Title: Can NeRFs "See" without Cameras?
Venue: NeurIPS 2025
Accepted: yes
Keywords: NeRF

Indoor floorplan
Abstract: Neural Radiance Fields (NeRFs) have been remarkably successful at synthesizing novel views of 3D scenes by optimizing a volumetric scene function. This scene function models how optical rays bring color information from a 3D object to the camera pixels. Radio frequency (RF) or audio signals can also be viewed as a vehicle for delivering information about the environment to a sensor. However, unlike camera pixels, an RF/audio sensor receives a mixture of signals that contain many environmental reflections (also called “multipath”). Is it still possible to infer the environment using such multipath signals? We show that with redesign, NeRFs can be taught to learn from multipath signals, and thereby “see” the environment. As a grounding application, we aim to infer the indoor floorplan of a home from sparse WiFi measurements made at multiple locations inside the home. Although a difficult inverse problem, our implicitly learnt floorplans look promising, and enables forward applications, such as indoor signal prediction and basic ray tracing.

Can NeRFs 'See' without Cameras?

Abstract

Neural Radiance Fields (NeRFs) have been remarkably successful at synthesizing novel views of 3D scenes by optimizing a volumetric scene function. This scene function models how optical rays bring color information from a 3D object to the camera pixels. Radio frequency (RF) or audio signals can also be viewed as a vehicle for delivering information about the environment to a sensor. However, unlike camera pixels, an RF/audio sensor receives a mixture of signals that contain many environmental reflections (also called 'multipath'). Is it still possible to infer the environment using such multipath signals? We show that with redesign, NeRFs can be taught to learn from multipath signals, and thereby 'see' the environment. As a grounding application, we aim to infer the indoor floorplan of a home from sparse WiFi measurements made at multiple locations inside the home. Although a difficult inverse problem, our implicitly learnt floorplans look promising, and enables forward applications, such as indoor signal prediction and basic ray tracing.

1 Introduction

NeRFs [25, 43, 2, 45] have delivered impressive results in solving inverse problems, resulting in 3D scene rendering. While NeRFs have mostly used pictures (from cameras or LIDARs) to infer a 3D scene, we ask if the core ideas can generalize to the case of wireless signals (such as RF or audio). Unlike camera pixels that receive line-of-sight (LoS) rays, a wireless receiver (e.g., a WiFi antenna on a smartphone) would receive a mixture of LoS and many reflections, called multipath . If the receiver moves, it receives a sequence of N measurements. Using these N wireless measurements, is it possible to learn a representation of the scene, such as the floorplan of the user's home? A vanilla NeRF understandably fails since it is not equipped to handle multipath. This paper is focused on redesigning NeRFs so they can learn to image the environment, thereby solving the inverse problem from ambient wireless signals.

A growing body of work [3, 26, 47, 22, 23, 19] is investigating connections between NeRFs and wireless. While none have concentrated on imaging, NeRF2 [47] and NeWRF [22] have augmented NeRFs to correctly synthesize WiFi signals at different locations inside an indoor space. However, correct synthesis is possible without necessarily learning the correct signal propagation models. We find that NeRFs with adequate model complexity can overfit a function to correctly predict signals at test locations, but this function does not embed the true behavior of multipath signal propagation. We re-design the NeRF's objective function so that it learns the environment through line-of-sight (LoS) paths and reflections. This teaches the NeRF an implicit representation of the scene, which can then be utilized for various forward tasks, including WiFi signal prediction and ray tracing.

In our model, EchoNeRF , each voxel is parameterized by its opacity δ ∈ [0 , 1] and orientation ω ∈ [ -π, π ] . When trained perfectly, free-space air voxels should be transparent ( δ = 0 ), wall voxels should be opaque ( δ = 1 ), and each opaque voxel's orientation should match its wall's orientation.

As measurements, we use the received signal power . Thus, the input to our EchoNeRF model is the transmitter ( Tx ) location, a sequence of known receiver ( Rx ) locations, and the signal power measured at each Rx location. The output of EchoNeRF is an (implicitly learnt) floorplan of the indoor space. We expect to visualize the floorplan by plotting the learnt voxel opacities.

Voxels:

=1

8=0

Rx

Tx

(a)

(b)

(c)

(d)

Tx

Tx

>Rx

Rx

VirtualTx

Walls

→LoS rays

Learning floorplans requires modeling the correct reflections (see Fig. 1) since these reflections help reveal where the walls are. However, without knowledge of the walls, the reflections are difficult to model, leading to a type of chicken and egg problem. Additionally, the number of wireless measurements is relatively sparse compared to the number of pixels measured in image-trained NeRFs. Finally, measured signals will have 'blind spots', meaning that rays that bounced off certain regions of the walls may not have arrived at any of the Rx locations. This leaves gaps or holes in the floorplan and NeRF's interpolation through these gaps will produce error or blur.

EchoNeRF approaches this problem by modeling the received signal power as a combination of the LoS power and the power from first order reflections. The LoS model is inherited from classical NeRFs. The main departure from past work is in modeling the reflections. Since opaque voxels are unknown during training, the reflection surfaces are not known; hence, the reflection power at the Rx is modeled as an aggregate over all plausible reflections. Given the planar structure of walls, the plausible set of reflections can be heavily pruned to reduce the optimization complexity. Reflections aggregated over this plausible set models the total (LoS + reflection) power at a receiver Rx .

EchoNeRF trains to minimize the loss between the modeled and measured power across all Rx locations, and in the process, learns the voxel's opacities that best explain the measured dataset. Some regularization is necessary to cope with sparse measurements and to ensure smoothness of walls. Lastly, to handle some gradient imbalance issues, EchoNeRF freezes the LoS model once it converges, and uses this intermediate state to partly supervise the reflection model.

To evaluate EchoNeRF , we train on 2 . 4 GHz WiFi signals from NVIDIA's Sionna simulator [14], with floorplans from the Zillow's Indoor Dataset (ZIND) [9]. Results show consistent improvement over baselines in terms of the estimated floorplan's IoU and F1 score. Qualitative results show visually legible floorplans without any post-processing. Applying forward functions on the floorplan, EchoNeRF can predict the received signal power for new ⟨ Tx,Rx ⟩ locations (outperforming existing baselines). Lastly, basic ray tracing explains the predictions, offering interpretability to its results.

2 Related Work and Research Scope

Wireless (WiFi) channel prediction using NeRFs. NeWRF [22] and NeRF2 [47] are recent papers that have used NeRFs to predict the wireless channel impulse response (CIR) [40] at unknown locations inside a room. Drawing a parallel to optical NeRFs, a voxel's color in optics becomes a voxel's transmit power in wireless. The voxel's density in optics remains the same in wireless, modeling how that voxel attenuates signals passing through it. NeRF2 and NeWRF assign transmit power and attenuation to each voxel such that they best explain the measured CIR. The authors explain that voxels assigned non-zero transmit power will be called virtual transmitters ; these voxels represent the reflection points on the walls. However, many assignments are possible that fit the CIR training data , especially when the data is sparse. Fig. 2(a,b) illustrates 2 possible assignments. While the predicted CIRs could achieve low error for all such assignments, only one of the assignments will model the true reflections, forcing the virtual transmitters to be located on the wall surfaces (Fig. 2(b)). We have plotted NeRF2 and NeWRF 's assignment of voxel densities (see Fig. 2(c,d)) to confirm

that the high accuracy in CIR prediction is not an outcome of correctly learning the wall layout. Our goal is to repair this important issue, i.e., assign voxel densities that obey the basic physics of wall reflections. Correct voxel assignment leads to the correct layouts, which then makes the (forward) CIR prediction easy.

Neural radiance fields for audio. Another active line of research focuses on predicting room impulse response (RIR) for audio [23, 37, 19, 6]. Neural Acoustic Field (NAF) [23] extended the classical NeRF to train on RIR measurements in a room and predict the RIR (magnitude and phase) at new ⟨ Tx,Rx ⟩ locations. NAF identified the possibility of overfitting to the RIR and proposed to learn, jointly, the local geometric features of the environment (as spatial latents) and the NAF parameters. The spatial latents embed floorplan information but a decoder needs to be trained using the partial floorplan data. EchoNeRF requires no floorplan supervision, and secondly, relies entirely on signal power (less informative than RIR) to estimate the floorplan.

Follow up work are embracing more information about the surroundings (pictures [20, 37, 19, 24], LIDAR scans [27], meshes and optical NeRFs [6]), to boost RIR accuracy. Results are steadily improving, however, this sequence of ideas is unaligned with solving the core inverse problem. Our goal is to first invert the signal power to a floorplan, which can then enable CIR/RIR predictions.

Modeling reflections in optical NeRFs Optical NeRFs have tackled reflections [10, 44, 33] for synthesizing glossy surfaces and mirrors, and for re-lighting [32, 39]. NeRFRen [12] proposes to decompose a viewed image into a transmitted and a reflected component. Ref-NeRF [41] also focuses on reflections through a similar decomposition of the transmitted and reflected color, however, the reflected color is modeled as a function of the viewing angle and the surface-normal, resulting in accurate models of specular reflection. Recent proposals such as NeRF-Casting [42] and oRCA [38] have further improved the models of multipath for glossy and mirrored surfaces, and others [5, 46] have developed similar ideas, with the core insights centering around solving a two-component decomposition problem. EchoNeRF faces the challenge of not knowing the number of rays adding up from all possible directions in the environment. Hence, EchoNeRF must solve a many-component decomposition problem by leveraging the physics of multipath signal propagation.

In the context of LIDARs, PlatoNeRF [18] and NeTF [34] cope with unknown reflections, however, LIDARs have very high time resolution (due to high clock frequency), and is therefore able to assign the incoming rays to different time buckets. This temporal separation allows the NeRF to make separate measurements for different surfaces in the scene. Since EchoNeRF uses only signal power-a single scalar measurement that contains a mixture of the LoS and all the reflections-the inverse problem of recovering the voxel attributes from only the power is far more complex.

3 EchoNeRF Model

Setup and Overview. At a Rx location, we model the received signal power ψ as

where ψ LoS is the power from the direct line-of-sight (LoS) path, and ψ ref k is the aggregate power from all k th order reflections (i.e., all signal paths that underwent exactly k reflections before arriving at the Rx ) 2 We assume M fixed transmitters and move the Rx to N known locations and measure ψ at each of them. EchoNeRF accepts M × N measurements as input and outputs the 2D floor-plan F , a binary matrix of size L × L , where L denotes the maximum floorplan length.

We train EchoNeRF on the measured data using our proposed objective function. This function only models the LoS and the first order reflections. We disregard the higher orders since they are very complex to model and contribute, on average, < 6% of the total power (see statistics in Appendix C). The NeRF model we use is a remarkably simple MLP designed to predict the density δ ∈ [0 , 1] and orientation ω ∈ [ -π, π ] of a specified voxel in the indoor scene. The orientation aids in modeling reflections. The proposed objective function - parameterized by voxel attributes ⟨ δ, ω ⟩ and the ⟨ Tx,Rx ⟩ locations - models an approximation of the received power ψ at that Rx location. Minimizing L 2 loss of this power across all Rx locations trains the MLP. Plotting out all the voxel densities in 2D gives us the estimated floorplan F .

3.1 The LoS Model

Friss' equation [1] from electromagnetics models the free-space received power as P r = K d 2 where d is the distance of signal propagation, and K is a product of transmit-power, wavelength, and antenna-related constants [1]. We model this free-space (LoS) behavior in the NeRF framework through the following equation.

where K can be empirically measured, and d is the known distance between the ⟨ Tx,Rx ⟩ . The numerator includes the product of voxel densities over all voxels along the LoS ray from Tx to Rx (with an abuse of notion, we write this as v i ∈ LoS ). This models occlusions. When the LoS path is completely free of any occlusions (i.e., δ i = 0 , ∀ i where { i | v i ∈ LoS } ), we expect the received power to only be attenuated by the pathloss factor d 2 (in the denominator). Eq. 1 has a slight difference to classical NeRF's volumetric scene function. In our case, voxels along the ray do not contribute to the received power (whereas in NeRF, each voxel's color is aggregated to model the final pixel color at the image). In other words, we have modeled a single transmitter in Eq. 1.

3.2 The Reflection Model

To model reflections, consider a voxel v j . Whether v j reflects a ray from the Tx towards Rx depends on (1) v j 's density δ j and orientation ω j , (2) the ⟨ Tx,Rx ⟩ locations, and (4) whether the path from Tx to v j , and from v j to Rx are both occlusion-free. Parameterized by these, Eq. 2 models ψ ref ( v j ) , which is the received power at Rx due to the signal that reflected off voxel v j .

Let us explain this equation briefly. The leading δ j ensures that voxel v j is not a reflector when δ j = 0 . The f ( θ, β ) term models the wave-surface interactions, i.e., how signals get attenuated as a function of the incident angle θ and how signals scatter as a function of the offset angle β (which is the angle between the reflected ray and the direction of the Rx from v j ). The next two product terms ensure that for the Rx to receive this reflection, the voxels along the 2 segments ( Tx to v j and v j to Rx ) must be non-opaque; if any δ k or δ l equals 1 , that reflection path is blocked, producing no power contribution via this voxel v j to the receiver Rx . Finally, the denominator is the squared distance from Tx to v j , and from v j to Rx , modeling signal attenuation.

To compute the full reflection power, the natural question is: which voxels are contributing to the received power? Geometrically, any opaque voxel can be a plausible reflection point between any ⟨ Tx,Rx ⟩ pair. This is because, for triangle formed by Tx , v j , and Rx , the voxel orientation ω j can be assigned a direction that bisects the angle at v j . For this ω j , the reflected ray will perfectly arrive at the Rx . Thus, without the knowledge of orientation and density, the total first order reflection power at the Rx should be modeled as the sum of reflections on all voxels. This makes the optimization problem excessively under-determined.

We address this by modeling ω j as a discrete value-multiples of π K ω . Larger K ω is needed when the environment has complex surface orientations; however, most floorplans exhibit perpendicular walls [48, 8, 11] and K ω = 4 is adequate. Once ω j becomes discrete, the voxels that can produce plausible reflections become far fewer - we call this the 'plausible set' V . Fig. 3 visualizes V and shows 3 out of many plausible reflections from voxels with ω j = 135 ◦ . Eq. 3 sums up the power from all reflections that occur on the plausible set:

Thus, the final modeled power at a specific Rx location becomes ˜ ψ = ψ LoS + ψ ref 1 .

135°

Tx

(cli)

··..

w=0°

=45°

22

。06=m

w=135°

Rx

3.3 Gradient Issues during Training

Training against a L 2 loss, L = ∥ ˜ ψ -ψ ∗ ∥ 2 2 3 , did not generate legible floorplans. We found that the ψ LoS dominated the loss term, drowning the reflection model's influence on learning. At a high level, the gradient of the LoS model (Eq. 1) w.r.t. δ i has fewer terms in the numerator's product, and a smaller d 2 in the denominator. The reflection model's gradient w.r.t. δ i has many more terms since the reflection path is much longer; the denominator is also larger. Since (1 -δ j ) ≤ 1 , their products force the gradient to decrease geometrically with more terms, causing the reflection gradient to be much smaller compared to LoS. We formalize this explanation below by considering the LoS and reflection losses individually 4 .

Consider the gradient of L LoS w.r.t the density of v i .

̸

where LoS ( n ) is the n -th LoS path passing through voxel v i .

The gradient of L ref has a nearly identical expression with the only difference being many more product terms and that ∇ δ i ψ ( n ) ref depends on where v i is present in the n -th set of reflection path voxels (denoted by Ref ( n ) ). For example,

̸

Stage 1

LOS

0 0

Eq.(1)

(x,y)

MLP

(8,@)

Tx,Rxlocations

Copy weights

to stage 2

Stage 2

00

ref1

LOS

Eq.(2)

Lstage2(*,Los,ref1)

Tx,Rxlocations

here ∇ δ i ψ ( n ) ,Tx ref denotes the gradient when v i is between Tx to the reflection point v .

Finally, since the modeled power approximates the measured power, the residual error will remain non-zero even if the floorplan is accurately learnt. As a result, the optimization is biased towards voxels of higher gradients, i.e., voxels on the LoS path, suppressing the importance of reflections. To address this, we train EchoNeRF in 2 stages.

3.4 Multi-stage Training

Stage 1: We first use the LoS model against the measured ground truth power ψ ∗ (see Fig. 4). This converges quickly because the network easily learns the transparent voxels ( δ = 0 ) located along LoS paths. For LoS paths that are occluded, the network incorrectly learns excessive opaque voxels between the ⟨ Tx,Rx ⟩ , but this does not affect the LoS error since the path is anyway occluded. Hence, the outcome is a crude floorplan but a near-perfect LoS power estimate ˜ ψ LoS . We utilize this ˜ ψ LoS in stage 2 (discussed soon).

As Stage 1 training progresses, some opaque voxels emerge, offering crude contours of some walls. We estimate a voxel's spatial gradient, ∇ δ i , and use it to supervise the orientation ω i of that voxel. The intuition is that a voxel's orientation - needed to model reflections in Stage 2 - is essentially determined by the local surface around that voxel. The gradient ∇ δ i offers an opportunity for weak supervision. Thus, the loss for Stage 1 is:

with λ 1 , λ 2 > 0 being tunable hyperparameters. The regularization term L reg will be discussed soon. Finally, the near-perfect estimate of LoS power, denoted ˜ ψ LoS , is also carried over to Stage 2 to ensure the reflection model is penalized when it veers away from this LoS estimate.

Stage 2 focuses on training the reflection model using the following loss function.

The first term in the RHS ensures that the Stage 1 's LoS estimate is honored in Stage 2 . The second term subtracts Stage 1 's LoS power from the measured power, ( ψ ∗ -˜ ψ LoS ); this models the total power only due to reflections . Our (first order) reflection model ψ ref 1 is trained to match this aggregate power ( L 2 loss). The supervision on orientation and the regularization terms are the same as in Stage 1 .

■ Regularization : Floorplans demonstrate significant local similarity in orientation, hence we penalize differences in orientation among neighbors, using a regularization (Eq. 8) similar to Total Variation [31]. This can be achieved without additional computational cost to the neural network by directly utilizing voxel orientations obtained from each ray.

Here n v is the number of voxels queried from the plausible set V and n r is the number of voxels along the each ray.

4 Experiments

Floorplan and Wireless Simulation Dataset. Floorplans are drawn from the Zillow Indoor Dataset [9]. In each floorplan, we use the A ∗ algorithm [13] to generate a walking trajectory that traverses all rooms. We use the NVIDIA Sionna RT [15, 14] - a ray tracer for radio propagation modeling - to compute the ground truth signal power (also known as received signal strength index (RSSI)). We randomly place M Tx s, one in each room, denoted as T m . To simulate omnidirectional transmissions

at 2 . 4 GHz from each Tx location, we shoot 10 7 rays into the given floorplan. For receiver locations, we sample the user trajectory at a fixed time interval to obtain N Rx locations, denoted as R n . Sionna accounts for specular reflections and refraction when these rays interact with walls in the specified floor plan; we use the default materials for the walls. As with most WiFi simulators, Sionna does not model signal penetration through walls - this means that a Tx and Rx located on opposite sides of a wall will not receive any RSSI. Overall, we gather M × N RSSI measurements ( T m , R n , ψ m,n ) that serve as input to EchoNeRF .

Baselines used for comparison are:

NeRF2 [47]: Models WiFi reflections via virtual transmitters to predict channel impulse response (CIR).

Heatmap Segmentation [21]: Interpolates CIR across the whole floorplan and applies an image segmentation algorithm (on the interpolated RSSI heatmap) to isolate each room. Essentially, the algorithm identifies the contours of sharp RSSI change since such contours are likely to correspond to walls. Implementation details are included in the Appendix E.4.

MLP : Trains an MLP network to directly estimate the RSSI based on Tx and Rx locations.

EchoNeRF _ LoS : Reports EchoNeRF 's result considering only LoS path (ablation study).

Metrics. We evaluate using 3 metrics:

(A) Wall Intersection over Union (Wall_IoU) : This metric measures the degree to which the predicted walls and the true walls superimpose over each other in the 2D floorplan. The following equation defines the metric:

where WP denotes the set of predicted wall pixels and WP ∗ denotes the true wall pixels. This is a harsh metric given wall pixels are a small fraction of the total floorplan; if a predicted wall is even offset by one pixel from the true wall, the Wall_IoU drops significantly. IoU [30] has often been defined in terms of room pixels (instead of wall pixels); this is an overestimate in our opinion, since predicting even an empty floorplan results in an impressively high IoU.

(B) F1 score [35]: Defined as F 1 = 2 × P × R P + R , where P is the precision and R is the recall of the bitmap. P and R are defined based on wall pixels, similar as above.

(C) RSSI Prediction Error (RPE) : We split all Rx locations into a training and test set. RPE reports the average median RSSI error over all the test locations across floorplans.

4.1 Overall Summarized Results

Table 1 reports comparative results between EchoNeRF and baselines, averaged over 20 different experiments, using all 3 metrics. The number of measurements are sparse ( N = 2000 and N = 1000 ), given that apartment sizes in our dataset are more than 250 , 000 pixels. Mean and standard deviation are reported in the table. EchoNeRF outperforms all models in terms of Wall_IoU and F1 Score . Compared to EchoNeRF _ LoS , EchoNeRF demonstrates visible improvements, highlighting the advantage of modeling reflections. The absolute Wall_IoU values are understandably low because the metric penalizes small errors.

NeRF2 is unable to predict the floor plan (opaque voxels) well and is only able to achieve better RPE than EchoNeRF _ LoS . EchoNeRF outperforms both EchoNeRF _ LoS and NeRF2 . Interestingly, MLP incurs a lower RPE than NeRF2 suggesting that RSSI is amenable to interpolation, and NeRF2 's implicit representation may not be an advantage for this interpolation task.

Ground

Truth

Heatmap

Seg.

NeRF2

EchoNeRF

LoS

EchoNeRF

5-

11

LM

r

4.2 Qualitative Results: Visual floorplans, RSSI heatmap, and basic ray tracing

■ Visual floorplans. Figure 5 presents visualization from all baselines and a comparison with our LoS-only model (as ablation). All the floorplans use N = 2000 receiver locations. We make the following observations. (1) Heatmap Segmentation leverages the difference of RSSI on opposite sides of a wall, however, reflections pollute this pattern, especially at larger distances between Tx and Rx . Further, signals leak through open doors, injecting errors in the room boundaries. (2) NeRF2 performs poorly since its MLP learns one among many possible assignments of virtual transmitters to fit the RSSI training data. The virtual transmitters hardly correlate to the walls of the environment. (3) EchoNeRF _ LoS can infer the position of inner walls. However, these walls are thick and slanted because while EchoNeRF _ LoS can identify occlusions between a ⟨ Tx,Rx ⟩ pair, it cannot tell the shape and pattern of these occlusions. Crucially, EchoNeRF _ LoS also cannot infer the boundary walls since no receivers are located outside the house. (4) EchoNeRF outperforms the baselines, sharpens the inner walls compared to EchoNeRF _ LoS , and constructs the boundary walls well.

Shortcomings: Recall that some parts of the floorplan are in the 'blind spots' of our dataset since no reflection arrives from those parts to any of our sparse Rx locations (e.g., see bottom left corner of the 1 st floorplan; no signals reflect off this region to arrive at any of the Rx locations). Hence, EchoNeRF is unable to construct the bottom of the left wall in this floorplan. Finally, note that areas outside the floorplan (e.g., the regions on the right of 6 th floorplan) cannot be estimated correctly since no measurements are available from those regions (hence, those voxels do not influence the gradients).

■ RSSI prediction. Figure 6 visualizes and compares predicted RSSI. The top row shows predictions at new Rx locations with the Tx held at the trained location; the bottom row shows predictions when

EchoNeRF

NeRF2

MLP

both Tx and Rx are moved to new locations. Two key observations emerge: (1) EchoNeRF is limited by Sionna's inability to simulate through-wall signal penetration; NeRF2 has access to an expensive license for a through-wall simulation and shows better predictions inside the rooms. However, in areas that EchoNeRF can "see" (e.g., corridors in the top row), the awareness of reflecting surfaces leads to significantly better predictions. (2) When the Tx location differs from that used in training, EchoNeRF 's improvement over NeRF2 is significant. This is the core advantage of first solving the inverse problem and then leveraging it for the (forward) RSSI prediction.

■ Learning reflected rays. For a given ⟨ Tx,Rx ⟩ pair, we examine the points in the plausible set V that contribute to the reflections. Fig. 7 compares the ray-tracing results from the NVIDIA Sionna simulator (we pick only first order reflections). EchoNeRF captures many of the correct reflections. Of course, some are incorrect - a false positive occurs in the bottom right room since some wall segment is missing in our estimate; false negatives also occur in the top right room where again some parts of the wall are missing.

4.3 Relaxing Assumptions & Sensitivity Study

■ Transmitter's location. We assumed knowledge of Tx locations, however, we relax this by applying maximum likelihood estimation on observed RSSI power, ψ ∗ (see Appendix D). On average, the estimated Tx location error is 2 . 08 pixels in floorplans of sizes ≈ 512 × 512 pixels.

■ Receiver location error. Table 2 shows EchoNeRF 's sensitivity to Rx location errors. We inject Gaussian noise N (0 , σ 2 I ) to the Rx locations; σ = 1 implies a physical error of 1 m. Wall_IoU accuracy obviously drops with error but 0 . 5 meter of error is tolerable without destroying the floorplan structure. Advancements in WiFi positioning systems have demonstrated robust sub-meter error.

■ Effect of Furniture. Fig. 8 visualizes inferred floorplans when toy objects are scattered in open spaces ( Rx locations remain N = 2000 ). EchoNeRF is able to identify some of the object blobs but sharpening the small objects is challenging due to more higher order reflections from furniture. Follow up

降：H

7

work is needed, either in modeling 2 nd order reflections or by imposing stronger regularizations.

■ Material Sensitivity. Table 3 shows the mean Wall_IoU of EchoNeRF on five different materials averaged across six scenes (shown in Fig. 5) Materials with higher reflectivity, such as concrete and glass, yield better performance than absorptive materials like wood. This is because more reflections allow better performance for EchoNeRF ´ s reflection model.

■ Robustness to RSSI error. We added Gaussian noise to the RSSI measurements with a mean equal to the noise floor (in dB) and a variance of 4 dB. We vary the noise floor levels ranging from -80 dB to -130 dB across the 6 floorplans shown in Fig. 5. The SNR at a receiver is computed as the difference between the received signal power and the noise floor (e.g., a received power of -70 dB with a noise floor of -80 dB results in an SNR of 10 dB). We report the mean Wall_IoU for EchoNeRF _ LoS and EchoNeRF in Table 4. The performance drops with decreasing SNR; both EchoNeRF _ LoS and EchoNeRF 's floorplans are still legible till 30 dB, but below that (when noise power becomes comparable to the signal power) they break down, leading to missing and illegible walls. Our results are conservative; when we report a specific SNR level (e.g., 40dB), it represents the highest SNR (best-case) among all receivers in that scenario, meaning other receivers experience even lower SNRs. In practice, WiFi SNR ranges from 30-60dB depending on the distance from the router, with close-proximity measurements often exceeding 50-60dB. For average real-world SNR conditions around 45dB, the corresponding best-case SNR would be 60+dB, which aligns with the top rows where EchoNeRF demonstrates strong performance.

5 Follow ups and Conclusion

Follow-ups. (1) The ability to model 2 nd order reflections will boost EchoNeRF 's accuracy, allowing it to sharpen the scene and decode smaller objects. For short range applications, such as non-intrusive medical imaging, 2 nd and 3 rd order reflections would be crucial. This remains an important direction for follow-on research. (2) Extending EchoNeRF to 3D floorplans is also of interest, and since it is undesirable to increase the number of measurements, effective 3D priors, or 2D-to-3D post-processing, may be necessary. Such post-processing tools exist [7] but we have not applied them since our goal is to improve NeRF's inherent inverse solver. (3) Expanding evaluations beyond ZInD, which contains largely unfurnished, rectangular rooms, to richer datasets such as HM3D [29] and MVL [36] would also be valuable: furniture and clutter can introduce significant multipath effects that complicate RF signal modeling, and additional research is needed to understand these effects. We defer this to future work, as our focus in this paper is not so much to understand the limits of RF-based NeRFs, but to establish the feasibility of such frameworks. (4) Finally, EchoNeRF floorplans can offer valuable spatial context to Neural RIR synthesizers like [47, 22, 6, 19, 20]. Synthesized RIR could in-turn aid EchoNeRF 's floorplan inference, forming the basis for an alternating optimization strategy. We leave these ideas to follow-up research.

Conclusion. In summary, we re-design the NeRF framework so it can learn to "see" its environment by leveraging both line-of-sight (LoS) paths and multipath reflections. While such reflections bring to the sensor more information about the surroundings, their mixtures with the LoS path also complicates the core inverse problems. EchoNeRF takes a step towards solving this inverse problem, but also leaves room for further research in neural wireless imaging and varies downstream applications.

Acknowledgments

We would like to thank Prof. Shenlong Wang for his guidance in the initial phase of this work. We also thank the anonymous reviewers for their valuable feedback. This work was partially supported by NSF #2008338, #1909568, #2148583, and #MRI-2018966. This work used DELTA at NCSA through allocation CIS230230 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by U.S. National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296

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Appendix for Can NeRFs 'See' without Cameras?

A Background on Channel Impulse Response

When a wireless signal propagates, it is typically influenced by multipath effects such as reflections and scattering, as well as attenuation caused by the surrounding environment-collectively referred to as the channel. The overall impact of these phenomena on the signal is characterized by a linear model known as the Channel Impulse Response (CIR) [28].

Mathematically, the CIR is expressed as a sum of scaled and delayed impulses as shown in Eqn 9.

where N is the number of multipath components, a i denotes the amplitude (attenuation factor) of the i -th path, ϕ i represents the phase shift of the i -th path, and τ i is the delay of the i -th path.

For an input signal x ( t ) transmitted through the channel h ( t ) , the output signal measured at a Rx , y ( t ) is obtained by the convolution:

where w ( t ) represents zero-mean additive noise. For a simple two-path channel with a line of sight (LoS) path and one reflected path, the CIR h ( t ) is given as

The received signal y ( t ) would then be:

B Modelling Wideband Multipath Signal Power

This section shows how received power in multipath scenarios can be approximated as a sum of powers of LoS and all other multipaths. In frequency domain, the received signal y ( t ) at a particular receiver can be expressed as

Here, X ( f k ) and W ( f k ) represent the discrete Fourier transforms of the signal x ( t ) and the additive noise w ( t ) at subcarrier frequency f k with k ∈ { 0 , 1 , ..., K } . The channel can be written as H ( f k ) = ∑ L l =0 a lk exp( -j 2 πf k τ l ) where l ∈ { 1 , 2 , ..., L } is an index over separate multipaths. Here, a lk and τ l represents the attenuation and phase of the l -th multipath component at subcarrier k . We assume that the channel H ( f k ) and the signal X ( f k ) are independent.

The received power at each frequency k is given by ψ Y k = E [ | Y ( f k ) | 2 ] .

where ψ X k = E [ | X ( f k ) | 2 ] and ψ W k = E [ | W ( f k ) | 2 ] . Next,

̸

̸

̸

We assume that channel gains between different multipaths l, m with l = m have vanishingly small correlation. Therefore, the total received power ψ can be computed by summing all individual subcarrier powers.

Here, we separate out ∑ K k =1 E [ ψ X k | a 0 k | 2 ] = ψ LoS , to represent the LoS power over all subcarriers and ∑ K k =1 E [ ψ X k | a lk | 2 ] = ψ ref l , 1 ≤ l ≤ L , to denote the power of l -th order reflections.

C Approximating Channel with First-Order Reflections

EchoNeRF models the total received power at the Rx as the combination of the LoS power EchoNeRF _ LoS , and the contributions from all the first-order reflections. To validate the contribution of the achievable power from EchoNeRF when compared to the total received power ψ , we evaluate the relative contributions of these signals to the total power using the NVIDIA Sionna simulator [15]. To this end, we compute the ratios of the LoS signal ψ LoS , LoS with the first order reflections ψ LoS + ψ ref 1 , and LoS with the first two orders of reflections ψ LoS + ψ ref 1 + ψ ref 2 . These are compared to the total received power ψ , which is approximated as the sum of the LoS power and the power from the first ten reflections.

Fig 9 shows path power contribution ratio from different paths in histogram. While the ψ LoS power alone only accounts for approximately 70% of the total received power and is more spread out, ψ LoS + ψ ref 1 accounts to 95% of the total power, with a reduced spread. Moreover, secondary reflections ψ ref 2 only contribute to less than 3% of the total power. Hence, EchoNeRF models the first-order reflections along with the line-of-sight.

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D Relaxing Tx Assumptions

We relax the assumption that Tx locations are known. Given the set of receiver locations { Rx i } and the signal powers { ψ i } , the goal is to estimate the transmitter location Tx = ( Tx x , Tx y ) . To achieve this, we apply a maximum likelihood estimate (MLE). Briefly, among all the measured signal powers { ψ i } from a given Tx we identify the P strongest signal powers and their corresponding received locations. The rationale behind selecting the strongest powers is that they are significantly influenced by the LoS component, allowing us to model them effectively only using the Friss' equation [1]. We assume independence among the measurements since the received LoS power across locations, for a given a Tx location, are independent. So, the likelihood equation for all these P measurements can be written as:

We approximate that the ψ i is normally distributed with a mean modeled by the line-of-sight power K d 2 i and variance σ 2 where d i = || Tx -Rx i || is the distance between Tx and Rx i . The likelihood function for each observation ψ i is thus given by:

Maximizing log-likelihood L of { ψ i } ∀ i ∈ { 1 , . . . , P }

Minimizing the second term gives the optimal Tx ∗ as:

We use Scipy's 'minimize' with the BFGS method to numerically solve for Tx ∗ . Fig 13. visualizes the ground truth and the estimated Tx locations across 6 floorplans. The estimated Tx positions closely match the ground truth, and we report the Tx location error to be 2.08 pixels. Fig 10. demonstrates the performance of EchoNeRF _ LoS and EchoNeRF using the estimated Tx locations for the 6 floorplans in Fig 13. Performance is comparable to that achieved with ground truth Tx locations, highlighting robustness.

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E Details on Model Training

The signal power measured at the receiver is typically represented in a logarithmic scale. RSSI values generally range from -50 dB to -120 dB, where a higher value (e.g., -50 dB) corresponds to a stronger signal. Fig 11 illustrates a typical input to EchoNeRF where measurements have been collected from approximately 2000 Rx s positioned in the floorplan, with data gathered from five Tx s.

E.1 Linear-Scale RSSI Loss:

For the training of EchoNeRF , we optimize on the linear-scale RSSI values. Linear loss ensures that the receivers that capture stronger signals are given more importance during training. We partition our dataset into an 80-20 split, using 80% of the data for model training, including baselines.

For EchoNeRF 's network, we employ a simple 8-layer MLP with a hidden dimension of 256 units. For each voxel v j , the outputs from the final layer are passed through a sigmoid activation to obtain the opacity δ , and through a Gumbel softmax [16] layer to sample the output normal ω from one of the possible K ω orientations. This sampled orientation is then used in the subsequent stages of training, such as for calculating the direction of the reflected signal M . For the learnable baselines, such as MLP and NeRF2 , we adopt the same architecture as used in EchoNeRF .

E.2 Supervising Voxel Orientations

EchoNeRF leverages the spatial gradient of a voxel's opacity, ∇ δ , to supervise its orientation during the multi-stage training process. To compute this gradient, we evaluate the opacities of neighboring

Tc (g)

Rc

3

Uj

voxels along each of the K ω directions and apply finite difference methods. We found that this approach yielded superior results compared to using the gradient available via autograd.

In general, the power from reflections depends not only on the total distance traveled but also on the angle at which the reflection occurs at the voxel v j , and whether the reflected ray reaches the receiver ( Rx ). We model this behavior through θ and β respectively which parameterize a nonlinear function f . The incidence angle θ measures the angle between the Tx and the orientation ω j , and β denotes the angle Rx makes with the reflected ray M (see fig 12). Note that if v j ∈ V , and if ω j is correct, β = 0 . The reflected ray M can be computed as shown in Eqn 15.

Here ω j is a unit vector.

E.3 Detailed network parameters

We assume the floorplan is an unknown shape inside a 512 × 512 grid. For any ray or ray segment, we uniformly sample n r = 64 voxels on it. We choose λ 1 = λ 2 = 0 . 01 for LoS training followed by λ 1 = λ 2 = 0 . 1 for training the EchoNeRF model. We find that discretized opacity values to { 0 , 1 } improve our LoS model. We use the straight-through estimator [4] to avoid the unavailability of the gradient at the discretization step. To help optimization and to encourage sparsity of the number of reflections, we use only the topk contributions ( k = 10 ) while training the reflection model. We use the ADAM optimizer [17] with 1 . 0 -4 learning rate. We train our models on NVIDIA A100 GPUs.

口

E.4 Heatmap Segmentation Implementation Details

The raw trajectory signal power values are first interpolated to obtain a heatmap that provides a smoother representation of the input measurements. Of course, interpolating for regions without any data can lead to incorrect results, especially in larger unseen areas. A rule-based classifier is then applied for segmentation, using two criteria: (1) RSSI values above a threshold to identify potential room areas, and (2) smoothness of the RSSI signal, assessed through the second-order derivative, to ensure continuity within rooms. The initial segmentation is refined using morphological operations (via dilation and erosion) with a 3x3 kernel to smooth rough edges and eliminate small components. Overlapping regions are resolved by comparing gradient magnitudes, followed by additional morphological processing and connected component analysis to obtain the final, refined segmentation.

Code: We plan to release our code, data, and baselines soon. In the meantime, Section E provides sufficient details to allow readers to reproduce our results, especially since our network components are simple MLPs.

F Evaluation on Additional Floorplans

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G Societal Impact Statement

We acknowledge that NeRFs hold significant potential for positive societal impact. Applications span AR/VR, medical imaging, airport security, and education, where accurate 3D reconstructions can greatly enhance functionality and understanding. However, our work on EchoNeRF also introduces potential risks. In particular, the ability to infer detailed spatial layouts from limited sensory input could be misused to access private or sensitive floorplan information. We emphasize the importance of responsible use.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nEchoNeRF demonstrates that a NeRF-style volumetric model can recover the and predict the 3D indoor structure using only sparse RF power measurements. By introducing the virtual transmitters that can cast power RF beams through a voxel grid and learning per‐voxel reflectivity and density to match line-of-sight and single-bounce multipath signals, the method reconstructs floorplans and accurately forecasts unseen transmitter without any optical inputs. Also, this work clarify the limitation of single stage training - LoS model dominate the training due to the gradient issue and correspondently propose the two-stage training strategies. This work opens the door to camera-free mapping and localization driven by RF multipath.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper’s simple yet effective free-space LoS model and its natural extension to first-bounce reflections are well justified.\n\n2. Discretizing voxel orientations offers a clear, efficient way to handle multiple reflections.\n\n3. The two-stage training schedule successfully addresses gradient instability in single-stage methods.\n\nWeakness:\n1. The motivation is vague - what practical, efficiency and cost advantages do RF signals offer over camera-based 3D reconstruction?\n\n2.  The voxel-selection strategy for reflections needs more details. Summing reflected power by iterating over every voxel scale poorly as the voxel count grows. Although the authors accelerate this with discrete orientation angles, further implementation are needed.\n\n3. Lack of ablation study. Experiments isolating the reflection model's impact and comparing single-stage versus two-stage training are needed. \n\n4. Proposed method only models line-of-sight plus first-bounce reflections - which only account for less than 6 % of total RF power - so it ignores high-order multipath that can be substantial in cluttered or non-planar environment.\n\nOverall, the paper is well written and demonstrates a competitive improvement compared to other methods. However, I have several concerns - outlined in the weakness section. Although there are some limitations, the paper still has several commendable aspects. I would vote for a borderline accept, but I may adjust my score depending on the authors' rebuttal and the other reviewers' feedback.\n\nQUESTIONS:\n1. The voxel grid and discrete normal angles also impose coarse spatial and angular resolution, and iterating over every voxel (even with orientation pruning) can become expensive as scene size grows. Please clarify the impact of voxel grid density and normal angles discretion. \n\n2. Please provide more details of selection strategies of voxel for the reflection.\n\n3. More ablation study should be included, eg. 1) with and without reflection model and 2) only one stage training versus two-stages training.\n\nLIMITATIONS:\n1. EchoNeRF models only line-of-sight and first-bounce reflections (≤6 % of total RF power), ignoring higher-order multipath that can dominate in cluttered or non-planar scenes.\n\n2. Its voxel grid and discrete normal sampling yield coarse spatial/angular resolution, and—even with orientation pruning—iterating over all voxels becomes costly as scene size grows.\n\n3. The paper lacks a thorough ablation study isolating the reflection model and comparing single-stage versus two-stage training.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method to learn wall layouts from radio-frequency (RF) measurements of multiple transmitters (Txs) placed throughout the scene and emitting concurrently. The key to the approach is to learn a NeRF (MLP-based) that learns a mapping of locations to opacity and orientation such that the RF power is accurately reconstructed. The authors demonstrate through simulated results that this analysis-by-synthesis approach enables interpretable room layout reconstructions (with the assumption that any voxel orientation is at either 0, 45, 90, or 135 degrees, since walls tend to be perpendicular).\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**\n1. The paper's proposed _EchoNeRF_ model seems reasonable, novel, and effective (at least in simulation). In particular, I was impressed the model is able to handle multiple transmitters simultaneously (akin to multiplexed imaging), since this would result in measurements mixing together, making it much more difficult to separate power for each Tx such that geometry can be learned. This is a hard problem and may be relevant in domains beyond RF.\n\n2. I found the ablations and comparison between EchoNeRF and EchoNeRF_LOS helpful and informative. In particular, it was interesting to see what happens when furniture is in the scene. \n\n3. The paper is very well written and the techniques, for the most part, are well explained. The figures are clean and informative.\n\n**Weaknesses**\n1. The paper lacks any real-world validation, making it difficult to assess its practicality. This issue is exacerbated by a lack of comprehensive analysis or even discussion of the impact of real-world noise (aside from noise in receiver location in Sec 4.3 and mentioning the use of additive noise in the background on modelling in the appendix). \n\n2. The paper claims on L22 that \"optical NeRF understandably fails since it is not equipped to handle multipath\", which is a misleading generalization, and subsequently misses several works related to optical multipath NeRF that should be cited and/or discussed. Some of the multipath NeRF from lidar literature is similar to this work, but isn't discussed. In particular, PlatoNeRF [1] models first-order reflections from multiple \"virtual Txs\" and uses a similar two-stage training approach (however, it does not model multiple Txs at once as in this work). A more comprehensive list of papers that should be cited/discussed is below.\n\n3. One of the main advantages of modeling reflections is stated to be occlusion-awareness (L128-129), but this occlusion-awareness is minimally ablated. it's discussed on L263-266, but it's unclear to me why EchoNeRF_LOS cannot see the outer walls as the Txs (red stars) are directly adjacent to them - maybe if the Rx location was shown in the GT, it would become more clear.\n\n4. The authors discuss NeWRF, but don't offer quantitative comparison. Fig 1 is helpful and clearly shows this method isn't adequate for reconstruction (so this point is fairly minor), but it would be helpful to at least show qual. results on one of the same scenes as EchoNeRF for apples to apples comparison.\n\nMultipath modeling with LiDAR:\n\n[1] PlatoNeRF. https://doi.org/10.1109/CVPR52733.2024.01380. (models first-order reflections with NeRF)\n\n[2] Non-Line-of-Sight Imaging via Neural Transient Fields. https://doi.org/10.1109/TPAMI.2021.3076062 (models second-order reflections with NeRF)\n\nMultipath modeling with RGB:\n\n[3] NeRF-Casting. https://doi.org/10.1145/3680528.3687585\n\n[4] oRCA. https://doi.org/10.1109/CVPR52729.2023.01990\n\nQUESTIONS:\nI enjoyed the paper and it's well written, but the first two weaknesses listed above make it difficult to recommend for acceptance in its current form. Thus, adding real-world results and sufficient discussion to past work would help mitigate my concerns.\n\nA few other smaller comments:\n\n- L154 The nomenclature for wj is confusing - if wj is an angle, why is the set of discrete values = (1, 2, 3, …) instead of (45, 90, 135, …)? It did not become clear that these values should be multiplied by 45 degrees until later in the text.\n\n- While there is more thorough background on RF in the appendix, a brief background section in text would be very helpful for a broad audience like NeurIPS. This could briefly describe at a high level questions, such as how do we interpret the data? Is there a temporal dimension or is it just an intensity image? Do RF signals reflect like optical signals (scatters on diffuse objects, reflects in one direction on specular objects)?\n\n- In training stage 1, is there any way to filter out pixels that correspond to occlusions and only supervise other pixels?\n\n- An ablation with varying numbers of discretized voxel orientations would be informative (increasing K_w)\n\n- This paper calls itself a NeRF based method but there is no notion of *radiance* in the formulation - seems like more of a neural implicit representation (NIR). The authors may consider revising their terminology or motivating why they call this method a NeRF.\n\n- It would be helpful if the Fig 5 caption was a bit more descriptive (e.g. mention how the reader can interpret the red stars and lightly colored lines in the first row)\n\n- Why is voxel orientation used as an output of the NIR rather than using more traditional neural SDF approaches that represent scene geometry and can easily be used to compute reflected ray directions?\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper addresses the problem of floor plan estimation from *multipath* signals (e.g., radio frequency (RF) signals such as WiFi or audio). The paper proposes a novel and interesting approach, **EchoNeRF**, by redefining Neural Radiance Fields (NeRF) to learn, implicitly, the environment structure through many line-of-sight (LoS) paths of multiple reflection RF measures. This manuscript presents a compelling evidence of the efficacy to predict floor plan geometries solely from RF signals.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n* The paper is well-written and organized. The manuscript stands clearly the motivation, challenges, and implications of the proposed solution. It also present a clear description of details and assumption towards the modification of NeRF-like pipeline for RF signals.\n* The benchmarks and baselines are suitable for the task and relevant for evaluations. \n* The idea behind the proposed **EchoNeRF** is novel and it sounds feasible and valid. Although, the floor plan estimation results significantly differ from other solutions that use cameras or direct geometry sensors, the quality of the estimated geometry are impressive. \n\n# Weaknesses\n\n* One minor weakness in the presented manuscript is the lack of experiments using real RF signal like UWB sensors or RF IC-boards, which are relatively easy to use and inexpensive. \n\n* One major weakness in the presented manuscript is that the evaluation is limited to the ZinD dataset [9], which primarily contains sparsely furnished and geometrically simple rectangular rooms. Expanding the experiments to include more complex datasets such as MVL-dataset or HM3D may enhance the discussion of the limitations of the proposed **EchoNeRF**.\n> Solarte, B., Wu, C. H., Jhang, J. C., Lee, J., Tsai, Y. H., & Sun, M. (2024, September). Self-training Room Layout Estimation via Geometry-Aware Ray-Casting. In European Conference on Computer Vision (pp. 253-269). Cham: Springer Nature Switzerland.\n\n  > Ramakrishnan, S. K., Gokaslan, A., Wijmans, E., Maksymets, O., Clegg, A., Turner, J., ... & Batra, D. (2021). Habitat-matterport 3d dataset (hm3d): 1000 large-scale 3d environments for embodied ai. NeurIPS 2022\n\nQUESTIONS:\nQ1: Did the authors consider to evaluate EchoNeRF in environments with walls exhibiting different RF absorption and reflection properties. For example, brick, wood, concrete, and glass windows? If so, how do the reconstruction results differ across such diverse environments?\n\nQ2: Since multipath signals arise not only from walls but also from ceilings and floors, can the proposed EchoNeRF reconstruct full 3D room geometry, including floor and ceiling. If so, I suggest you to add those experiments to enhance your novelty and the discussion for future works.\n\nQ3: I recommend that the authors expand the discussion in Section 5 to address the challenges associated with multiple receivers (RX) and transmitters (TX). open challenges in complementing previous solution that uses RGB cameras or depth/lidar sensors (multimodal approaches), and open concerns related to data privacy.\n\nQ4: Fig. 3 requires significant improvement. In its current form, it is really difficult to interpret and does not effectively convey the intended information. For instance, the purple shadow (representing the manifold of reflexions at $\\omega$=45$^\\circ$) present incident and reflected lines that is not at $\\omega=45^\\circ$ in the illustration. Can you elaborate on this?\n\nQ5: In L154-L157, the paper stands that $\\omega_j = [{1,..,K_\\omega}]$ with $K_\\omega=4$, However, in L158 and Fig.3  $\\omega$=45$^\\circ$. can you elaborate on this? Is this related to the number of reflations of the signal and the shape of the room?\nif so, how this affect more complex room shapes? What happens if $\\omega$ is overestimated, e.g 64? what about underestimated e.g. 1?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces EchoNeRF–a method for reconstructing floorplans from WiFi measurements. In contrast to prior works, EchoNeRF specifically targets reconstructing geometry rather than just WiFi signals. To achieve this, the method proposes two key ideas: (1) a multi-path model for WiFi signals that represents simulated signal as a sum of multi-bounce paths and (2) a floorplan representation which uses opacity and a discretized normal to describe walls. The multi-path signal is then simulated, for the first-and second bounce, using a two-stage algorithm which first recovers the line-of-sight paths before geometry with first-order reflections. In practice, the method recovers significantly more accurate floorplans than prior work and as a result also can simulate WiFi signals for new transmitter locations much more accurately.\n\nSTRENGTHS AND WEAKNESSES:\nstrengths:\n\n1. The paper develops a principled technique for reconstructing floorplans with WiFi signals and in the process makes an interesting observation that existing WiFi based NeRF methods really do not reconstruct the geometry in any sort of meaningful way. This is a similar to the series of papers a few years ago, e.g. NeuS [Wang et al. 2021] and VolSDF [Yariv et al. 2021], which demonstrated that NeRF was failing to capture high quality surfaces even though novel views were extremely high quality. In this case, the gap between the geometry recovered by EchoNeRF and methods like NeWR and NeRF2 is even more drastic.\n\n2. The paper has extensive discussion of both the design decisions, implementation, and the limitations of the method. This should make the paper and the method extremely useful to the broader NeurIPS community as it improves reproducibility and motivates future work.\nThe approach itself is very novel and provides a new framing of how to simulate WiFi with NeRF, both in terms of theory and practical approaches.\n\nweaknesses:\n1. A very minor point, it would have been great to have an example with real world data.\n\n\nreferences:\n```\n@article{wang2021neus,\n  title={NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction}, \n  author={Peng Wang and Lingjie Liu and Yuan Liu and Christian Theobalt and Taku Komura and Wenping Wang},\n  journal={NeurIPS},\n  year={2021}\n}\n@inproceedings{yariv2021volume,\n  title={Volume rendering of neural implicit surfaces},\n  author={Yariv, Lior and Gu, Jiatao and Kasten, Yoni and Lipman, Yaron},\n  booktitle={Thirty-Fifth Conference on Neural Information Processing Systems},\n  year={2021}\n}\n```\n\nQUESTIONS:\n1. Do the authors have a sense of how this method would work in 3D where scenes exhibit some variation in the added Z dimension? Separately, have the authors thought about how 2D floorplans may be useful in reconstructing components of indoor scenes with visible light?\n\n1. Is there any reason to expect that parameterizing the occupancy with a signed distance function (SDF) as in [Wang et al. 2021, Yariv et al. 2021, Miller et al. 2024] would improve the quality of the reconstructed floorplans?\n\nreferences:\n```\n@article{wang2021neus,\n  title={NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction}, \n  author={Peng Wang and Lingjie Liu and Yuan Liu and Christian Theobalt and Taku Komura and Wenping Wang},\n  journal={NeurIPS},\n  year={2021}\n}\n@inproceedings{yariv2021volume,\n  title={Volume rendering of neural implicit surfaces},\n  author={Yariv, Lior and Gu, Jiatao and Kasten, Yoni and Lipman, Yaron},\n  booktitle={Thirty-Fifth Conference on Neural Information Processing Systems},\n  year={2021}\n}\n@InProceedings{Miller:VOS:2024,\n  author    = {Miller, Bailey and Chen, Hanyu and Lai, Alice and Gkioulekas, Ioannis},\n  title     = {Objects as Volumes: A Stochastic Geometry View of Opaque Solids},\n  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},\n  month     = {June},\n  year      = {2024},\n  pages     = {87-97}\n}\n```\n\nLIMITATIONS:\nYes.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 4, "ORIGINALITY": 4, "DATE": "2025-07-03"}