R1A-PC: Physics-Guided Electromagnetic Inversion of Three-Dimensional Human Point Clouds in Complex Static Environments

1 Introduction

• Strong multipath can dominate the target increment, while finite aperture makes spatial support ambiguous and measurements lack pointwise correspondence with an unordered cloud.A global measurement code gives each generated point little location-specific evidence, and adjoint backprojection is blurred by the point-spread function and sidelobes.Source: §1 · p. 2
• Paired complex subtraction emphasizes target-induced amplitude and phase changes while retaining the background field as an environmental condition.The discrete Born adjoint maps measurements to a common DOI grid, whose multiscale evidence is queried at current point coordinates and queried again after the first deformation.Source: §1 · p. 2
• R1A-PC reduces env 004 squared Chamfer distance by 70.28% relative to TopNet; removing physical guidance or background subtraction increases it by 242.06% or 241.18%.The method combines paired complex subtraction and background conditioning with multiscale adjoint features queried at current point positions.Source: §1 · p. 2
• The paper evaluates full-wave simulations using background-disjoint splits, component ablations, environment transfer, and seven additional pose groups.The introduction also points readers to the acquisition geometry and outlines the paper's inverse-task, method, analysis, and experiment sections.Source: §1 · p. 2, Figure 1 · p. 3

2.1 Learning-Based Electromagnetic Inverse Scattering

• Electromagnetic inverse scattering combines a propagation model, measurement error, and prior regularization, while learned inversion absorbs some regularization or iteration into training.Generalization depends on the training distribution, regularization, and forward-model error.Source: §2.1 · p. 3
• Physics-guided electromagnetic methods use operators and physical features, but most outputs are regular-grid images rather than unordered human point clouds in cluttered rooms.Such recovery requires distinguishing target perturbations from scene-dependent propagation.Source: §2.1 · p. 3
• Paired background subtraction attenuates the shared static-scene response, but drift and independent noise remain in the difference when acquisitions are inconsistent.The paper retains the background field separately and uses environment-level data separation to test changed propagation conditions.Source: §2.1 · p. 3

2.2 Physics-Guided Three-Dimensional Point-Cloud Recovery

• A global physical-consistency loss or compressed backprojection may not give each output point location-specific evidence, while high-valued adjoint voxels inherit aperture blur and sidelobes.Keeping a multiscale spatial field and querying it continuously at current point positions connects grid evidence to coordinate updates.Source: §2.2 · p. 4
• Point-set generators represent surfaces with fixed point counts, while prior electromagnetic point-cloud methods mainly consider free space or simpler backgrounds.R1A-PC adds paired background conditioning and updates the adjoint evidence used by each point as its coordinates change.Source: §2.2 · p. 4

3 Problem Formulation

• Each sample pairs target-present and background responses acquired under the same geometry and in the same environment.The tensor dimensions are four transmitters, three frequencies, twelve receivers, and three field components; frequencies are 300, 450, and 600 MHz.Source: §3 · p. 4
• The target-related observation is the elementwise complex difference, which suppresses common scattering while preserving target-induced amplitude and phase changes.Multipath, occlusion, and target–background coupling remain, so the inverse map also receives the background field; subtracting complex components preserves relative phase information.Source: §3 · p. 4
• The model predicts 2048 metric coordinates, and the common DOI grid provides a spatial knowledge representation distinct from the full-wave solver's finite-element degrees of freedom.The paired responses yield measurement, background, and adjoint spatial conditions for the point-cloud architecture.Source: §3 · p. 5, Figure 2 · p. 5
• The input is a complex tensor indexed by transmitter, frequency, receiver, and field component, while the output is an unordered point set that must recover position, limb orientation, and surface coverage within Ω.The spatial distribution is underdetermined by limited acquisition channels, so the reconstruction must not depend on arbitrary point ordering.Source: §3 · p. 5

4.1 Overview

• R1A-PC combines complex measurement encoding, background conditioning, a frequency-balanced adjoint, multiscale physical features, and two-stage deformation of a 2048-point template.The measurement and background representations are shared across points, while each point queries local physical evidence at its current coordinates.Source: §4.1 · pp. 5–6

4.2 Complex Difference and Background Conditioning

• Paired complex subtraction emphasizes target-induced amplitude and phase changes, while a separate background encoder retains scene-dependent propagation information.The branches address residual background effects and target–environment interactions that subtraction alone does not remove.Source: §4.2 · p. 6

4.3 Frequency-Balanced Adjoint Knowledge

• Frequency balancing scales the adjoint across frequencies, and magnitude aggregation avoids cancellation among illuminations with different phases.The DOI map supplies support evidence rather than direct surface points; the normal-operator interpretation applies to the raw adjoint before scaling, magnitude aggregation, and normalization.Source: §4.3 · p. 7

4.4 Multiscale Volumetric Encoding and Current-Point Queries

• Multiscale physical features are queried at each point’s current coordinates, with the second stage querying again after the first update.Fine-scale features preserve differences near adjoint peaks, while coarser scales provide wider context; trilinear interpolation gives continuous features between voxel centers.Source: §4.4 · pp. 7–8

4.5 Two-Stage Bounded Point-Cloud Deformation

• Each point update combines measurement attention, background modulation, and local physical features, with a larger first-stage change followed by a smaller refinement constrained to the DOI.Template indices preserve point identities across updates, but no explicit topological edges are imposed; Fig. 3 compares P1, P2, and ground truth for four poses using shared display settings.Source: §4.5 · p. 8, Figure 3 · p. 9

4.6 Cross-Environment Consistency and Geometry Objective

• The geometry objective anchors predictions to ground truth and penalizes drift between predictions for the same target in two training backgrounds.The consistency term acts on final point sets, which need not be index-matched, and has a relatively small weight beside direct geometric supervision.Source: §4.6 · pp. 8–9

5.1 Residual Bound for Background Subtraction

• Paired subtraction cancels shared background scattering, while unshared drift and observation errors remain in the residual without assumptions about their phases or correlations.Background conditioning can account for structured scene effects still present in the difference.Source: §5.1 · p. 10

5.2 Weighted Normal-Operator Interpretation

• For a Hermitian positive-semidefinite frequency-weight matrix, the weighted normal operator is positive semidefinite and maps observable contrast back to the DOI.Finite aperture and frequency coverage shape broadened peaks, sidelobes, and the null space; the adjoint supplies coarse support and location for learned interpretation.Source: §5.2 · pp. 10–11

5.3 Feasible Set of the Bounded Point Cloud

• The two-stage displacement bounds and box projection keep all 2048 predicted points within the DOI and constrain extreme coordinate drift.Reconstruction accuracy still depends on template coverage, local evidence, and predicted displacement directions.Source: §5.3 · p. 11

6.1 Experimental Setup

• Data use full-wave simulations with four transmitters, twelve receiver locations, and three frequencies; environment-disjoint splits assign env 000–002 to training, env 003 to validation, and env 004 to the principal test set.Env 005 provides 70 extended-pose samples; baselines are Born-adjoint reconstruction and data-only TopNet, with three separately retrained component ablations.Source: §6.1 · pp. 11–12, Table 1 · p. 12

6.2 Main Test Results

• On env 004, R1A-PC reaches CD-L2 0.001434±0.000087 m2 and F@0.05 0.963080±0.003883, reducing CD-L2 70.28% versus TopNet.H95 is 0.045617±0.001183 m, 50.47% lower than TopNet; the Holm-adjusted p values for these three comparisons are 2.66454 × 10−14. Qualitatively, R1A-PC more closely follows raised-arm, bent, and side-facing shapes than the baselines in four env 003 examples.Source: Table 2 · p. 12, §6.2 · pp. 12–13, Figure 4 · p. 13

6.3 Component Ablations

• Removing physical guidance or background subtraction increases CD-L2 by 242.06% or 241.18%, respectively.Without cross-environment consistency, CD-L2 is 0.001459 m2, a 1.70% increase; adjusted p values for F@0.05 and H95 are 0.908598 and 0.408952.Source: Table 3 · p. 15, §6.3 · p. 15

6.4 Cross-Environment Results

• Across env 002, env 003, and env 004, reconstruction errors vary with background propagation structure but remain of a similar order of magnitude.The reported interpretation is that background encoding conditions difference measurements on the scene, while the adjoint map preserves spatial localization.Source: Table 4 · p. 15, §6.4 · p. 15

6.5 Extended Pose Results

• In env 005, R1A-PC obtains CD-L2 0.004845 ± 0.000270 m2, F@0.05 0.863498 ± 0.012397, and H95 0.092827 ± 0.008801 m across seven pose groups.It reduces CD-L2 and H95 and raises F@0.05 versus TopNet; the table summarizes all 70 samples, while Fig. 5 shows one example per group.Source: Figure 5 · p. 14, §6.5 · p. 15, Table 5 · p. 16

6.6 Computational Efficiency

• R1A-PC has 1,114,023 trainable parameters, averages 6.460 ± 0.415 ms per sample, and uses 68.3 MiB peak memory on the reported hardware.TopNet takes 2.164 ms and uses 16.8 MiB; direct Born reconstruction takes 29.803 ms and uses 140.3 MiB. R1A-PC’s added work mainly comes from physical-feature encoding and multiscale queries at 2048 point positions.Source: Table 6 · p. 16, §6.6 · p. 16

• R1A-PC combines paired complex background subtraction, a frequency-balanced conjugate Born adjoint, and multiscale physical features queried at deforming point locations.Complex measurements, a background condition, and local spatial evidence drive two bounded stages from a shared template to a 2048-point cloud.Source: §7 · p. 16
• On env 004, CD-L2 is 0.001434 m2, F@0.05 is 0.963080, and H95 is 0.045617 m; CD-L2 is 70.28% below TopNet.Source: §7 · p. 16
• Removing physical guidance or background subtraction increases CD-L2 by 242.06% or 241.18%, respectively; new-background pose evaluation yields CD-L2 0.004845 m2 and F@0.05 0.863498.Source: §7 · p. 16
• The evaluation uses full-wave simulation under one fixed acquisition configuration and predetermined DOI and material settings; real deployment requires array and material calibration plus a practicable paired-background reference.Source: §7 · pp. 16–17

Funding.

• The authors received no funding for this study.Source: Funding · p. 17

Competing interests.

• The authors declare no competing interests.Source: Competing interests · p. 17

Data availability.

• Simulation data are not publicly available but may be obtained from the corresponding author upon reasonable request.Source: Data availability · p. 17