing thousands of hours of laparoscopic video footage to provide an objective assessment of surgical skills. However, the traditional end-to-end setting of deep learning (video in, skill assessment out) is not explainable. Our strategy is to utilize the surgical process modeling framework to divide the surgical process into understandable components. This provides the opportunity to employ deep learning for superior yet automatic detection and evaluation of several aspects of laparoscopic cholecystectomy such as surgical tool and phase detection.
We employ ZIBNet for the detection of surgical tool presence. ZIBNet employs pre-processing based on tool usage imbalance, a transfer learned 50-layer residual network (ResNet-50) and temporal smoothing. To encode the temporal evolution of tool usage (over the entire video sequence) that relates to the surgical phases, Long Short Term Memory (LSTM) units are employed with long-term dependency.
Dataset: We used CHOLEC 80 dataset that consists of 80 videos of laparoscopic cholecystectomy performed by 13 surgeons, divided equally for training and testing. In these videos, up to three different tools (among 7 types of tools) can be present in a frame.
Results: The mean average precision of the detection of all tools is 93.5 ranging between 86.8 and 99.3, a significant improvement (p <0.01) over the previous state-of-the-art. We observed that less frequent tools like Scissors, Irrigator, Specimen Bag etc. are more related to phase transitions. The overall precision (recall) of the detection of all surgical phases is 79.6 (81.3).
Conclusion: While this is not the end goal for surgical skill analysis, the development of such a technological platform is essential toward a data-driven objective understanding of surgical skills. In future, we plan to investigate surgeon-in-the-loop analysis and feedback for surgical skill analysis.
We present an automated method for extrapolating missing
regions in label data of the skull in an anatomically plausible manner. The ultimate goal is to design patient-specic cranial implants for correcting large, arbitrarily shaped defects of the skull that can, for example, result from trauma of the head. Our approach utilizes a 3D statistical shape model (SSM) of the skull and a 2D generative adversarial network (GAN) that is trained in an unsupervised fashion from samples of healthy patients alone. By tting the SSM to given input labels containing the skull defect, a First approximation of the healthy state of the patient is obtained. The GAN is then applied to further correct and smooth the output of the SSM in an anatomically plausible manner. Finally, the defect region is extracted using morphological operations and subtraction between the extrapolated healthy state of the patient and the defective input labels. The method is trained and evaluated based on data from the MICCAI 2020 AutoImplant challenge. It produces state-of-the art results on regularly
shaped cut-outs that were present in the training and testing data of the challenge. Furthermore, due to unsupervised nature of the approach, the method generalizes well to previously unseen defects of varying shapes that were only present in the hidden test dataset.
We propose generalizations of the T²-statistics of Hotelling and the Bhattacharayya distance for data taking values in Lie groups.
A key feature of the derived measures is that they are compatible with the group structure even for manifolds that do not admit any bi-invariant metric.
This property, e.g., assures analysis that does not depend on the reference shape, thus, preventing bias due to arbitrary choices thereof.
Furthermore, the generalizations agree with the common definitions for the special case of flat vector spaces guaranteeing consistency.
Employing a permutation test setup, we further obtain nonparametric, two-sample testing procedures that themselves are bi-invariant and consistent.
We validate our method in group tests revealing significant differences in hippocampal shape between individuals with mild cognitive impairment and normal controls.
This study’s objective was the generation of a standardized geometry of the healthy nasal cavity.
An average geometry of the healthy nasal cavity was generated using a statistical shape model based on 25 symptom-free subjects. Airflow within the average geometry and these geometries was calculated using fluid simulations. Integral measures of the nasal resistance, wall shear stresses (WSS) and velocities were calculated as well as cross-sectional areas (CSA). Furthermore, individual WSS and static pressure distributions were mapped onto the average geometry.
The average geometry featured an overall more regular shape that resulted in less resistance, reduced wall shear stresses and velocities compared to the median of the 25 geometries. Spatial distributions of WSS and pressure of average geometry agreed well compared to the average distributions of all individual geometries. The minimal CSA of the average geometry was larger than the median of all individual geometries (83.4 vs. 74.7 mm²).
The airflow observed within the average geometry of the healthy nasal cavity did not equal the average airflow of the individual geometries. While differences observed for integral measures were notable, the calculated values for the average geometry lay within the distributions of the individual parameters. Spatially resolved parameters differed less prominently.
In most vertebrates the embryonic cartilaginous skeleton is replaced by bone during development. During this process, cartilage cells (chondrocytes) mineralize the extracellular matrix and undergo apoptosis, giving way to bone cells (osteocytes). In contrast, sharks and rays (elasmobranchs) have cartilaginous skeletons throughout life, where only the surface mineralizes, forming a layer of tiles (tesserae). Elasmobranch chondrocytes, unlike those of other vertebrates, survive cartilage mineralization and are maintained alive in spaces (lacunae) within tesserae. However, the function(s) of the chondrocytes in the mineralized tissue remain unknown. Applying a custom analysis workflow to high-resolution synchrotron microCT scans of tesserae, we characterize the morphologies and arrangements of stingray chondrocyte lacunae, using lacunar morphology as a proxy for chondrocyte morphology. We show that the cell density is comparable in unmineralized and mineralized tissue from our study species and that cells maintain the similar volume even when they have been incorporated into tesserae. This discovery supports previous hypotheses that elasmobranch chondrocytes, unlike those of other taxa, do not proliferate, hypertrophy or undergo apoptosis during mineralization. Tessera lacunae show zonal variation in their shapes—being flatter further from and more spherical closer to the unmineralized cartilage matrix and larger in the center of tesserae— and show pronounced organization into parallel layers and strong orientation toward neighboring tesserae. Tesserae also exhibit local variation in lacunar density, with the density considerably higher near pores passing through the tesseral layer, suggesting pores and cells interact (e.g. that pores contain a nutrient source). We hypothesize that the different lacunar types reflect the stages of the tesserae formation process, while also representing local variation in tissue architecture and cell function. Lacunae are linked by small passages (canaliculi) in the matrix to form elongate series at the tesseral periphery and tight clusters in the center of tesserae, creating a rich connectivity among cells. The network arrangement and the shape variation of chondrocytes in tesserae indicate that cells may interact within and between tesserae and manage mineralization differently from chondrocytes in other vertebrates, perhaps performing analogous roles to osteocytes in bone.
In most vertebrates the embryonic cartilaginous skeleton is replaced by bone during development. During this process, cartilage cells (chondrocytes) mineralize the extracellular matrix and undergo apoptosis, giving way to bone cells (osteocytes). In contrast, sharks and rays (elasmobranchs) have cartilaginous skeletons throughout life, where only the surface mineralizes, forming a layer of tiles (tesserae). Elasmobranch chondrocytes, unlike those of other vertebrates, survive cartilage mineralization and are maintained alive in spaces (lacunae) within tesserae. However, the function(s) of the chondrocytes in the mineralized tissue remain unknown. Applying a custom analysis workflow to high-resolution synchrotron microCT scans of tesserae, we characterize the morphologies and arrangements of stingray chondrocyte lacunae, using lacunar morphology as a proxy for chondrocyte morphology. We show that the cell density is comparable in unmineralized and mineralized tissue from our study species and that cells maintain the similar volume even when they have been incorporated into tesserae. This discovery supports previous hypotheses that elasmobranch chondrocytes, unlike those of other taxa, do not proliferate, hypertrophy or undergo apoptosis during mineralization. Tessera lacunae show zonal variation in their shapes—being flatter further from and more spherical closer to the unmineralized cartilage matrix and larger in the center of tesserae— and show pronounced organization into parallel layers and strong orientation toward neighboring tesserae. Tesserae also exhibit local variation in lacunar density, with the density considerably higher near pores passing through the tesseral layer, suggesting pores and cells interact (e.g. that pores contain a nutrient source). We hypothesize that the different lacunar types reflect the stages of the tesserae formation process, while also representing local variation in tissue architecture and cell function. Lacunae are linked by small passages (canaliculi) in the matrix to form elongate series at the tesseral periphery and tight clusters in the center of tesserae, creating a rich connectivity among cells. The network arrangement and the shape variation of chondrocytes in tesserae indicate that cells may interact within and between tesserae and manage mineralization differently from chondrocytes in other vertebrates, perhaps performing analogous roles to osteocytes in bone.
Phage display biopanning with Illumina next-generation sequencing (NGS) is applied to reveal insights into peptide-based adhesion domains for polypropylene (PP). One biopanning round followed by NGS selects robust PP-binding peptides that are not evident by Sanger sequencing. NGS provides a significant statistical base that enables motif analysis, statistics on positional residue depletion/enrichment, and data analysis to suppress false-positive sequences from amplification bias. The selected sequences are employed as water-based primers for PP?metal adhesion to condition PP surfaces and increase adhesive strength by 100\% relative to nonprimed PP.
The images of D’Arcy Wentworth Thompson’s book “On Growth and Form” got an iconic status and became influential for biometrics and other mathematical approaches to organismic form. In particular, this is true for those of the chapter on the theory of transformation, which even has an impact on art and humanities. Based on his approach, Thompson formulated far-reaching conclusions with a partly anti-Darwinian stance. Here, we use the example of Thompson’s transformation of crab carapaces to test to what degree the transformation of grids, landmarks, and shapes result in congruent images. For comparison, we applied the same series of tests to digitized carapaces of real crabs. Both approaches show similar results. Only the simple transformations show a reasonable form of congruence. In particular, the transformations to majoid spider crabs reveal a complicated transformation of grids with partly crossing lines. By contrast, the carapace of the lithodid species is relatively easily created despite the fact that it is no brachyuran, but evolved a spider crab-like shape convergently from a hermit crab ancestor.
Surgical tool segmentation in endoscopic videos is an important component of computer assisted interventions systems. Recent success of image-based solutions using fully-supervised deep learning approaches can be attributed to the collection of big labeled datasets. However, the annotation of a big dataset of real videos can be prohibitively expensive and time consuming. Computer simulations could alleviate the manual labeling problem, however, models trained on simulated data do not generalize to real data. This work proposes a consistency-based framework for joint learning of simulated and real (unlabeled) endoscopic data to bridge this performance generalization issue. Empirical results on two data sets (15 videos of the Cholec80 and EndoVis'15 dataset) highlight the effectiveness of the proposed Endo-Sim2Real method for instrument segmentation. We compare the segmentation of the proposed approach with state-of-the-art solutions and show that our method improves segmentation both in terms of quality and quantity.
We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall’s shape space. Using the derived expressions,
we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude over common,
nonlinear constrained approaches. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example
application we have chosen 3D shapes of knee bones, reconstructed from image
data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.
More and more diseases have been found to be strongly correlated with disturbances in the microbiome constitution, e.g., obesity, diabetes, or some cancer types. Thanks to modern high-throughput omics technologies, it becomes possible to directly analyze human microbiome and its influence on the health status. Microbial communities are monitored over long periods of time and the associations between their members are explored. These relationships can be described by a time-evolving graph. In order to understand responses of the microbial community members to a distinct range of perturbations such as antibiotics exposure or diseases and general dynamical properties, the time-evolving graph of the human microbial communities has to be analyzed. This becomes especially challenging due to dozens of complex interactions among microbes and metastable dynamics. The key to solving this problem is the representation of the time-evolving graphs as fixed-length feature vectors preserving the original dynamics. We propose a method for learning the embedding of the time-evolving graph that is based on the spectral analysis of transfer operators and graph kernels. We demonstrate that our method can capture temporary changes in the time-evolving graph on both synthetic data and real-world data. Our experiments demonstrate the efficacy of the method. Furthermore, we show that our method can be applied to human microbiome data to study dynamic processes.
A prerequisite for many analysis tasks in modern comparative biology is the segmentation of 3-dimensional (3D) images of the specimens being investigated (e.g. from microCT data). Depending on the specific imaging technique that was used to acquire the images and on the image resolution, different segmentation tools will be required. While some standard tools exist that can often be applied for specific subtasks, building whole processing pipelines solely from standard tools is often difficult. Some tasks may even necessitate the implementation of manual interaction tools to achieve a quality that is sufficient for the subsequent analysis. In this work, we present a pipeline of segmentation tools that can be used for the semi-automatic segmentation and quantitative analysis of voids in tissue (i.e. internal structural porosity). We use this pipeline to analyze lacuno-canalicular networks in stingray tesserae from 3D images acquired with synchrotron microCT.
* The first step of this processing pipeline, the segmentation of the tesserae, was performed using standard marker-based watershed segmentation. The efficient processing of the next two steps, that is, the segmentation of all lacunae spaces belonging to a specific tessera and the separation of these spaces into individual lacunae required modern, recently developed tools.
* For proofreading, we developed a graph-based interactive method that allowed us to quickly split lacunae that were accidentally merged, and to merge lacunae that were wrongly split.
* Finally, the tesserae and their corresponding lacunae were subdivided into anatomical regions of interest (structural wedges) using a semi- manual approach.
A prerequisite for many analysis tasks in modern comparative biology is the segmentation of 3-dimensional (3D) images of the specimens being investigated (e.g. from microCT data). Depending on the specific imaging technique that was used to acquire the images and on the image resolution, different segmentation tools will be required. While some standard tools exist that can often be applied for specific subtasks, building whole processing pipelines solely from standard tools is often difficult. Some tasks may even necessitate the implementation of manual interaction tools to achieve a quality that is sufficient for the subsequent analysis. In this work, we present a pipeline of segmentation tools that can be used for the semi-automatic segmentation and quantitative analysis of voids in tissue (i.e. internal structural porosity). We use this pipeline to analyze lacuno-canalicular networks in stingray tesserae from 3D images acquired with synchrotron microCT.
* The first step of this processing pipeline, the segmentation of the tesserae, was performed using standard marker-based watershed segmentation. The efficient processing of the next two steps, that is, the segmentation of all lacunae spaces belonging to a specific tessera and the separation of these spaces into individual lacunae required modern, recently developed tools.
* For proofreading, we developed a graph-based interactive method that allowed us to quickly split lacunae that were accidentally merged, and to merge lacunae that were wrongly split.
* Finally, the tesserae and their corresponding lacunae were subdivided into anatomical regions of interest (structural wedges) using a semi- manual approach.
An advantageous property of mesh-based geometric morphometrics (GM) towards landmark-based approaches, is the possibility of precisely examining highly irregular shapes and highly topographic surfaces. In case of spherical-harmonics-based GM the main requirement is a completely closed mesh surface, which often is not given, especially when dealing with natural objects. Here we present a methodological workflow to prepare 3D segmentations containing large cavity openings for the conduction of spherical-harmonics-based GM. This will be exemplified with a case study on claws of hermit crabs (Paguroidea, Decapoda, Crustacea), whereby joint openings – between manus and “movable finger” – typify the large-cavity-opening problem. We found a methodology including an ambient-occlusion-based segmentation algorithm leading to results precise and suitable to study the inter- and intraspecific differences in shape of hermit crab claws. Statistical analyses showed a significant separation between all examined diogenid and pagurid claws, whereas the separation between all left and right claws did not show significance. Additionally, the procedure offers other benefits. It is easy to reproduce and creates sparse variance in the data, closures integrate smoothly into the total structures and the algorithm saves a significant amount of time.
An advantageous property of mesh-based geometric morphometrics (GM) towards landmark-based approaches, is the possibility of precisely examining highly irregular shapes and highly topographic surfaces. In case of spherical-harmonics-based GM the main requirement is a completely closed mesh surface, which often is not given, especially when dealing with natural objects. Here we present a methodological workflow to prepare 3D segmentations containing large cavity openings for the conduction of spherical-harmonics-based GM. This will be exemplified with a case study on claws of hermit crabs (Paguroidea, Decapoda, Crustacea), whereby joint openings – between manus and “movable finger” – typify the large-cavity-opening problem. We found a methodology including an ambient-occlusion-based segmentation algorithm leading to results precise and suitable to study the inter- and intraspecific differences in shape of hermit crab claws. Statistical analyses showed a significant separation between all examined diogenid and pagurid claws, whereas the separation between all left and right claws did not show significance. Additionally, the procedure offers other benefits. It is easy to reproduce and creates sparse variance in the data, closures integrate smoothly into the total structures and the algorithm saves a significant amount of time.
In order to better understand the relationship between shape of the nasal cavity and to find objective classification for breathing obstruction, a population of 25 cases of healthy nasal cavity and 27 cases with diagnosed nasal airway obstruction (NAO) was examined for correlations between morphological, clinical and CFD parameters. For this purpose a workflow was implemented in Tcl to perform automatic measurements of morphological parameters of nasal cavity surfaces in Amira, which has as output a table with all estimated values. Furthermore, the statistical analysis was designed using Python to find the most probable subset of parameters that are predictors of nasal cavity pathology and consisted of correlation analysis, the selection of the best possible subset of parameters that could be used as predictors of clinically stated pathology of the nasal cavity by a logistic regression classifier. As a result, 10 most promising parameters were identified: mean distance between the two isthmuses, left isthmus contour, area ratio between the two isthmuses, left isthmus height, height ratio between the two isthmuses, left isthmus width, right isthmus width, right isthmus hydraulic diameter, mean distance of septal curvature between the septum enclosing walls of the nasal cavity, velocities volume average by expiration. As it turns out, most parameters refer to the isthmus region. This was to be expected since this region
plays an important role in the airflow system of the nasal cavity.
Intrinsic and parametric regression models are of high interest for the statistical analysis of manifold-valued data such as images and shapes. The standard linear ansatz has been generalized to geodesic regression on manifolds making it possible to analyze dependencies of random variables that spread along generalized straight lines. Nevertheless, in some scenarios, the evolution of the data cannot be modeled adequately by a geodesic.
We present a framework for nonlinear regression on manifolds by considering Riemannian splines, whose segments are Bézier curves, as trajectories.
Unlike variational formulations that require time-discretization, we take a constructive approach that provides efficient and exact evaluation by virtue of the generalized de Casteljau algorithm.
We validate our method in experiments on the reconstruction of periodic motion of the mitral valve as well as the analysis of femoral shape changes during the course of osteoarthritis, endorsing Bézier spline regression as an effective and flexible tool for manifold-valued regression.
Quantitative PA tomography of high resolution 3-D images: experimental validation in tissue phantoms
(2020)
Quantitative photoacoustic tomography aims recover the spatial distribution of absolute chromophore concentrations and their ratios from deep tissue, high-resolution images. In this study, a model-based inversion scheme based on a Monte-Carlo light transport model is experimentally validated on 3-D multispectral images of a tissue phantom acquired using an all-optical scanner with a planar detection geometry. A calibrated absorber allowed scaling of the measured data during the inversion, while an acoustic correction method was employed to compensate the effects of limited view detection. Chromophore- and fluence-dependent step sizes and Adam optimization were implemented to achieve rapid convergence. High resolution 3-D maps of absolute concentrations and their ratios were recovered with high accuracy. Potential applications of this method include quantitative functional and molecular photoacoustic tomography of deep tissue in preclinical and clinical studies.
We present a software-assisted workflow for the alignment and matching of filamentous structures across a 3D stack of serial images. This is achieved by combining automatic methods, visual validation, and interactive correction. After an initial alignment, the user can continuously improve the result by interactively correcting landmarks or matches of filaments. Supported by a visual quality assessment of regions that have been already inspected, this allows a trade-off between quality and manual labor. The software tool was developed to investigate cell division by quantitative 3D analysis of microtubules (MTs) in both mitotic and meiotic spindles. For this, each spindle is cut into a series of semi-thick physical sections, of which electron tomograms are acquired. The serial tomograms are then stitched and non-rigidly aligned to allow tracing and connecting of MTs across tomogram boundaries. In practice, automatic stitching alone provides only an incomplete solution, because large physical distortions and a low signal-to-noise ratio often cause experimental difficulties. To derive 3D models of spindles despite the problems related to sample preparation and subsequent data collection, semi-automatic validation and correction is required to remove stitching mistakes. However, due to the large number of MTs in spindles (up to 30k) and their resulting dense spatial arrangement, a naive inspection of each MT is too time consuming. Furthermore, an interactive visualization of the full image stack is hampered by the size of the data (up to 100 GB). Here, we present a specialized, interactive, semi-automatic solution that considers all requirements for large-scale stitching of filamentous structures in serial-section image stacks. The key to our solution is a careful design of the visualization and interaction tools for each processing step to guarantee real-time response, and an optimized workflow that efficiently guides the user through datasets.
Automatic recognition of surgical phases is an important component for developing an intra-operative context-aware system. Prior work in this area focuses on recognizing short-term tool usage patterns within surgical phases. However, the difference between intra- and inter-phase tool usage patterns has not been investigated for automatic phase recognition. We developed a Recurrent Neural Network (RNN), in particular a state-preserving Long Short Term Memory (LSTM) architecture to utilize the long-term evolution of tool usage within complete surgical procedures. For fully automatic tool presence detection from surgical video frames, a Convolutional Neural Network (CNN) based architecture namely ZIBNet is employed. Our proposed approach outperformed EndoNet by 8.1% on overall precision for phase detection tasks and 12.5% on meanAP for tool recognition tasks.
We present time-space trade-offs for computing the Euclidean minimum spanning tree of a set S of n point-sites in the plane. More precisely, we assume that S resides in a random-access memory that can only be read. The edges of the Euclidean minimum spanning tree EMST(S) have to be reported sequentially, and they cannot be accessed or modified afterwards. There is a parameter s in {1, ..., n} so that the algorithm may use O(s) cells of read-write memory (called the workspace) for its computations. Our goal is to find an algorithm that has the best possible running time for any given s between 1 and n.
We show how to compute EMST(S) in O(((n^3)/(s^2)) log s) time with O(s) cells of workspace, giving a smooth trade-off between the two best-known bounds O(n^3) for s = 1 and O(n log n) for s = n. For this, we run Kruskal's algorithm on the "relative neighborhood graph" (RNG) of S. It is a classic fact that the minimum spanning tree of RNG(S) is exactly EMST(S). To implement Kruskal's algorithm with O(s)
cells of workspace, we define s-nets, a compact representation of planar graphs. This allows us to efficiently maintain and update the components of the current minimum spanning forest as the edges are being inserted.
We present a transductive learning approach for morphometric osteophyte grading based on geometric deep learning. We formulate the grading task as semi-supervised node classification problem on a graph embedded in shape space. To account for the high-dimensionality and non-Euclidean structure of shape space we employ a combination of an intrinsic dimension reduction together with a graph convolutional neural network. We demonstrate the performance of our derived classifier in comparisons to an alternative extrinsic approach.
The historical importance of ancient manuscripts is unique since they provide information about the heritage of ancient cultures. Often texts are hidden in rolled or folded documents. Due to recent impro- vements in sensitivity and resolution, spectacular disclosures of rolled hidden texts were possible by X-ray tomography. However, revealing text on folded manuscripts is even more challenging. Manual unfolding is often too risky in view of the fragile condition of fragments, as it can lead to the total loss of the document. X-ray tomography allows for virtual unfolding and enables non-destructive access to hid- den texts. We have recently demonstrated the procedure and tested unfolding algorithms on a mockup sample. Here, we present results on unfolding ancient papyrus packages from the papyrus collection of the Musée du Louvre, among them objects folded along approximately orthogonal folding lines. In one of the packages, the first identification of a word was achieved, the Coptic word for “Lord”.