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DOE OSTI2020

LiDAR-Aided Interior Orientation Parameters Refinement Strategy for Consumer-Grade Cameras Onboard UAV Remote Sensing Systems

Unmanned aerial vehicles (UAVs) are quickly emerging as a popular platform for 3D reconstruction/modeling in various applications such as precision agriculture, coastal monitoring, and emergency management. For such applications, LiDAR and frame cameras are the two most commonly used sensors for 3D mapping of the object space. For example, point clouds for the area of interest can be directly derived from LiDAR sensors onboard UAVs equipped with integrated global navigation satellite systems and inertial navigation systems (GNSS/INS). Imagery-based mapping, on the other hand, is considered to be a cost-effective and practical option and is often conducted by generating point clouds and orthophotos using structure from motion (SfM) techniques. Mapping with photogrammetric approaches requires accurate camera interior orientation parameters (IOPs), especially when direct georeferencing is utilized. Most state-of-the-art approaches for determining/refining camera IOPs depend on ground control points (GCPs). However, establishing GCPs is expensive and labor-intensive, and more importantly, the distribution and number of GCPs are usually less than optimal to provide adequate control for determining and/or refining camera IOPs. Moreover, consumer-grade cameras with unstable IOPs have been widely used for mapping applications. Therefore, in such scenarios, where frequent camera calibration or IOP refinement is required, GCP-based approaches are impractical. To eliminate the need for GCPs, this study uses LiDAR data as a reference surface to perform in situ refinement of camera IOPs. The proposed refinement strategy is conducted in three main steps. An image-based sparse point cloud is first generated via a GNSS/INS-assisted SfM strategy. Then, LiDAR points corresponding to the resultant image-based sparse point cloud are identified through an iterative plane fitting approach and are referred to as LiDAR control points (LCPs). Finally, IOPs of the utilized camera are refined through a GNSS/INS-assisted bundle adjustment procedure using LCPs. Seven datasets over two study sites with a variety of geomorphic features are used to evaluate the performance of the developed strategy. The results illustrate the ability of the proposed approach to achieve an object space absolute accuracy of 3–5 cm (i.e., 5–10 times the ground sampling distance) at a 41 m flying height.

47 OTHER INSTRUMENTATION↗

NASA NTRS2018

Overview of the Digitization Workflow Post Image Acquisition of Apollo Lunar and Antarctic Meteorite Samples Using Agisoft Photoscan for the NASA 3D Astromaterials Virtual Samples Collection

The 3D Virtual Astromaterials Samples (3DVAS) collection is a multi-year funded project to create a digital database of sixty Apollo Lunar and Antarctic Meteorite samples following non-destructive documentation conservation protocols. After initial image processing, the photos are evaluated and processed using unique structure-from-motion photogrammetric techniques in a high performance modelling software designed to create a 3D model from 2D images: Agisoft Photoscan Pro. Agisoft Photoscan Pro uses image processing algorithms and techniques originating in computer vision to resolve 3D models for accurate and detailed visualization of a subject. The software provides a stepwise process that is tailored per model based on spatial and specular reflectance properties, for example. The process includes: photo alignment, creation of a dense point cloud, mesh, and finally texture. Photo alignment is dependent on model properties. The 3DVAS process requires a special rotation platform with calibrated photogrammetric targets, specific distance rotation protocols, and a contrasting background for alignment and scale accuracy. As a result of the photographic process, alignment will complete with two mirrored hemispheres that, in a sense, represent the 2D images overlapping to create a 3D model. Each dense point cloud is analyzed with provided statistical measures in a gradual selection process to eliminate outliers. The point cloud is reduced to include only data valuable to the final model. When a precise dense point cloud is achieved, a mesh and texture are applied. Each model is scaled with scale bar accuracies within 100 microns. Each sample has its own intimate process for modelling; there is no standard for the parameters required in the final creation of a high resolution model. By processing multiple samples, a skill is gained in practice to allow a close definition of the original sample and will result in the most detailed version of the sample shell. This process completes one-fifth of the 3DVAS protocol for providing accurate digital documentation. Each model shell is merged with X-ray Computed Tomography data to create a full volumetric sample. All 3DVAS data will be served on NASA's Astromaterials Acquisition and Curation website with an early subset of data available in 2019 and the 3D Virtual Astromaterials Samples Collection launch in 2020.

Thomas, Andi B.↗

NASA NTRS2022

Simulating Mars: Enabling Testing of the Perseverance Rover Sampling and Caching Subsystem on Earth

The development of the Sampling and Caching Subsystem (SCS) on the JPL Perseverance Rover lies at the intersection of testing, robotics, and geology. The SCS team established three primary system test campaigns and venues to aid in the development of SCS through verification and validation testing – Qualification Model Dirty Testing (QMDT) to provide a venue for testing in a Martian environment, Vehicle System Testbed (VSTB) for testing while integrated with the mobility subsystem on Martian-like terrain, and the Flight Software Testbed (FSWTB) for conducting tests using the flight motor controllers and software system on a hexapod which had the ability to simulate rover tilt. Each venue contributed a vital piece to the SCS building blocks. However, the QMDT venue operating within a 10-ft diameter Thermal Vacuum chamber to simulate Martian environment provided a sui generis opportunity to fine tune the entire sampling and caching process while building the team’s knowledge base about rock drillability, system life, and target selection. On Earth, because Martian rocks are not readily available, the development team must utilize geoanalogs to the rocks and regolith on Mars. Geologists on the team helped establish a set of standard rock types to use for Mars missions, like Basalt, Sandstone, Mudstone, Gypsum, and other related geoanalogs. These geoanalogs are characterized with a standard suite of tests for density, compressibility, and other characteristics to categorize potential drillability. This concept of drillability is what links the geoanalogs on Earth to the samples we collect on Mars. With the simulant characteristics defined, these geoanalog rocks are ready to be drilled into as we do on the Martian surface. A key aspect of interacting with the surface on Mars is rock target identification and selection. The Perseverance robotic system uses the on-board cameras, instrumentation, and software to collect enough information to identify potential scientific targets. With the targets identified, SCS can place the Corer and abrade the surface or collect a sample. For a ground test activity like QMDT, the test team did not have all of the camera and instrumentation systems that the rover does, so the team developed ground test equivalents to process a rock, build a target map, and define the target. The team constructed a Rock Scanning Station to build a 3D point cloud of the rock. This point cloud was then processed and evaluated with predefined and programmed criteria in a Target Downselect Tool. A primary output of the Target Downselect Tool is a defined target that can be uploaded directly to the robotic software system to simulate and build the robotic sequences used in tests. With these insights and programmatic definition of targets, the QMDT test team was able to make the same decisions that the Perseverance surface operations team does. In addition, valuable lessons learned from developing the target selection ground tools and using them were implemented into the tools used for surface operations.

Kim, Junggon↗

DOE OSTI2022

Root system architecture and environmental flux analysis in mature crops using 3D root mesocosms

Current methods of root sampling typically only obtain small or incomplete sections of root systems and do not capture their true complexity. To facilitate the visualization and analysis of full-sized plant root systems in 3-dimensions, we developed customized mesocosm growth containers. While highly scalable, the design presented here uses an internal volume of 45 ft 3 (1.27 m 3 ), suitable for large crop and bioenergy grass root systems to grow largely unconstrained. Furthermore, they allow for the excavation and preservation of 3-dimensional root system architecture (RSA), and facilitate the collection of time-resolved subterranean environmental data. Sensor arrays monitoring matric potential, temperature and CO 2 levels are buried in a grid formation at various depths to assess environmental fluxes at regular intervals. Methods of 3D data visualization of fluxes were developed to allow for comparison with root system architectural traits. Following harvest, the recovered root system can be digitally reconstructed in 3D through photogrammetry, which is an inexpensive method requiring only an appropriate studio space and a digital camera. We developed a pipeline to extract features from the 3D point clouds, or from derived skeletons that include point cloud voxel number as a proxy for biomass, total root system length, volume, depth, convex hull volume and solidity as a function of depth. Ground-truthing these features with biomass measurements from manually dissected root systems showed a high correlation. We evaluated switchgrass, maize, and sorghum root systems to highlight the capability for species wide comparisons. We focused on two switchgrass ecotypes, upland (VS16) and lowland (WBC3), in identical environments to demonstrate widely different root system architectures that may be indicative of core differences in their rhizoeconomic foraging strategies. Finally, we imposed a strong physiological water stress and manipulated the growth medium to demonstrate whole root system plasticity in response to environmental stimuli. Hence, these new “3D Root Mesocosms” and accompanying computational analysis provides a new paradigm for study of mature crop systems and the environmental fluxes that shape them.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Correlation approach for quality assurance of additive manufactured parts based on optical metrology

Surface topography and surface finish are two significant factors for evaluating the quality of products in additive manufacturing (AM). AM parts are fabricated layer by layer, which is quite different from traditional formative or subtractive methods. Despite rapid progress in additive manufacturing and associated optical metrology for quality control and in-situ monitoring, limited research has been conducted to investigate the reliability of 3D surface measurement data. The surface topologies scanned by multiple optical systems demonstrated significant differences due to varying sampling mechanisms, resolutions, system noises, etc. The 3D datasets should be trustworthy in order to extract parameters for quality assurance or feedback control from 3D surface measurements. In this paper, we set up new standards to evaluate the reliability of 3D surface measurement data and analyze the variation in the topographical profile. In this study, two non-contact optical methods based on Focus Variation Microscopy (FVM) and Structured Light System (SLS) were adopted to measure the surface topography of the target components. The two optical metrology systems generated two entirely different point cloud datasets. Statistical methods were applied to test the difference between the data obtained from the two systems. By using a data analytics approach for comparison, it was found that the surface roughness estimated from the point cloud data sets of FVM and SLS has no significant difference, though the point cloud data sets were completely different. This paper provides standard validation approach to evaluate the plausibility of metrology data from in-situ real-time surface analysis for process planning of AM.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Terrestrial laser scanning data (Levels 0 and 1) for Pasoh, Malaysia, Sep 2024

This data package contains data from terrestrial laser scanning (TLS) at the Pasoh Forest Reserve, Malaysia. The Pasoh Forest Reserve is a facility of the Forest Research Institute Malaysia, and contains evergreen lowland dipterocarp forest. The Next-Generation Ecosystem Experiments Tropics (NGEE-Tropics) study areas at Pasoh were established to study how different species respond to climatic variation and soil water availability. Two study areas were chosen representing different topography and species. The TLS data archived here were collected to provide detailed, three-dimensional information about forest structure. Specifically, data were collected to allow tree-level characterization of woody structure and leaf area for 12 focal trees with FloraPulse and sap flux sensors, facilitating estimation of woody biomass and leaf area to allow upscaling of water content and transpiration data to the tree-level. Scan positions were not selected to provide consistent data for non-focal trees with the study areas. This data package contains the following data: - High-level files document further details of the campaign and data package: 1_CampaignSummary.csv provides details about the campaign and study site, 2_ScanAreasDetail.csv provides details about each separate scan area (groups of scans post-processed into a single point cloud), 3_TerrestrialLidarSensor.csv provides further technical details about the Riegl VZ-400i TLS sensor, TLS_CSV_dd.csv is a CSV Data Dictionary providing information about the fields in CSV files following the ESS-DIVE CSV File Formatting Guidelines Reporting Format, TLS_flmd.csv is a File Level Metadata file providing information about each file in the data package following the ESS-DIVE File Level Metadata Reporting Format, and README.txt is a text file describing the overall project and file structure. - Level 0 data are the raw data (.PROJ folders) as recorded by the Riegl VZ-400i TLS instrument before scan co-registration and post-processing with the Riegl's proprietary RiSCAN PRO software, which requires a license. - Level 1 data contain post-processed, co-registered data from each scan area. The "PointClouds" folder for each scan area contains a .las file with 1 cm resolution point cloud data exported from RiSCAN PRO. These are the main files likely to be of interest to most users and can be further processed with any software capable of manipulating .las files (e.g. Python, R CloudCompare). The "Project Information" folder contains log files from post-processing in RiSCAN PRO that may be of interest to users who want to see detailed records of post-processing, including all PDF reports generated by RiSCAN PRO. The "ScanPositions" folder contains information about the final position of all TLS scans, after post-processing, in multiple formats. The file ScanPositions_*.csv provides final geo-referenced scan positions, and the file SOP_backup_*.csv can be used in RiSCAN PRO to restore the co-registered scan positions if users wish to re-process raw data (Level 0 .PROJ folders) with RiSCAN PRO software (e.g., subsample to a different resolution, exclude a certain scan position, or apply different filters on reflectance or deviation values) without redoing time-consuming co-registration steps.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Terrestrial laser scanning data (Levels 0 and 1) from Urban Biogeochemistry Pilot Project sites, Knoxville, Tennessee, Jul 2024 - Jul 2025

This data package contains data from terrestrial laser scanning (TLS) at five urban park sites in Knoxville, Tennessee, USA. All parks include open-grown and/or closed-canopy trees and mixed nearby land use. These study sites were established as part of the Urban Biogeochemistry Pilot Project, which has an overall goal of better understanding how hydrobiogeochemical cycling is altered within the human environment. These five sites represent a gradient of urbanization, and were instrumented to understand hydrological and biogeochemical cycling (e.g., soil moisture, soil physical properties and biogeochemistry, tree transpiration, species type). The TLS data archived here were collected to provide detailed, three-dimensional information about forest structure. Specifically, data were collected to allow tree- and stand-level characterization of woody structure and leaf area. TLS scans were placed to capture the area around trees with sap flow sensors, and as much of a 50 m radius area around the meteorological station as possible given site property limits. Derived products will allow upscaling of water content and transpiration data. This data package contains the following data: - High-level files document further details of the campaign and data package: 1_CampaignSummary.csv provides details about the campaign and study site, 2_ScanAreasDetail.csv provides details about each separate scan area (groups of scans post-processed into a single point cloud), 3_TerrestrialLidarSensor.csv provides further technical details about the Riegl VZ-400i TLS sensor, TLS_CSV_dd.csv is a CSV Data Dictionary providing information about the fields in CSV files following the ESS-DIVE CSV File Formatting Guidelines Reporting Format, TLS_flmd.csv is a File Level Metadata file providing information about each file in the data package following the ESS-DIVE File Level Metadata Reporting Format, and README.txt is a text file describing the overall project and file structure. - Level 0 data are the raw data (.PROJ folders) as recorded by the Riegl VZ-400i TLS instrument before scan co-registration and post-processing with the Riegl's proprietary RiSCAN PRO software, which requires a license. - Level 1 data contain post-processed, co-registered data from each scan area. The "PointClouds" folder for each scan area contains a .las file with 1 cm resolution point cloud data exported from RiSCAN PRO. These are the main files likely to be of interest to most users and can be further processed with any software capable of manipulating .las files (e.g. Python, R CloudCompare). The "Project Information" folder contains log files from post-processing in RiSCAN PRO that may be of interest to users who want to see detailed records of post-processing, including all PDF reports generated by RiSCAN PRO. The "ScanPositions" folder contains information about the final position of all TLS scans, after post-processing, in multiple formats. The file ScanPositions_*.csv provides final geo-referenced scan positions, and the file SOP_backup_*.csv can be used in RiSCAN PRO to restore the co-registered scan positions if users wish to re-process raw data (Level 0 .PROJ folders) with RiSCAN PRO software (e.g., subsample to a different resolution, exclude a certain scan position, or apply different filters on reflectance or deviation values) without redoing time-consuming co-registration steps.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Real-time kinematic (RTK) Drone-collected Data and Processed Models of Port Arthur Coastal Neighborhood and Pleasure Island Golf Course, June 2024

The Southeast Texas Urban Integrated field lab’s Co-design team captured aerial photos in the Port Arthur Coastal Neighborhood Community and the Golf Course on Pleasure Island, Texas, in June 2024. Aerial photos taken were through autonomous flight, and models were processed through the DroneDeploy engine. All aerial photos are in .JPG format and contained in zipped files for each area. The processed data package includes 3D models, geospatial data, mappings, and point clouds. Please be aware that DTM, Elevation toolbox, Point Cloud, and Orthomosaic use EPSG: 6588. And 3D Model uses EPSG: 3857.For using these data:- The Adobe Suite gives you great software to open .Tif files.- You can use LASUtility (Windows), ESRI ArcGIS Pro (Windows), or Blaze3D (Windows, Linux) to open a LAS file and view the data it contains.- Open an .OBJ file with a large number of free and commercial applications. Some examples include Microsoft 3D Builder, Apple Preview, Blender, and Autodesk.- You may use ArcGIS, Merkaartor, Blender (with the Google Earth Importer plug-in), Global Mapper, and Marble to open .KML files.- The .tfw world file is a text file used to georeference the GeoTIFF raster images, like the orthomosaic and the DSM. You need suitable software like ArcView to open a .TFW file.This dataset provides researchers with sufficient geometric data and the status quo of the land surface at the locations mentioned above. This dataset will support researchers' decision-making processes under uncertainties.

2D mapping↗

DOE OSTI2024

Aerial Data and Processed Models of Port Arthur Coastal Neighborhood and Pleasure Island Golf Course, June 2024

Our Co-design team is from the University of Texas, working on a Department of Energy-funded project focused on the Beaumont-Port Arthur area. As part of this project, we will be developing climate-resilient design solutions for areas of the region. More on www.caee.utexas.edu.We captured aerial photos in the Port Arthur Coastal Neighborhood Community and the Golf Course on Pleasure Island, Texas, in June 2024.Aerial photos taken were through DroneDeploy autonomous flight, and models were processed through the DroneDeploy engine as well. All aerial photos are in .JPG format and contained in zipped files for each area.The processed data package includes 3D models, geospatial data, mappings, and point clouds. Please be aware that DTM, Elevation toolbox, Point cloud, and Orthomosaic use EPSG: 6588. And 3D Model uses EPSG: 3857.For using these data:- The Adobe Suite gives you great software to open .Tif files.- You can use LASUtility (Windows), ESRI ArcGIS Pro (Windows), or Blaze3D (Windows, Linux) to open a LAS file and view the data it contains.- Open an .OBJ file with a large number of free and commercial applications. Some examples include Microsoft 3D Builder, Apple Preview, Blender, and Autodesk.- You may use ArcGIS, Merkaartor, Blender (with the Google Earth Importer plug-in), Global Mapper, and Marble to open .KML files.- The .tfw world file is a text file used to georeference the GeoTIFF raster images, like the orthomosaic and the DSM. You need suitable software like ArcView to open a .TFW file.This dataset provides researchers with sufficient geometric data and the status quo of the land surface at the locations mentioned above. This dataset could streamline researchers' decision-making processes and enhance the design as well.

2D mapping↗

DOE OSTI2023

Learning Canonical Embeddings for Unsupervised Shape Correspondence With Locally Linear Transformations

We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE)-originally designed for nonlinear dimensionality reduction-for shape correspondence. The key idea is to find dense correspondences between shapes by first obtaining high-dimensional neighborhood-preserving embeddings of low-dimensional point clouds and subsequently aligning the source and target embeddings using locally linear transformations. We demonstrate that learning the embedding using a new LLE-inspired point cloud reconstruction objective results in accurate shape correspondences. More specifically, the approach comprises an end-to-end learnable framework of extracting high-dimensional neighborhood-preserving embeddings, estimating locally linear transformations in the embedding space, and reconstructing shapes via divergence measure-based alignment of probability density functions built over reconstructed and target shapes. Our approach enforces embeddings of shapes in correspondence to lie in the same universal/canonical embedding space, which eventually helps regularize the learning process and leads to a simple nearest neighbors approach between shape embeddings for finding reliable correspondences. Comprehensive experiments show that the new method makes noticeable improvements over state-of-the-art approaches on standard shape correspondence benchmark datasets covering both human and nonhuman shapes.

deformation↗

NASA NTRS2019

Bounding Methods for Heterogeneous Lidar-derived Navigational Geofences

Safe Unmanned Aerial Vehicle (UAV) operations near the ground require navigation methods that avoid fixed obstacles such as buildings, power lines and trees. Aerial lidar surveys of ground structures are available with the precision and accuracy to geolocate obstacles, but the high volume of raw survey data can exceed the compute power of onboard processors and the rendering ability of ground-based flight planning maps. Representing ground structures with bounding polyhedra instead of point clouds greatly reduces the data size and can enable effective obstacle avoidance, as long as the bounding geometry envelopes the structures with high spatial fidelity. This report describes in detail four methods to compute bounding geometries of ground obstacles from lidar point clouds. The four methods are: 1) 2.5D Maximum Elevation Box, 2) 2.5D Ground Map Extrusion, 3) 3D Bounding Cylinder, and 4) 3D Bounding Box. The methods are applied to five point cloud datasets from lidar surveys of UAV flight research sites in Georgia and Virginia with an average point spacing that ranges from 0.1m to 0.6m. The methods are assessed using survey areas with geometrically heterogeneous ground structures: buildings, vegetation, power lines, and sub-meter structures such as road signs and guy wires. The 2.5D Maximum Elevation Box method is useful for simple structures. The 2.5D Ground Map Extrusion method efficiently encloses vegetation, but requires handdrawn ground footprints. The 3D Bounding Cylinder method excels at enclosing linear structures such as power lines and fences. The 3D Bounding Box method excels at enclosing planar structures such as buildings. The methods are compared on the basis of data compression and boundary fidelity on selected areas. The 2.5D methods yield the highest data compression but the polyhedra produced by them enclose significant amounts of empty space. Boundary fidelity is superior for the 3D methods, though this fidelity comes at the cost of a roughly thirtyfold lower data compression ratio than the 2.5D Maximum Elevation Box method. A mix of these output geometries is proposed for autonomous UAV navigation with limited on-board computing. Both the accuracy and spatial detail of emerging satellite-based survey technology lower than that of aerial lidar scanning survey technology. Sub-meter structures and thin linear structures are not reliably mapped at present by satellite-based surveys.

Moore, Andrew J.↗

DOE OSTI2020

A conservative, consistent, and scalable meshfree mimetic method

Mimetic methods discretize divergence by restricting the Gauss theorem to mesh cells. Because point clouds lack such geometric entities, construction of a compatible meshfree divergence remains a challenge. In this work, we define an abstract Meshfree Mimetic Divergence (MMD) operator on point clouds by contraction of field and virtual face moments. This MMD satisfies a discrete divergence theorem, provides a discrete local conservation principle, and is first-order accurate. We consider two MMD instantiations. The first one assumes a background mesh and uses generalized moving least squares (GMLS) to obtain the necessary field and face moments. This MMD instance is appropriate for settings where a mesh is available but its quality is insufficient for a robust and accurate mesh-based discretization. The second MMD operator retains the GMLS field moments but defines virtual face moments using computationally efficient weighted graph-Laplacian equations. This MMD instance does not require a background grid and is appropriate for applications where mesh generation creates a computational bottleneck. It allows one to trade an expensive mesh generation problem for a scalable algebraic one, without sacrificing compatibility with the divergence operator. We demonstrate the approach by using the MMD operator to obtain a virtual finite-volume discretization of conservation laws on point clouds. Finally, numerical results in the paper confirm the mimetic properties of the method and show that it behaves similarly to standard finite volume methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Visualization and 3D Mesh Generation for ASSEMBLERS Range of Motion

In an effort to create a base and foundation for ASSEMBLERS with an informed layout, data representing the range of motion of varying heights of Stewart platforms were analyzed. 3D shapes were generated first to be approximately representative of these data in the form of rotationally symmetric shells, making use of 2D alpha shapes to create a border that did not account for asymmetry inherent in the true range of motion. Further work was performed to generate mesh files more fully representative of reach, creating 3D alpha shapes based directly on point clouds generated from uniformly random platform positions. These shapes were initially not representative of the entire range of motion of a platform stack due to the low likelihood of the most extreme positions being added to a given point cloud but were more representative of the asymmetry inherent in the possible positions of a Stewart platform as they no longer relied on a single 2D contour. The same algorithm for generating 3D alpha shapes was then applied to point clouds designed to represent extreme positions, generating larger smooth shells with six clear planes of symmetry. All shells were converted to STLs to aid in further modeling of range of motion for base layouts and in visualizing reachable area for varying stack heights, successfully creating closed shells representative of typical and extreme positions for platform stacks of varying heights.

Jonah DeGuire Vanke↗

DOE OSTI2023

Three-dimensional phenotyping of peach tree-crown architecture utilizing terrestrial laser scanning

Tree training systems for temperate fruit have been developed throughout history by pomologists to improve light interception, fruit yield, and fruit quality. These training systems direct crown and branch growth to specific configurations. Quantifying crown architecture could aid the selection of trees that require less pruning or that naturally excel in specific growing/training system conditions. Regarding peaches [Prunus persica (L.) Batsch], access tools such as branching indices have been developed to characterize tree-crown architecture. However, the required branching data (BD) to develop these indices are difficult to collect. Traditionally, BD have been collected manually, but this process is tedious, time-consuming, and prone to human error. These barriers can be circumnavigated by utilizing terrestrial laser scanning (TLS) to obtain a digital twin of the real tree. TLS generates three-dimensional (3D) point clouds of the tree crown, wherein every point contains 3D coordinates (x, y, z). To facilitate the use of these tools for peach, we selected 16 young peach trees scanned in 2021 and 2022. These 16 trees were then modeled and quantified using the open-source software TreeQSM. As a result, “in silico” branching and biometric data for the young peach trees were calculated to demonstrate the capabilities of TLS phenotyping of peach tree-crown architecture. The comparison and analysis of field measurements (in situ) and in silico BD, biometric data, and quantitative structural model branch uncertainty data were utilized to determine the reconstructive model’s reliability as a source substitute for field measurements. Mean average deviation when comparing young tree (YT) height was approx. 5.93%, with crown volume was approx. 13.26% across both 2021 and 2022. All point clouds of the YTs in 2022 showed residuals lower than 12 mm to cylinders fitted to all branches, and mean surface coverage greater than 40% for both the trunk and primary branching orders.

09 BIOMASS FUELS↗

DOE OSTI2023

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗

DOE OSTI2024

Haar-Like Wavelets on Hierarchical Trees

Here, discrete wavelet methods, originally formulated in the setting of regularly sampled signals, can be adapted to data defined on a point cloud if some multiresolution structure is imposed on the cloud. A wide variety of hierarchical clustering algorithms can be used for this purpose, and the multiresolution structure obtained can be encoded by a hierarchical tree of subsets of the cloud. Prior work introduced the use of Haar-like bases defined with respect to such trees for approximation and learning tasks on unstructured data. This paper builds on that work in two directions. First, we present an algorithm for constructing Haar-like bases on general discrete hierarchical trees. Second, with an eye towards data compression, we present thresholding techniques for data defined on a point cloud with error controlled in the $L$ $\infty$ norm and in a Hölder-type norm. In a concluding trio of numerical examples, we apply our methods to compress a point cloud dataset, study the tightness of the $L$ $\infty$ error bound, and use thresholding to identify MNIST classifiers with good generalizability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗