Omnidirectional Reuse Strategy in Multi-Domains

• The omnidirectional reusing strategy is a family of methodologies that converts limited or directional measurements into reusable representations across domains like mmWave, 3D reconstruction, quantum experiments, and robotics.
• It employs deterministic reprojection, synthesis, and optimization techniques to create artifacts such as isotropic path-loss models, robust 3D initialization assets, near-optimal circuit reuse parameters, and omnidirectional policies from a single demonstration.
• The approach streamlines expensive data collection by reusing structured observations, reducing the need for exhaustive measurements while maintaining critical performance metrics.

Searching arXiv for the papers on arXiv and related "omnidirectional reusing" terminology. In contemporary technical literature, “omnidirectional reusing strategy” does not denote a single canonical algorithm. Across several domains, the phrase refers to procedures that repurpose directional, partial, or expensive observations into artifacts that remain usable across a broader directional domain: in millimeter-wave propagation, directional horn measurements are synthesized into omnidirectional received power and path loss; in large-scale scene reconstruction, archived omnidirectional RGB-LiDAR logs are transformed into 3D Gaussian Splatting initialization assets; in randomized quantum experiments, a fixed circuit-reuse parameter is chosen to perform well across arbitrary circuit ensembles and unknown noise channels; and in robotics, a single demonstration is expanded into an imagined dataset from which an omnidirectional policy is learned (Sun et al., 2015, Bae et al., 6 Mar 2026, Chen et al., 2024, Ren et al., 7 Sep 2025).

1. General notion and semantic range

The cited works use “omnidirectional” in two related but not identical senses. In wireless propagation, digital-twin reconstruction, and robot policy learning, it is literal: the objective is coverage over azimuth, elevation, or viewpoint. In circuit reusing, it is methodological: the reuse prescription is designed to work across arbitrary circuit ensembles and unknown noise channels rather than a fixed directional field (Chen et al., 2024).

Domain	Reused asset	Resulting omnidirectional object
mmWave communications	Directional horn measurements over azimuth and elevation	Omnidirectional antenna pattern, received power, and path loss
3D Gaussian Splatting	Archived omnidirectional RGB and LiDAR logs	Robust initialization assets for 3DGS
Randomized benchmarking	Repeated execution of each sampled circuit	A reuse parameter that performs well across arbitrary circuit ensembles
Robot learning	A single real-world demonstration	An imagined dataset and an omnidirectional policy

A common structural motif is present in all four settings. Each method begins with a constrained acquisition protocol—directional beams, ERP panoramas, repeated circuit shots, or a single wrist-camera trajectory—and then introduces an overview, reprojection, optimization, or generative step that enlarges the operational domain of the data. This suggests that “omnidirectional reusing” is best understood as a family of domain-specific reuse mechanisms rather than a single standardized framework.

2. Spherical power synthesis in millimeter-wave propagation

In 5G millimeter-wave propagation studies, high-gain steerable horns are used because low-gain omnidirectional antennas would incur severe free-space loss. The central reuse idea is that one can recover the omnidirectional received power by exhaustively sweeping the transmit and receive antennas in azimuth and elevation at one half-power-beamwidth increments, summing the measured powers over all non-overlapping steering angles, and removing the known transmit and receive antenna gains. If the transmitter and receiver scan $N_{\rm az}^{\rm TX}\times N_{\rm el}^{\rm TX}$ and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$ pointings, respectively, then the synthesized omnidirectional power is

$$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$

and the corresponding path loss is

$$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$

The physical rationale is expressed in the horn far-field pattern

$$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$

with $a$ and $b$ chosen so that the response falls to half-power at the azimuth and elevation HPBW points. When the horn is stepped by exactly one HPBW and the resulting offset patterns are superposed, the aggregate gain becomes almost flat versus azimuth and similarly in elevation. The method therefore synthesizes an isotropic pattern over $4\pi$ sr from directional measurements (Sun et al., 2015).

The beamwidth-independence proof is central. For a true omnidirectional link with $N$ multipath components of amplitudes $a_n$, the total power is $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$0. For directional horns with boresight gains $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$1, a given steering pair $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$2 captures only the subset of $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$3 components inside that beam, so

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$4

Summing over all non-overlapping steer pairs yields

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$5

After dividing out $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$6, the exact omnidirectional power is recovered, irrespective of the horn beamwidth, provided the sphere is tiled without overlap or gaps.

Outdoor validation was reported at 28 GHz and 73 GHz in Manhattan. At 28 GHz, TX horns with 24.5 dBi gain and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$7 HPBW were used, while the RX employed both the same narrowbeam horn and a 15 dBi widebeam horn with $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$8 HPBW. Comparing a single widebeam pointing to the sum of the corresponding $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$9 narrowbeam measurements that fill its angular footprint gave a difference typically $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$0 dB. When the full-sphere sums were formed at both beamwidths, the close-in free-space reference path-loss exponents and shadow-fading statistics were essentially identical. At 73 GHz, 27 dBi, $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$1 horns were swept in $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$2 steps; analysis of 36 LOS and NLOS links showed that $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$3–$$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$4 of the power over three adjacent elevation scans lay in the strongest plane. These results establish that directional measurements can be reused to produce beamwidth-agnostic omnidirectional path-loss models for link-budget analysis and network simulation (Sun et al., 2015).

A recurrent misconception is that omnidirectional path-loss models require omnidirectional antennas at measurement time. The method shows the opposite: accurate omnidirectional power and path loss can be synthesized from directional scans, while benefiting from the range extension provided by high-gain horns.

3. Deterministic reuse of omnidirectional RGB-LiDAR logs for 3D Gaussian Splatting

For digital twins in robotics and autonomous driving, the reuse problem is different. Here the starting point is not directional horn data but archived omnidirectional RGB and LiDAR logs that are “directly discarded or strictly underutilized” because of transmission constraints and the lack of a scalable reuse pipeline. The reported workflow converts these logs into robust initialization assets for 3D Gaussian Splatting by combining ERP-to-cubemap conversion, PRISM color-stratified downsampling, FPFH-based global registration, and ICP refinement (Bae et al., 6 Mar 2026).

The first step addresses the geometric pathologies of equirectangular projection. Given ERP longitude $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$5 and latitude $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$6, each pixel is mapped to a unit ray

$$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$7

The dominant coordinate of $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$8 selects one of the six cubemap faces $$P_{\rm omni} = \sum_{m=1}^{N_{\rm az}^{\rm TX}} \sum_{n=1}^{N_{\rm el}^{\rm TX}} \sum_{k=1}^{N_{\rm az}^{\rm RX}} \sum_{\ell=1}^{N_{\rm el}^{\rm RX}} P_r(\varphi_m,\vartheta_n,\phi_k,\theta_\ell),$$9, and standard pinhole projection is then applied; for the $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$0 face, $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$1 and $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$2. Because the mapping from $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$3 to $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$4 is bijective and face selection is a sign check on the coordinates of $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$5, the process is deterministic. Its purpose is to replace severe ERP pole distortion with six rectilinear images that can be processed by COLMAP under the usual pinhole model $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$6.

The second step, PRISM, reduces dense colorized LiDAR clouds while preserving photometrically informative structure. If $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$7 is a uniform partition of RGB space and $$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$8 is the per-bin cap, then

$$PL_{\rm omni}[{\rm dB}] = 10\log_{10}P_t - 10\log_{10}(P_{\rm omni}).$$9

The paper reports that raw LiDAR clouds of $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$0–$$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$1 M points are reduced to as few as $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$2 K points for $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$3 or $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$4 K points for $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$5, with reduction ratios up to $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$6. The stated rationale is that fewer points imply fewer Gaussians to initialize and fewer primitives to optimize, lowering VRAM usage and per-iteration cost during Gaussian splitting and rendering.

Cross-modal alignment is performed by FPFH descriptors and Open3D RANSAC, followed by ICP. For each point, SPFH is computed from the angular triplet $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$7 between local normals and neighbor vectors, and FPFH augments that local histogram with second-order neighborhood information:

$$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$8

RANSAC estimates an initial rigid transform subject to a maximum correspondence distance such as $$f(\phi,\theta)= G\;\bigl[\mathrm{sinc}^2(a\sin\phi)\cos^2\phi\bigr] \bigl[\mathrm{sinc}^2(b\sin\theta)\cos^2\theta\bigr],$$9 m, and ICP refines

$a$0

with convergence declared when the change in RMSE falls below $a$1, for example $a$2, or after a fixed number of iterations, for example $a$3.

After alignment, the SfM sparse cloud and the metric LiDAR cloud are merged into $a$4, and each point becomes the center $a$5 of a Gaussian primitive,

$a$6

with covariance based on local density and color spline coefficients seeded from projected RGB. Although no explicit extra loss term is introduced, the paper states that one may view the initialization as adding a hard anchor,

$a$7

Quantitatively, LiDAR-reinforced initialization improved final 3DGS rendering fidelity in structurally complex scenes. For Dormitory 1, PSNR improved from $a$8 to $a$9 at $b$0, with SSIM $b$1 and LPIPS $b$2. For the College of Engineering, the gains at $b$3 were PSNR $b$4, SSIM $b$5, and LPIPS $b$6. The College of Physical Edu showed smaller gains of about $b$7 PSNR at higher $b$8. End-to-end preprocessing on three sequences of approximately five minutes each ran on a single RTX 4080 in under two hours, with keyframe reuse ratios of about $b$9–$4\pi$0 and SfM reconstruction ratios of about $4\pi$1–$4\pi$2; 3DGS training at $4\pi$3 K iterations took $4\pi$4–$4\pi$5 minutes per variant.

The limitations are explicit. Residual ERP distortion around the poles can still miscolor LiDAR points at extreme latitudes. The experiments cover only three outdoor trajectories on one sensor platform. PRISM and ICP hyperparameters were not exhaustively tuned per scene. The pipeline is offline and assumes static scenes. These caveats delimit the sense in which the reuse is omnidirectional: it is deterministic and broad in angular coverage, but not yet universal across sensors, dynamics, or scene classes.

4. Cost-optimal circuit reusing in randomized quantum experiments

In quantum learning tasks, “reusing” refers to repeated execution of the same random circuit. The omnidirectional aspect is not spatial; it lies in a reuse rule that remains effective across arbitrary circuit ensembles and unknown noise channels. The formal setting samples $4\pi$6 independent random circuits and performs $4\pi$7 repeated single-shot measurements for each circuit. If $4\pi$8 is the $4\pi$9-th measurement outcome for circuit $N$0, then

$N$1

Assuming i.i.d. shots within a fixed circuit and independent circuit sampling across $N$2, the law of total variance gives

$N$3

With the abbreviations

$N$4

and per-circuit implementation cost $N$5, a fixed experimental budget $N$6 implies $N$7, so

$N$8

Under the linear cost model $N$9 with $a_n$0, the optimal continuous reuse parameter is

$a_n$1

and equivalently

$a_n$2

with equality at $a_n$3. For integer $a_n$4, the nearest integer is used (Chen et al., 2024).

The difficulty is that $a_n$5 and $a_n$6 are generally unknown. The near-optimal strategy instead assumes only linear bounds on the true cost,

$a_n$7

and sets

$a_n$8

This choice guarantees

$a_n$9

In the exact-linear case, where lower and upper bounds coincide, the ratio is $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$00, so $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$01 is “2-optimal.” The proposed procedure is operationally simple: sample the per-circuit cost for a few values of $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$02, fit linear bounds, round $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$03 to an integer, and use it uniformly throughout the experiment.

Application to standard randomized benchmarking makes the decomposition concrete. Each observation is a Bernoulli trial with success probability $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$04. The variance coefficients become

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$05

where $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$06 and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$07. Hence

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$08

For global depolarizing noise, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$09 depends only on sequence length $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$10, so $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$11 and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$12, implying $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$13: one should reuse each circuit as much as possible. For single-qubit amplitude-damping or phase-damping, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$14, while $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$15 must be estimated by twirling of $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$16, leading to a finite optimal reuse that decreases as noise strength increases.

A major empirical correction concerns cost nonlinearity. The paper reports a non-linear relationship between $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$17 and cost on a superconducting platform, contradicting earlier assumptions. A ladder model,

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$18

is bounded by linear envelopes, which leads to the near-optimal prescription

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$19

In a two-qubit superconducting randomized-benchmarking experiment, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$20, giving $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$21, within about $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$22 of the variance minimum; the true optimum lies around $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$23–$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$24. The term “omnidirectional” here is therefore best read as robustness across unknown experimental conditions rather than full angular coverage in physical space.

5. Imagined omnidirectional policies from a single demonstration

In robot learning, the reuse problem is framed around extreme data scarcity. OP-Gen defines a single demonstration

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$25

where $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$26 is a wrist-camera RGB image, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$27 is its 6-DoF pose, and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$28 is the end-effector action. The omnidirectional reusing strategy $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$29 maps $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$30 to a much larger imagined dataset

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$31

with $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$32 and, in practice, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$33. The formal objective is to infer a full 3D object model from partial views, sample novel camera poses, render synthetic images, generate collision-free trajectories back to the original demonstration trajectory, and pair each rendered image with the corresponding relative end-effector action. The resulting behavioral-cloning policy is described as omnidirectional because it has seen “the object from every angle” (Ren et al., 7 Sep 2025).

The 3D generator is EscherNet. It is presented as a conditional latent-variable model with Gaussian posterior

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$34

prior $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$35, and view-decoder

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$36

Training uses a conditional-VAE ELBO,

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$37

or equivalently

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$38

The implementation uses 5 context views, 100 query views, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$39, and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$40. The encoder is a shared ResNet-style CNN with a 16-dimensional pose embedding aggregated by cross-attention, and the decoder is a lightweight MLP producing $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$41 RGB outputs.

Dataset expansion proceeds through several deterministic and planned stages. First, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$42 novel camera poses are sampled on an Archimedean spiral around the object. Second, synthetic images are rendered with EscherNet and used to build a fast NeRF with Instant-NGP. Third, Anchored Trajectory Generation samples new start poses uniformly in the reachable workspace, plans collision-free paths to a bottleneck pose using CuRobo, samples anchor points along those paths, re-orients the cameras to look at the object with small random perturbations, and smooths the trajectory by SLERP. Finally, each augmented end-effector pose is converted into a camera pose, rendered through the NeRF, and labeled with a relative transform plus gripper status.

Policy learning uses an image-conditioned diffusion policy $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$43 that outputs a 7-dimensional action sequence with horizon $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$44. Forward diffusion is defined by

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$45

and the network $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$46 predicts the noise from the corrupted action, image, and diffusion step. The training objective is

$N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$47

At test time, actions are sampled by iterative DDIM denoising. The implementation uses a ResNet18 image encoder, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$48 diffusion steps in training, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$49 in inference, and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$50 gradient steps.

The real-world evaluation spans six 6-DoF tasks: drill grasp, mug grasp, plane grasp, coffee-pot grasp, opening an air-fryer drawer, and trash-into-bin. Success is measured over 20 rollouts per task in two initial-pose regimes, Narrow and Omni. Averaged over six tasks, the reported results are: No Augmentation, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$51 success in both regimes; OP-PCD, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$52 Narrow and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$53 Omni; SPARTN, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$54 Narrow and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$55 Omni; OP-Gen, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$56 Narrow and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$57 Omni; Upper Bound using full-scan NeRF, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$58 Narrow and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$59 Omni. Data collection times are approximately $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$60 s for No Augmentation, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$61 s for OP-PCD, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$62 min for SPARTN, $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$63 min for OP-Gen, and $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$64 h for the Upper Bound. Additional design findings are also reported: consistency across views with SSIM $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$65 everywhere was more important than peak fidelity, and removing the re-focus step in Anchored Trajectory Generation reduced real-world success from $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$66 to $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$67.

A common misconception is that omnidirectional behavior here implies multi-demonstration training. The reported method instead constructs omnidirectional coverage from a single demonstration by reusing that demonstration through 3D generative modeling, synthetic rendering, and trajectory synthesis.

6. Shared structure, assumptions, and boundary conditions

Across the four domains, the factual pattern is consistent. The starting data are restricted or underutilized: directional horn scans in mmWave propagation, archived omnidirectional RGB-LiDAR logs in digital-twin construction, repeated shots of the same random circuit in quantum experiments, and a single wrist-camera demonstration in robotics. The resulting synthesized objects are broader than the original measurements: an omnidirectional path-loss model, reusable 3DGS initialization assets, a reuse parameter with provable near-optimality under unknown circuits and noise, and a policy that generalizes to viewpoints far from the demonstrated one (Sun et al., 2015, Bae et al., 6 Mar 2026, Chen et al., 2024, Ren et al., 7 Sep 2025).

The assumptions differ sharply. The mmWave method requires beam tiling at about one HPBW with minimal overlap or gaps, and more elevation planes may be needed indoors or in highly reflective environments. The RGB-LiDAR workflow is deterministic but offline, and its generality is constrained by residual ERP pole distortion, one sensor platform, and static-scene assumptions. The quantum framework depends on a cost model $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$68, with the most precise guarantees obtained under linear or bounded-by-linear costs. OP-Gen depends on the fidelity and cross-view consistency of the learned 3D model, as well as on limited model-to-reality misalignment.

These differences matter because the term “omnidirectional” can otherwise be overstated. In the propagation and perception settings, it refers to explicit angular or viewpoint coverage over $N_{\rm az}^{\rm RX}\times N_{\rm el}^{\rm RX}$69 sr or over full object pose manifolds. In the circuit-reuse setting, it refers to robustness with respect to arbitrary circuit ensembles and unknown noise channels. A plausible implication is that the phrase should be treated as a reuse principle—extending the domain of validity of costly measurements—rather than as a single field-independent technique.

From an encyclopedic standpoint, the main significance of omnidirectional reusing strategies is methodological. They show that exhaustive remeasurement is often unnecessary when the acquisition process has enough structure to support synthesis, deterministic reprojection, provable variance control, or generative augmentation. The literature therefore uses the phrase to mark a transition from task-specific raw observations to reusable, direction-agnostic or viewpoint-agnostic intermediate representations.