Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi

Registration of 3D Point Clouds and Meshes: A Survey From Rigid to Non-Rigid

Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization. Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends

µMatch: 3D shape correspondence for biological image data

Modern microscopy technologies allow imaging biological objects in 3D over a wide range of spatial and temporal scales, opening the way for a quantitative assessment of morphology. However, establishing a correspondence between objects to be compared, a first necessary step of most shape analysis workflows, remains challenging for soft-tissue objects without striking features allowing them to be landmarked. To address this issue, we introduce the μMatch 3D shape correspondence pipeline. μMatch implements a state-of-the-art correspondence algorithm initially developed for computer graphics and packages it in a streamlined pipeline including tools to carry out all steps from input data pre-processing to classical shape analysis routines. Importantly, μMatch does not require any landmarks on the object surface and establishes correspondence in a fully automated manner. Our open-source method is implemented in Python and can be used to process collections of objects described as triangular meshes. We quantitatively assess the validity of μMatch relying on a well-known benchmark dataset and further demonstrate its reliability by reproducing published results previously obtained through manual landmarking

Surface-guided computing to analyze subcellular morphology and membrane-associated signals in 3D

Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have limited quantitative understanding of the processes implicated in the regulation of molecular signals at the whole cell scale. In particular, complex and transient cell surface morphologies challenge the complete sampling of cell geometry, membrane-associated molecular concentration and activity and the computing of meaningful parameters such as the cofluctuation between morphology and signals. Here, we introduce u-Unwrap3D, a framework to remap arbitrarily complex 3D cell surfaces and membrane-associated signals into equivalent lower dimensional representations. The mappings are bidirectional, allowing the application of image processing operations in the data representation best suited for the task and to subsequently present the results in any of the other representations, including the original 3D cell surface. Leveraging this surface-guided computing paradigm, we track segmented surface motifs in 2D to quantify the recruitment of Septin polymers by blebbing events; we quantify actin enrichment in peripheral ruffles; and we measure the speed of ruffle movement along topographically complex cell surfaces. Thus, u-Unwrap3D provides access to spatiotemporal analyses of cell biological parameters on unconstrained 3D surface geometries and signals.Comment: 49 pages, 10 figure

Report on shape analysis and matching and on semantic matching

In GRAVITATE, two disparate specialities will come together in one working platform for the archaeologist: the fields of shape analysis, and of metadata search. These fields are relatively disjoint at the moment, and the research and development challenge of GRAVITATE is precisely to merge them for our chosen tasks. As shown in chapter 7 the small amount of literature that already attempts join 3D geometry and semantics is not related to the cultural heritage domain. Therefore, after the project is done, there should be a clear ‘before-GRAVITATE’ and ‘after-GRAVITATE’ split in how these two aspects of a cultural heritage artefact are treated.This state of the art report (SOTA) is ‘before-GRAVITATE’. Shape analysis and metadata description are described separately, as currently in the literature and we end the report with common recommendations in chapter 8 on possible or plausible cross-connections that suggest themselves. These considerations will be refined for the Roadmap for Research deliverable.Within the project, a jargon is developing in which ‘geometry’ stands for the physical properties of an artefact (not only its shape, but also its colour and material) and ‘metadata’ is used as a general shorthand for the semantic description of the provenance, location, ownership, classification, use etc. of the artefact. As we proceed in the project, we will find a need to refine those broad divisions, and find intermediate classes (such as a semantic description of certain colour patterns), but for now the terminology is convenient – not least because it highlights the interesting area where both aspects meet.On the ‘geometry’ side, the GRAVITATE partners are UVA, Technion, CNR/IMATI; on the metadata side, IT Innovation, British Museum and Cyprus Institute; the latter two of course also playing the role of internal users, and representatives of the Cultural Heritage (CH) data and target user’s group. CNR/IMATI’s experience in shape analysis and similarity will be an important bridge between the two worlds for geometry and metadata. The authorship and styles of this SOTA reflect these specialisms: the first part (chapters 3 and 4) purely by the geometry partners (mostly IMATI and UVA), the second part (chapters 5 and 6) by the metadata partners, especially IT Innovation while the joint overview on 3D geometry and semantics is mainly by IT Innovation and IMATI. The common section on Perspectives was written with the contribution of all

A Numerical and Experimental Study on Effect of Composition of Ar-N2 Shielding Gas on the Weld Bead Profile and its Prediction for Hot Wire Arc Additive Manufacturing

Wire arc additive manufacturing is a process of making three-dimensional metal parts in a layer-by-layer approach using a feed wire and electric arc as a heat source. Wire arc additive manufacturing (WAAM) is becoming more popular due to its ability to create complex 3D parts, less build time, high deposition rate, and significant cost savings. Out of the many parameters used in WAAM, one of the important parameters is shielding gas which plays a significant role in material quality, properties, and defects. In this study, a controlled amount of Argon (Ar) and Nitrogen (N2) shielding gases are used to see the effect on the weld bead depth and width. In addition, a computational fluid dynamics (CFD) model is used to perform numerical analysis. The data collected from the experiment is used to perform a regression analysis to predict future values. The amount of shielding gas mixture is controlled through a flowmeter to three different total flowrates. The result shows there is an increase in the depth and width of the weld bead with the increase in N2 percentage in the Ar-N2 shielding gas mixture. With the increase in Nitrogen percentage, the tungsten arc is observed unstable and spattering is noticed. The temperature of the surface of the base metal is increased while using the Ar-N2 mixture. The experiment result is further verified by developing and analyzing a three-dimensional computational fluid dynamics model using a volume of fluid (VOF) method. Support vector machine (SVM) regression model with Gaussian kernel function is used to perform the predictive regression analysis. Out of all the regression models, SVM has the lowest model loss for the collected data