Geometry Constraints Research Articles

GNSS-Assisted Visual Dynamic Localization Method in Unknown Environments

Autonomous navigation and localization are the foundations of unmanned intelligent systems, therefore, continuous, stable, and reliable position services in unknown environments are especially important for autonomous navigation and localization. Aiming at the problem where GNSS cannot continuously localize in complex environments due to weak signals, poor penetration ability, and susceptibility to interference and that visual navigation and localization are only relative, this paper proposes a GNSS-aided visual dynamic localization method that can provide global localization services in unknown environments. Taking the three frames of images and their corresponding GNSS coordinates as the constraint data, the GNSS coordinate system and world coordinate system transformation matrix are obtained through horn coordinate transformation, and the relative positions of the subsequent image sequences in the world coordinate system are obtained through epipolar geometry constraints, homography matrix transformations, and 2D–3D position and orientation solving, which ultimately yields the global position data of unmanned carriers in GNSS coordinate systems when GNSS is temporarily unavailable. Both the dataset validation and measured data validation showed that the GNSS initial-assisted positioning algorithm could be applied to situations where intermittent GNSS signals exist, and it can provide global positioning coordinates with high positioning accuracy in a short period of time; however, the algorithm would drift when used for a long period of time. We further compared the errors of the GNSS initial-assisted positioning and GNSS continuous-assisted positioning systems, and the results showed that the accuracy of the GNSS continuous-assisted positioning system was two to three times better than that of the GNSS initial-assisted positioning system, which proved that the GNSS continuous-assisted positioning algorithm could maintain positioning accuracy for a long time and it had good reliability and applicability in unknown environments.

Curved Geometric Networks for Visual Anomaly Recognition.

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that curved spaces might encode more structural information, leading to better discriminative power and hence richer representations. In this work, we investigate the benefits of the curved space for analyzing anomalous, open-set, or out-of-distribution (OOD) objects in data. This is achieved by considering embeddings via three geometry constraints, namely, spherical geometry (with positive curvature), hyperbolic geometry (with negative curvature), or mixed geometry (with both positive and negative curvatures). Three geometric constraints can be chosen interchangeably in a unified design, given the task at hand. Tailored for the embeddings in the curved space, we also formulate functions to compute the anomaly score. Two types of geometric modules (i.e., geometric-in-one (GiO) and geometric-in-two (GiT) models) are proposed to plug in the original Euclidean classifier, and anomaly scores are computed from the curved embeddings. We evaluate the resulting designs under a diverse set of visual recognition scenarios, including image detection (multiclass OOD detection and one-class anomaly detection) and segmentation (multiclass anomaly segmentation and one-class anomaly segmentation). The empirical results show the effectiveness of our proposal through consistent improvement over various scenarios. The code is made available at https://github.com/JHome1/GiO-GiT.

NVDS +: Towards Efficient and Versatile Neural Stabilizer for Video Depth Estimation.

Video depth estimation aims to infer temporally consistent depth. One approach is to finetune a single-image model on each video with geometry constraints, which proves inefficient and lacks robustness. An alternative is learning to enforce consistency from data, which requires well-designed models and sufficient video depth data. To address both challenges, we introduce NVDS + that stabilizes inconsistent depth estimated by various single-image models in a plug-and-play manner. We also elaborate a large-scale Video Depth in the Wild (VDW) dataset, which contains 14,203 videos with over two million frames, making it the largest natural-scene video depth dataset. Additionally, a bidirectional inference strategy is designed to improve consistency by adaptively fusing forward and backward predictions. We instantiate a model family ranging from small to large scales for different applications. The method is evaluated on VDW dataset and three public benchmarks. To further prove the versatility, we extend NVDS + to video semantic segmentation and several downstream applications like bokeh rendering, novel view synthesis, and 3D reconstruction. Experimental results show that our method achieves significant improvements in consistency, accuracy, and efficiency. Our work serves as a solid baseline and data foundation for learning-based video depth estimation. Code and dataset are available at: https://github.com/RaymondWang987/NVDS.

Robust Lane Keeping Control for Tractor With Multi-Unit Trailer Under Parametric Uncertainty

In this paper, a lane-keeping system is proposed for the tractor with two articulated trailers. For Tractor with Multi-Unit Trailer (T-MUT) vehicles, the motions of each unit of the vehicle are quite different from those of ordinary single-unit vehicles. Based on the dynamic model of the T-MUT vehicle, the lane-keeping control system of a T-MUT vehicle is designed with Model Predictive Control (MPC). In order to consider the uncertainty of the weight change at each trailer, a model uncertainty analysis is performed through the transfer functions for each hitch angle. For lane-keeping performance, the geometry constraints on each unit of the T-MUT vehicle are described to prevent the vehicle from lane invasion. Also, by applying the constraint tightening method to the output of the controller, a robust MPC is designed against model uncertainty, such as weight changes at each trailer. The performance of the proposed controller is validated in simulations with various curvature scenarios.

A Unified Framework Integrating Trajectory Planning and Motion Optimization Based on Spatio-Temporal Safety Corridor for Multiple AGVs

Planning safe and smooth trajectories for multiple autonomous ground vehicles (MAGVs) in a complex dynamic unstructured environment is a fundamental and challenging task. In this paper, a novel unified framework integrating trajectory planning and motion optimization (TPMO) is proposed based on spatio-temporal safety corridor (STSC), which guarantees collision avoidance and trajectory smoothness. The proposed TPMO framework consists of two parts. The first part is to establish the STSC for each AGV based on the mixed integer quadratic programming (MIQP) algorithm. The proposed STSC method ensures collision avoidance in the environment of static and dynamic obstacles, and provides a longitudinal and lateral coupled trajectory (LLCT) for trajectory planning. The second part is to design a motion optimization methodology, which considers the constraints of AGV geometry as well as longitudinal and lateral coupled motion characteristics. Moreover, our formulation provides a theoretical guarantee that the entire trajectory is optimal under collision avoidance. Finally, the proposed TPMO framework is applied to solve the optimal cooperative trajectory and motion planning problem of MAGVs in a near-natural simulation and real vehicle environments, validating the proposed framework's effectiveness and practicality.

Sketch2Human: Deep Human Generation with Disentangled Geometry and Appearance Constraints.

Geometry- and appearance-controlled full-body human image generation is an interesting but challenging task. Existing solutions are either unconditional or dependent on coarse conditions (e.g., pose, text), thus lacking explicit geometry and appearance control of body and garment. Sketching offers such editing ability and has been adopted in various sketch-based face generation and editing solutions. However, directly adapting sketch-based face generation to full-body generation often fails to produce high-fidelity and diverse results due to the high complexity and diversity in the pose, body shape, and garment shape and texture. Recent geometrically controllable diffusion-based methods mainly rely on prompts to generate appearance. It is hard to balance the realism and the faithfulness of their results to the sketch when the input is coarse. This work presents Sketch2Human, the first system for controllable full-body human image generation guided by a semantic sketch (for geometry control) and a reference image (for appearance control). Our solution is based on the latent space of StyleGAN-Human with inverted geometry and appearance latent codes as input. Specifically, we present a sketch encoder trained with a large synthetic dataset sampled from StyleGAN-Human's latent space and directly supervised by sketches rather than real images. Considering the entangled information of partial geometry and texture in StyleGAN-Human and the absence of disentangled datasets, we design a novel training scheme that creates geometry-preserved and appearance-transferred training data to tune a generator to achieve disentangled geometry and appearance control. Although our method is trained with synthetic data, it can also handle hand-drawn sketches. Qualitative and quantitative evaluations demonstrate the superior performance of our method to state-of-the-art methods.

DarkLoc+: Thermal Image-Based Indoor Localization for Dark Environments With Relative Geometry Constraints

DarkLoc+: Thermal Image-Based Indoor Localization for Dark Environments With Relative Geometry Constraints

Design and Control of a Permanent Magnet Assisted Synchronous Reluctance Motor

In recent years, studies aiming to use different motor types for traction purpose, such as in electric vehicles, have become increasingly widespread. Among these motor types, permanent magnet assisted synchronous reluctance motor (PMa-SynRM) has become in-creasingly preferred in commercially electric vehicles nowadays. This study addresses the design and control of a PMa-SynRM, also the comparison with the synchronous reluc-tance motor (SynRM). The motor design process is carried out using the finite element method in Ansys-Maxwell environment. A series of a simulation studies is conducted in the MATLAB/Simulink environment for controlling the obtained motor designed in An-sys-Maxwell. The field-oriented control (FOC) approach is chosen for precise speed con-trol. As a result of the simulation studies, it is observed that the designed motor tracks the reference with minimal error under various load conditions within a closed-loop system. Also, this paper investigates how the PM implementation affects the machine perfor-mance comparing to SynRMs. In addition, such a study takes into account that the de-sign of machines involves always several constraints, including geometry, materials, sup-ply limits, and performance constraints.

Multi-material structural discrete variable topology optimization with minimum length scale control under mass constraint

Topology optimization of multi-material structure has a larger design space compared with single material optimization, and it also requires efficient material selection methods to provide references for designers. The multi-material additive manufacturing ensures the manufacturability of topology design of multi-material structures, but also puts forward new manufacturability requirements, such as the minimum size of multi-material and the connection interface. This paper focuses on the development of a topology optimization algorithm for multi-material structures under the total mass constraint based on discrete variables. Recursive multiphase materials interpolation (RMMI) scheme is utilized to establish the relationship between discrete design variables and element elastic modulus and density, and sequential approximate integer programming (SAIP) and canonical relaxation algorithms are constructed to update the discrete design variables. It is shown that this method can obtain multi-material topology design with clear interface display, and has the ability of free material coexistence and degradation, which indicates that the discrete variables have more advantages than the continuous variables in the RMMI scheme. Based on this, the material selection under mass constraints is discussed in depth, and it is pointed out that the traditional determination of material coexistence or degradation in design based on specific stiffness has limitations. Thus, the present work expands the necessary conditions of material coexistence. Then, a minimum size control method of multi-material design based on post-processing is proposed to solve the minimum size geometry constraint problem by SAIP. Numerical examples show that this method can not only precisely control the minimum size of each material phase (including void phase), but also resolve the problem of interface and boundary diffusion of the multi-material phase, and significantly improve the manufacturability of multi-material design. Finally, it is applied to optimization problems with complex design domain and irregular meshes which are closer to engineering design.

Feature Scalar Field Grid-Guided Optical-Flow Image Matching for Multi-View Images of Asteroid

Images captured by deep space probes exhibit large-scale variations, irregular overlap, and remarkable differences in field of view. These issues present considerable challenges for the registration of multi-view asteroid sensor images. To obtain accurate, dense, and reliable matching results of homonymous points in asteroid images, this paper proposes a new scale-invariant feature matching and displacement scalar field-guided optical-flow-tracking method. The method initially uses scale-invariant feature matching to obtain the geometric correspondence between two images. Subsequently, scalar fields of coordinate differences in the x and y directions are constructed based on this correspondence. Next, interim images are generated using the scalar field grid. Finally, optical-flow tracking is performed based on these interim images. Additionally, to ensure the reliability of the matching results, this paper introduces three methods for eliminating mismatched points: bidirectional optical-flow tracking, vector field consensus, and epipolar geometry constraints. Experimental results demonstrate that the proposed method achieves a 98% matching correctness rate and a root mean square error of 0.25 pixels. By combining the advantages of feature matching and optical-flow field methods, this approach achieves image homonymous point matching results with precision and density. The matching method exhibits robustness and strong applicability for asteroid images with cross-scale, large displacement, and large rotation angles.

TSG-SLAM: SLAM Employing Tight Coupling of Instance Segmentation and Geometric Constraints in Complex Dynamic Environments.

Although numerous effective Simultaneous Localization and Mapping (SLAM) systems have been developed, complex dynamic environments continue to present challenges, such as managing moving objects and enabling robots to comprehend environments. This paper focuses on a visual SLAM method specifically designed for complex dynamic environments. Our approach proposes a dynamic feature removal module based on the tight coupling of instance segmentation and multi-view geometric constraints (TSG). This method seamlessly integrates semantic information with geometric constraint data, using the fundamental matrix as a connecting element. In particular, instance segmentation is performed on frames to eliminate all dynamic and potentially dynamic features, retaining only reliable static features for sequential feature matching and acquiring a dependable fundamental matrix. Subsequently, based on this matrix, true dynamic features are identified and removed by capitalizing on multi-view geometry constraints while preserving reliable static features for further tracking and mapping. An instance-level semantic map of the global scenario is constructed to enhance the perception and understanding of complex dynamic environments. The proposed method is assessed on TUM datasets and in real-world scenarios, demonstrating that TSG-SLAM exhibits superior performance in detecting and eliminating dynamic feature points and obtains good localization accuracy in dynamic environments.

Impact of quintessence and cloud of strings on self-consistent d-dimensional charged thin-shell wormholes

This article evaluates the stability constraints of higher-dimensional geometry of thin-shell wormholes developed from the two equivalent copies of inner and outer d-dimensional charged anti-de Sitter black holes bounded by a cloud of strings and quintessence. Such geometrical structures are built using a cut-and-paste method that joins two identical forms of black hole solutions at the hypersurface. We develop the equation of motion for the constructed wormholes and then use the linear radial perturbation approach to examine the stable configuration. The stability constraints depend on the dimensions of the black holes, cloud, and quintessence parameters. It is worth mentioning that the possibility of a stable structure is greatest for the choice of d-dimensional charged anti-de Sitter black holes with quintessence and a cloud of strings.

Random epipolar constraint loss functions for supervised optical flow estimation

The majority of supervised models estimate optical flow through minimizing the numerical difference between the predicted flow and the ground truth, resulting in the loss of positional and geometric characteristics of the calculated flow fields. In addition, these models require a large number of parameters and high computational cost when computing optical flow. To address these issues, this paper presents a novel loss function and a lightweight framework for optical flow estimation. The proposed loss function, called the random epipolar constraint loss function (RECLoss), incorporates epipolar geometry into supervised optimization to transform the numerical difference into geometry constraint. The RECLoss can make the optical flow estimation models more effective and enhance their generalization abilities. Moreover, the design of RECLoss is more interpretable and the estimated optical flow fields from RECLoss have clearly defined mathematical meanings. A lightweight recurrent neural network for optical flow estimation (LRFlow) that balances computational cost and estimation accuracy is also proposed. The LRFlow, containing only 3.0M parameters, consists of a feature extractor, a correlation matching module, and an iterative update unit. The proposed lightweight network achieves state-of-the-art results compared to all other lightweight networks on the challenging MPI-Sintel and KITTI2015 datasets. The effectiveness of RECLoss in improving the accuracy of LRFlow and other state-of-the-art methods such as RAFT and GMA has been validated through extensive experiments. The source code of the project are available at https://github.com/Eryo-iPython/RECLoss.

COEB-SLAM: A Robust VSLAM in Dynamic Environments Combined Object Detection, Epipolar Geometry Constraint, and Blur Filtering

COEB-SLAM: A Robust VSLAM in Dynamic Environments Combined Object Detection, Epipolar Geometry Constraint, and Blur Filtering

Reliable Feature Matching for Spherical Images via Local Geometric Rectification and Learned Descriptor

Spherical images have the advantage of recording full scenes using only one camera exposure and have been becoming an important data source for 3D reconstruction. However, geometric distortions inevitably exist due to the spherical camera imaging model. Thus, this study proposes a reliable feature matching algorithm for spherical images via the combination of local geometric rectification and CNN (convolutional neural network) learned descriptor. First, image patches around keypoints are reprojected to their corresponding tangent planes based on a spherical camera imaging model, which uses scale and orientation data from the keypoints to achieve both rotation and scale invariance. Second, feature descriptors are then calculated from the rectified image patches by using a pre-trained separate detector and descriptor learning network, which improves the discriminability by exploiting the high representation learning ability of the CNN. Finally, after classical feature matching with the ratio test and cross check, refined matches are obtained based on an essential matrix-based epipolar geometry constraint for outlier removal. By using three real spherical images and an incremental structure from motion (SfM) engine, the proposed algorithm is verified and compared in terms of feature matching and image orientation. The experiment results demonstrate that the geometric distortions can be efficiently reduced from rectified image patches, and the increased ratio of the match numbers ranges from 26.8% to 73.9%. For SfM-based spherical image orientation, the proposed algorithm provides reliable feature matches to achieve complete reconstruction with comparative accuracy.

Vertex Position Optimization for LATTICE Therapy

LATTICE radiation therapy (RT) aims to deliver 3D heterogenous dose of high peak-to-valley dose ratio (PVDR) to the tumor target, with peak dose at lattice vertices inside the target and valley dose for the rest of the target. In current clinical practice the lattice vertex positions are constant during treatment planning. This work proposes a new LATTICE plan optimization method that can optimize lattice vertex positions as plan variables, which is the first lattice vertex position optimization study to the best of our knowledge. The new LATTICE treatment planning method optimizes lattice vertex positions as well as other plan variables (e.g., photon fluences or proton spot weights), with optimization objectives for target PVDR and organs-at-risk (OAR) sparing. To satisfy mathematical differentiability, the lattice vertices are approximated in sigmoid functions. For geometric feasibility, proper geometry constraints are enforced onto the lattice vertex positions. The lattice vertex position optimization problem is solved by iterative convex relaxation method, where lattice vertex positions and photon/proton plan variables are jointly updated via the Quasi-Newton method. Both photon and proton LATTICE RT were considered, and the optimal lattice vertex positions in terms of plan objectives were found by solving all possible combinations on given discrete positions via heuristic searching based on standard IMRT/IMPT, which served as the ground truth for validating the new LATTICE method ("NEW"). That is, the plan with the smallest optimization objective ("BEST"), the plan with the median optimization objective ("MID"), and the plan with the largest optimization objective ("WORST") were selected as the reference plans to be compared with NEW. The table was for an abdomen case with the large bowel as the OAR, where the parameters are total optimization objective f, the mean valley dose of target Dvalley, the mean peak dose of target Dpeak, PVDR = Dpeak/Dvalley, and the mean dose of large bowel Dbowel. The unit of doses is Gy. The results in the table show that the new method indeed provided the optimal lattice vertex positions with the smallest optimization objective, the largest target PVDR, and the best OAR sparing. A new LATTICE treatment planning method is proposed and validated that can optimize lattice vertex positions as well as other photon or proton plan variables for improving target PVDR and OAR sparing.

On-Orbit Geometric Calibration and Performance Validation of the GaoFen-14 Stereo Mapping Satellite

The GaoFen-14 satellite is primarily utilized for global high-precision positioning and generating 1:10,000 scale geographic information products, making it one of the most accurate stereo mapping satellites in China. With a long-stitched CCD (charge couple device) consisting of nine chips for the forward view camera and six chips for the backward view camera, it is crucial to validate the satellite’s geometric performance and achieve high uncontrolled global positioning precision. In this study, two calibration models were proposed for the on-orbit calibration of the GaoFen-14 satellite: one accounting for the inter-chip geometry constraint and another without the constraint. Correspondingly, five calibration schemes (A, B, C, D, and E) were designed, with varying settings of the external calibration parameters, interior parameters, and utilization of the optical axis measurement data. Schemes A and B utilized the same set of alignment angles for the forward and backward images and differed in the set of interior calibration parameters. Scheme A took a single set of interior calibration parameters for all chips within the same view, while Scheme B set independent interior calibration parameters for each chip in both the forward and backward views considering the inter-chip geometry constraint. Schemes C, D, and E set two groups of alignment angles for the forward and backward views, respectively. In addition, Schemes C, D, and E utilized GaoFen-14′s specific real-time recording data of the optical axis, incorporating a slight revision of the alignment angle calibration value using dichotomous search. The interior models of Schemes A and C were identical, and those of Schemes B and D were the same. In comparison with scheme D, scheme E only lacks the inter-chip geometry constraint. These five schemes were taken to validate the most suitable exterior model and interior model for the GaoFen-14 satellite. Calibration experiments were conducted using original multichip images and the stitched images from the Zhongwei, Ningxia, and Songshan (Henan) test fields. Additionally, four sets of data from around the world are used to verify the calibration effect. The results demonstrated significant improvements in uncontrolled positioning accuracy for all five calibration schemes, transitioning from the 100 m level to the meter or even the submeter level. However, Schemes A and B exhibited unstable controlled positioning accuracy, with fluctuations ranging from 1 m to 5 m. In contrast, Schemes C, D, and E achieved substantial enhancements in uncontrolled positioning accuracy, maintaining stability with variations ranging from 0.94 to 1.14 m in the X direction, 0.41 to 0.48 m in the Y direction, and 0.77 to 0.81 m in the Z direction. The positions of the CCD probes obtained from Schemes C and D demonstrated consistency, with over 80% of the probes falling within 0.1 pixels, and all of the sampled probes within 0.3 pixels. However, Scheme D behaves better in describing the geometric deformation of each CCD chip and keeping the integrity of the long-stitched CCD simultaneously. These experimental results validate the GaoFen-14 satellite’s ability to achieve stable uncontrolled positioning accuracy worldwide and a stable geometric structure between multichips. For the GaoFen-14 satellite, it is more appropriate to adopt two sets of alignment angles for the forward and backward views, respectively. As the satellite’s on-orbit operation time increases, it is recommended to employ Scheme D for monitoring inconsistent local geometric deformation in future calibration work.

VSLAM Optimization Method in Dynamic Scenes Based on YOLO-Fastest

Simultaneous localization and mapping (SLAM) is one of the core technologies for intelligent mobile robots. However, when robots perform VSLAM in dynamic scenes, dynamic objects can reduce the accuracy of mapping and localization. If deep learning-based semantic information is introduced into the SLAM system to eliminate the influence of dynamic objects, it will require high computing costs. To address this issue, this paper proposes a method called YF-SLAM, which is based on a lightweight object detection network called YOLO-Fastest and tightly coupled with depth geometry to remove dynamic feature points. This method can quickly identify the dynamic target area in a dynamic scene and then use depth geometry constraints to filter out dynamic feature points, thereby optimizing the VSLAM positioning performance while ensuring real-time and efficient operation of the system. This paper evaluates the proposed method on the publicly available TUM dataset and a self-made indoor dataset. Compared with ORB-SLAM2, the root-mean-square error of the Absolute Trajectory Error (ATE) can be reduced by 98.27%. The system successfully locates and constructs an accurate environmental map in a real indoor dynamic environment using a mobile robot. It is a VSLAM system that can run in real-time on low-power embedded platforms.

Automatic reconstruction and modeling of dormant jujube trees using three-view image constraints for intelligent pruning applications

Automatic reconstruction and modeling of dormant jujube trees provide a basis and prerequisite for intelligent pruning applications in large-scale, dwarf, and high-density planting orchards. For accurate 3D reconstruction of the trunk and pruning branches, this study presents a method based on a multi-view image sequence of dormant jujube trees. It involves four main steps. First, we determine the way of image acquisition, equipment parameters and posture, and reconstruction accuracy by investigating and analyzing their planting mode to meet the requirements of robot intelligent pruning operation. Second, performing image matching in images of dormant jujube trees is challenging due to few local feature regions, weak continuity, and difference in individual morphological structures. We provide a bilateral image-matching method based on the three-view geometry constraint. Third, this study optimizes a camera self-calibration algorithm based on image EXIF tags by broadening its applicability to improve reconstruction efficiency. It does not rely on the particular geometric constraints in the specific scenes. Finally, a dense 3D point cloud of a tree is built automatically with this improved SfM reconstruction strategy and combined with the PMVS algorithm. Both qualitative and quantitative evaluations are performed on generating 3D models of eight dormant jujube trees and their number of branches, average plant height, and crown are used as indicators. The results show that our method identifies the number of pruning branches with an accuracy of 92% and provides a performance of 95% for measuring the diameter of the plant height and canopy. The results provide visual research basis and technical support for the intelligent pruning of jujube trees.

High-resolution SOFIA/EXES Spectroscopy of Water Absorption Lines in the Massive Young Binary W3 IRS 5

We present in this paper mid-infrared (5–8 μm) spectroscopy toward the massive young binary W3 IRS 5, using the Echelon Cross Echelle Spectrograph (EXES) spectrometer in high-resolution mode (R ∼ 50,000) from the NASA Stratospheric Observatory for Infrared Astronomy (SOFIA). Many (∼180) ν 2 = 1–0 and (∼90) ν 2 = 2–1 absorption rovibrational transitions are identified. Two hot components over 500 K and one warm component of 190 K are identified through Gaussian fittings and rotation diagram analysis. Each component is linked to a CO component identified in the IRTF/iSHELL observations (R = 88,100) through their kinematic and temperature characteristics. Revealed by the large scatter in the rotation diagram, opacity effects are important, and we adopt two curve-of-growth analyses, resulting in column densities of ∼1019 cm−2. In one analysis, the model assumes a foreground slab. The other assumes a circumstellar disk with an outward-decreasing temperature in the vertical direction. The disk model is favored because fewer geometry constraints are needed, although this model faces challenges as the internal heating source is unknown. We discuss the chemical abundances along the line of sight based on the CO-to-H2O connection. In the hot gas, all oxygen not locked in CO resides in water. In the cold gas, we observe a substantial shortfall of oxygen and suggest that the potential carrier could be organics in solid ice.