Multi-Dimensional Medial Geometry: Formulation, Computation, and Applications

Medial axis is a classical shape descriptor. It is a piece of geometry that lies in the middle of the original shape. Compared to the original shape representation, the medial axis is always one dimension lower and it carries many intrinsic shape properties explicitly. Therefore, it is widely used in a large amount of applications in various fields. However, medial axis is unstable to the boundary noise, often referred to as its instability. A small amount of change on the object boundary can cause a dramatic change in the medial axis. To tackle this problem, a significance measure is often associated with the medial axis, so that medial points with small significance are removed and only the stable part remains. In addition to this problem, many applications prefer even lower dimensional medial forms, e.g., shape centers of 2D shapes, and medial curves of 3D shapes. Unfortunately, good significance measures and good definitions of lower dimensional medial forms are still lacking. In this dissertation, we extended Blum\u27s grassfire burning to the medial axis in both 2D and 3D to define a significance measure as a distance function on the medial axis. We show that this distance function is well behaved and it has nice properties. In 2D, we also define a shape center based on this distance function. We then devise an iterative algorithm to compute the distance function and the shape center. We demonstrate usefulness of this distance function and shape center in various applications. Finally we point out the direction for future research based on this dissertation

Midfrontal theta transcranial alternating current stimulation modulates behavioural adjustment after error execution

Cognitive control during conflict monitoring, error processing, and post-error adjustment appear to be associated with the occurrence of midfrontal theta (MFϴ). While this association is supported by correlational EEG studies, much less is known about the possible causal link between MFϴ and error and conflict processing. In the present study, we aimed to explore the role of band-specific effects in modulating the error system during a conflict resolution. In turn, we delivered transcranial alternating current stimulation (tACS) at different frequency bands (delta δ, theta θ, alpha α, beta β, gamma γ) and sham stimulation over the medial frontal cortex (MFC) in 36 healthy participants performing a modified version of the Flanker task. Task performance and reports about the sensations (e.g. visual flickering, cutaneous burning) induced by the different frequency bands, were also recorded. We found that online θ-tACS increased the response speed to congruent stimuli after error execution with respect to sham stimulation. Importantly, the accuracy following the errors did not decrease because of speed-accuracy trade off. Moreover, tACS evoked visual and somatosensory sensations were significantly stronger at α-tACS and β-tACS compared to other frequencies. Our findings suggest that theta activity plays a causative role in modulating behavioural adjustments during perceptual choices in a stimulus-response conflict task. © 2018 Federation of European Neuroscience Societies and John Wiley & Sons Lt

Medial Axis Approximation and Regularization

Medial axis is a classical shape descriptor. Among many good properties, medial axis is thin, centered in the shape, and topology preserving. Therefore, it is constantly sought after by researchers and practitioners in their respective domains. However, two barriers remain that hinder wide adoption of medial axis. First, exact computation of medial axis is very difficult. Hence, in practice medial axis is approximated discretely. Though abundant approximation methods exist, they are either limited in scalability, insufficient in theoretical soundness, or susceptible to numerical issues. Second, medial axis is easily disturbed by small noises on its defining shape. A majority of current works define a significance measure to prune noises on medial axis. Among them, local measures are widely available due to their efficiency, but can be either too aggressive or conservative. While global measures outperform local ones in differentiating noises from features, they are rarely well-defined or efficient to compute. In this dissertation, we attempt to address these issues with sound, robust and efficient solutions. In Chapter 2, we propose a novel medial axis approximation called voxel core. We show voxel core is topologically and geometrically convergent to the true medial axis. We then describe a straightforward implementation as a result of our simple definition. In a variety of experiments, our method is shown to be efficient and robust in delivering topological promises on a wide range of shapes. In Chapter 3, we present Erosion Thickness (ET) to regularize instability. ET is the first global measure in 3D that is well-defined and efficient to compute. To demonstrate its usefulness, we utilize ET to generate a family of shape revealing and topology preserving skeletons. Finally, we point out future directions, and potential applications of our works in real world problems

Quantification of the pore size distribution of soils:assessment of existing software using tomographic and synthetic 3D images

The pore size distribution (PSD) of the void space is widely used to predict a range of processes in soils. Recent advances in X-ray computed tomography (CT) now afford novel ways to obtain exact data on pore geometry, which has stimulated the development of algorithms to estimate the pore size distribution from 3D data sets. To date there is however no clear consensus on how PSDs should be estimated, and in what form PSDs are best presented. In this article, we first review the theoretical principles shared by the various methods for PSD estimation. Then we select methods that are widely adopted in soil science and geoscience, and we use a robust statistical method to compare their application to synthetic image samples, for which analytical solutions of PSDs are available, and X-ray CT images of soil samples selected from different treatments to obtain wide ranging PSDs. Results indicate that, when applied to the synthetic images, all methods presenting PSDs as pore volume per class size (i.e., Avizo, CTAnalyser, BoneJ, Quantim4, and DTM), perform well. Among them, the methods based on Maximum Inscribed Balls (Bone J, CTAnalyser, Quantim4) also produce similar PSDs for the soil samples, whereas the Delaunay Triangulation Method (DTM) produces larger estimates of the pore volume occupied by small pores, and Avizo yields larger estimates of the pore volume occupied by large pores. By contrast, the methods that calculate PSDs as object population fraction per volume class (Avizo, 3DMA, DFS-FIJI) perform inconsistently on the synthetic images and do not appear well suited to handle the more complex geometries of soils. It is anticipated that the extensive evaluation of method performance carried out in this study, together with the recommendations reached, will be useful to the porous media community to make more informed choices relative to suitable PSD estimation methods, and will help improve current practice, which is often ad hoc and heuristic

Five new species and three new subspecies of Erebidae and Noctuidae (Insecta, Lepidoptera) from Northwestern North America, with notes on Chytolita Grote (Erebidae) and Hydraecia Guenée (Noctuidae)

This is the publisher’s final pdf. The published article is copyrighted by Pensoft Publishers and can be found at: http://www.pensoft.net/journals/zookeys/.Several taxonomic issues in the moth families Erebidae and Noctuidae are addressed for Northwestern North America. Drasteria parallela Crabo & Mustelin and Cycnia oregonensis tristis Crabo in the Erebidae and Eudryas brevipennis bonneville Shepard & Crabo, Resapamea diluvius Crabo, Resapamea angelika Crabo, Resapamea mammuthus Crabo, Fishia nigrescens Hammond & Crabo, and Xestia perquiritata orca Crabo & Hammond in the Noctuidae are described as new. The following new synonyms are proposed: Chytolita petrealis Grote with Herminea morbidalis Guenee; Gortyna columbia Barnes & Benjamin and Gortyna ximena Barnes & Benjamin with Gortyna obliqua Harvey; and Hydroecia pallescens Smith with Hydroecia medialis Smith. The type locality of Gortyna intermedia Barnes & Benjamin is restricted to Lundbreck, Municipality of Crowsnest Pass, Alberta, Canada

Flashlight Search Medial Axis: A Pixel-Free Pore-Network Extraction Algorithm

Pore-network models (PNMs) have become an important tool in the study of fluid flow in porous media over the last few decades, and the accuracy of their results highly depends on the extraction of pore networks. Traditional methods of pore-network extraction are based on pixels and require images with high quality. Here, a pixel-free method called the flashlight search medial axis (FSMA) algorithm is proposed for pore-network extraction in a continuous space. The search domain in a two-dimensional space is a line, whereas a surface domain is searched in a three-dimensional scenario. Thus, the FSMA algorithm follows the dimensionality reduction idea; the medial axis can be identified using only a few points instead of calculating every point in the void space. In this way, computational complexity of this method is greatly reduced compared to that of traditional pixel-based extraction methods, thus enabling large-scale pore-network extraction. Based on cases featuring two- and three-dimensional porous media, the FSMA algorithm performs well regardless of the topological structure of the pore network or the positions of the pore and throat centers. This algorithm can also be used to examine both closed- and open-boundary cases. Finally, the FSMA algorithm can search dead-end pores, which is of great significance in the study of multiphase flow in porous media

The use of histological examination methods to distinguish between the burnt remains of human and non-human bones

Distinguishing between burnt human and non-human bone fragments using macroscopic methods has proved challenging and it was seen in the literature review that the previous research did not all come to the same conclusions. The aim of the research was to determine if, using histological methods, it was possible to distinguish between burned human and nonhuman bone fragments. A literature review was compiled to provide an overview of the anatomy of bones, morphological characteristics of bone, general bone histology, a comparison between human and non-human bones and the effect of temperature on bones. Bones of five different species (human, baboon, wildebeest, pig and cow) were burned in a muffle furnace for twenty minutes at either 600ᵒC or 800ᵒC. Following the burning procedure, thin ground bone sections of the burned and unburned bone specimens were prepared for microscopic analysis and the minimum canal diameter, maximum canal diameter, minimum Haversian system diameter, maximum Haversian system diameter, area of canal, and area of the Haversian system were measured. A comparative analysis was then done across species and temperature. A total of 523 osteons in unburned bone and 147 in the burned bone samples were analysed. ANOVA testing found overall significance (p < 0.0001) for all parameters measured, which suggests that temperature does affect the size of microstructures. Most parameter sizes increased with an increase in temperature. A greater increase was seen at 600 degrees than 800 degrees. Qualitatively, carbonation within the burned bone, made the measurement of parameters difficult in some samples. Human bone can easily be differentiated from pig, cow or wildebeest bone due to no or very few osteons present. Pig bone consisted almost entirely of plexiform bone, while the cow and wildebeest presented with only a few osteons in some parts of the bone. Human and baboon bone appeared similar on a microscopic level. The study revealed that temperature did not, in general, hamper the ability to differentiate between burned human and non-human bone, but it did impact on the number of measurable data points for each parameter

Extraction of physically-realistic pore network properties from three-dimensional synchrotron microtomography images of unconsolidated porous media

Algorithms were implemented to obtain high resolution three-dimensional images using synchrotron microtomography. Morphological algorithms were developed to extract physically-realistic pore-network structure from unconsolidated porous media systems imaged using synchrotron microtomography. The structure can be used to correlate pore-scale phenomena with the pore structure and can also be incorporated into a pore-network model to verify existing models, understand, or predict transport and flow processes and phenomena in complex porous media systems. The algorithms are based on the three-dimensional skeletonization of the pore space in the form of nodes connected to paths. Dilation algorithms were developed to generate inscribed spheres on the nodes and paths of the medial axis to represent pore-bodies and pore-throats of the network, respectively. Pore-network structure is captured by three-dimensional spatial distribution of pore-bodies and pore-throats, pore-body and pore-throat size distributions, and the connectivity. Theoretical packings were used to verify the algorithms. Systems of glass bead and natural sand were used in this study to investigate the applicability of the algorithms. Additionally, porosity, specific surface area, and representative elementary volume (REV) analysis of porosity were calculated. The impact of resolution was investigated using perfect glass bead and natural sand systems. Finally, semivariograms and integral scale concepts were used as a tool to investigate the spatial correlation of the network. Results showed that microtomography is an effective tool to provide quantitative analysis of three-dimensional systems. The quality of the datasets depends on photon energy, photon flux, size and type of the sample, and the number of projections. The resolution has a significant impact on the construction of the medial axis and extraction of pore network parameters. This impact varies in its significance based on the system and the properties being calculated. Results highlighted the difficulty of creating a unique network from a complex, continuum pore space. Results showed that the algorithms developed are general in use and can be applied to any three-dimensional unconsolidated porous media system. Spatial correlation results showed that systems have different correlation behavior; therefore, it might be not correct if a correlation model is assigned a priori into a pore-network model

Structural characterization and statistical-mechanical model of epidermal patterns

In proliferating epithelia of mammalian skin, cells of irregular polygonal-like shapes pack into complex nearly flat two-dimensional structures that are pliable to deformations. In this work, we employ various sensitive correlation functions to quantitatively characterize structural features of evolving packings of epithelial cells across length scales in mouse skin. We find that the pair statistics in direct and Fourier spaces of the cell centroids in the early stages of embryonic development show structural directional dependence, while in the late stages the patterns tend towards statistically isotropic states. We construct a minimalist four-component statistical-mechanical model involving effective isotropic pair interactions consisting of hard-core repulsion and extra short-ranged soft-core repulsion beyond the hard core, whose length scale is roughly the same as the hard core. The model parameters are optimized to match the sample pair statistics in both direct and Fourier spaces. By doing this, the parameters are biologically constrained. Our model predicts essentially the same polygonal shape distribution and size disparity of cells found in experiments as measured by Voronoi statistics. Moreover, our simulated equilibrium liquid-like configurations are able to match other nontrivial unconstrained statistics, which is a testament to the power and novelty of the model. We discuss ways in which our model might be extended so as to better understand morphogenesis (in particular the emergence of planar cell polarity), wound-healing, and disease progression processes in skin, and how it could be applied to the design of synthetic tissues