Improved surface reconstruction using high-frequency details
Anonymous Author(s)
AffiliationAddress email
Abstract
Neural rendering can be used to reconstruct implicit representations of shapes without 3D supervision.
However, current neural surface reconstruction methods havedifficulty learning high-frequency geometry details, so the reconstructed shapes areoften over-smoothed.
We develop a novel method to improve the quality of surfacereconstruction in neural rendering.
We follow recent work to model surfaces assigned distance functions (SDFs).
First, we offer a derivation to analyze the relationship between the SDF, the volume density, the transparency function, and theweighting function used in the volume rendering equation.
Second, we observethat attempting to jointly encode high-frequency and low-frequency componentsin a single SDF lead to unstable optimization.
We propose to decompose the SDFinto a base function and a displacement function with a coarse-to-fine strategy togradually increase the high-frequency details.
Finally, we design an adaptive optimization strategy that makes the training process focus on improving those regionsnear the surface where the SDF have artifacts.
Our qualitative and quantitativeresults show that our method can reconstruct fine-grained surface details and obtainbetter surface reconstruction quality than the current state of the art.
Introduction
3D reconstruction from a set of images is a fundamental challenge in computer vision [9].
In therecent past, the seminal framework NeRF [18] inspired a lot of follow up work by modeling 3Dobjects as a density function σ ( x ) and view-dependent color c ( x, v ) for each point x ∈ R 3 in thevolume.
The density function and view-dependent color function are implicit functions modeled bya neural network.
The results of this approach are very strong and therefore NeRF inspired a largeamount of follup up work, e g. [17, 16, 22, 33, 19, 2].
In particular, one direction of work tries to constrain the density field to make it more consistent witha density field stemming from a surface.
In the original formulation, almost arbitrary densities can bemodeled by the neural network and there is no guarantee that a meaningful surface can be extractedfrom the density.
Two noteworthy recent approaches, Neus [28] and VolSDF [30] proposed to embeda signed distance field in the volume rendering equation.
Therefore, instead of modeling the densityσ with a neural network, these approaches model a signed distance function f with a neural network.
This leads to greatly improved surface reconstruction.
We build on this exciting recent work and seek further improvement in the quality of surfaces that arebeing reconstructed.
To this end, we propose three building blocks.
First, we analyze the relationshipbetween the signed distance function on the one hand and the volume density, transparency, and theweighting function on the other hand.
We conclude from our derivation that it would be best to modela function that maps signed distances to the transparency and propose a class of functions that fulfillthe theoretical requirements.
Second, we observe that it is difficult to learn high-frequency details directly with a single signed distance function as shown in Fig.
We therefore propose to decomposethe signed distance function into a base function and a displacement function following related work.
We adapt this idea to the differentiable NeRF rendering framework and the NeRF training scheme.
Third, the functions that translate distance to transparency can be chosen to have a parameter, we callit scale s , that controls the slope of the function (or the deviation of the derivative).
The parameter scontrols how precise the surface is being localized and how strongly colors away from the surfaceinfluence the result.
In previous work, this parameter s is set globally, but is trainable so it can changefrom iteration to iteration.
We propose a novel spatially adaptive weighting scheme to influence thisparameter, so that the optimization focuses more on problematic regions in the distance field.
Thethree building blocks are the three main contributions of the paper.
In the results, we can see a clearimprovement in surface reconstruction.
On the 15 scene DTU benchmark we can improve from thecurrent best values of 0.87 (NeuS) and 0.86 (VolSDF) to 0.77 the Chamfer distance (See Figs.
1 and 3for a visual comparison).
The benchmark as well as the metric were proposed by previous work.
Related Work
Multi-view 3D reconstruction.
3D reconstruction based on multiple views is a fundamentalchallenge in the field of 3D vision.
Classical 3D reconstruction algorithms usually reconstructdiscrete 3D representations.
The methods can be roughly categorized into voxel-based methods andpoint-based methods.
Voxel-based methods [6, 25, 13, 4] first discretize the three-dimensional spaceuniformly into voxels, and then decide whether the surface occupies a particular voxel.
Point-basedmethods [1, 7, 24, 23, 8] usually use the correlation between multiple views to reconstruct depthmaps, and fuse multiple depth maps into a point cloud
The point cloud needs to be subsequentlyreconstructed into a mesh model using explicit algorithms ball-pivoting [ Delaunaytrianglulation [ or implicit algorithms Poisson surface reconstruction
Neural implicit surfaces.
Recently, neural implicit representations have received a lot of attention.
The corresponding methods aim to reconstruct continuous implicit function representations of shapesdirectly from 2D images.
A required building block is differentiable rendering, which maps the 3Dscene representation to a 2D image for a given camera pose.
DVR [20] utilizes surface renderingto model the occupancy function of a 3D shape, which uses a root search approach to obtain thelocation of the surface and predicts a 2D image.
IDR [31] models the signed distance function ofthe shape and uses a sphere tracking algorithm to render 2D images.
A significant milestone in 3Dreconstruction was the development of NeRF [18].
It uses volume rendering to map a 3D densityfield and a 3D directional color field to a 2D image.
The proposed representation is flexible enoughso that realistic images can be synthesized.
To model more complex scenes, NeRF++ [33] proposesto model the background scene with an additional neural radiance field, which handles the foregroundand background separately, and achieves better results for large scenes.
However, the density functionis not as easy to control as the occupancy function or the signed distance function, and it is difficultto guarantee the smoothness of the generated 3D shape.
Subsequently, UNISURF [21] embeds theoccupancy function into the volume rendering equation of NeRF.
They use a decay strategy to controlwhich region to sample around the surface during training without explicitely modeling volumetricdensity.
Using signed distance functions, VolSDF [30] embeds a signed distance function into thedensity formulation and proposes a sampling strategy that satisfies a derived error bound on thetransparency function.
NeuS [28] derive an unbiased density function equation using logistic sigmoidfunctions and introduce a learnable parameter to control the slope of the function during renderingand sampling.
Concurrent to our work, NeuralPatch [5] uses the homography matrix to warp thesource patches adjacent to the reference image to constrain colors in the volume to come from closebypatches.
However, the calculation of patch warping relies on the accurate surface normal, so it cannotbe trained from scratch.
Therefore, it is only used as a fine-tuning or post-processing method forother algorithms to optimize the surface.
We consider VolSDF and NeuS as the current state of theart and we will compare to these two methods.
High-frequency detail reconstruction.
It is generally difficult for neural networks to learn highfrequency information from raw signals.
Inspired by the field of natural language processing,positional encoding [18, 27] is used to guide the network to reconstruct high-frequency details.
Positional encoding spreads the original signal into different frequency bands using sin and cosfunctions of different frequency.
SIREN [26] proposes to use the sin function as activation function.
Park et al.
[22] proposed to use a coarse-to-fine learning strategy to gradually increase high-frequencyinformation, which was subsequently used for pose estimation [16].
Hertz et al.
[10] further proposea spatially adaptive progressive coding strategy.
For surface reconstruction, implicit displacementfields were proposed for single-view 3D reconstruction [15].
Based on the supervision of groundtruth SDF values of sampled points, the method utilizes separate networks to model the base SDF andimplicit displacement fields.
Subsequently, Wang et al.
[32] utilize the SIREN network to learn thebase implicit function and implicit displacement function, respectively, for point cloud reconstructiontasks.
In contrast to our proposed algorithm, these methods require 3D supervision.
Further, theydo not involve the NeRF formulation or volume rendering.
In our work, we build on these ideas todevelop a new state-of-the-art algorithm for multi-view reconstruction.
Method
As input we consider a set of N images I =
{ I 1 , I 2 ...I N } , and their corresponding intrinsic andextrinsic camera parameters
Π = { π 1 , π 2 ...
π N } .
Our goal is to reconstruct a representation of the3D surface S as implicit function.
Specifically, we encode surfaces as signed distance fields.
We willexplain our method in three parts: 1) First, we show how to embed the signed distance function intothe formulation of volume rendering and discuss how to model the relationship between distance andtransparency.
Then, we propose to utilize an additional displacement signed distance functionto add high-frequency details to the base signed distance function.
3) Finally, we observe that thefunction that maps signed distances to transparency is controlled by a parameter s that determinesthe slope of the function.
We propose a scheme to set this parameter s in a spatially varying mannerdepending on the gradient norm of the distance field, rather than keeping it constant for the completevolume within a single training iteration.
3.1 Volume rendering with signed distance functions
We first review the integral formula for volume rendering and derive a relationship between transparency and the weighting function (the product between density and transparency).
Based on thisanalysis we discuss the criteria for functions that are suitable to map signed distances to transparencyand propose a class of functions that fulfill the theoretical requirements.
Given a ray r ( t ) =
o + td , the volume rendering equation is used to calculate the radiance C ofthe pixel corresponding to the ray r .
The volume rendering equation is an integral along the ray andinvolves the following quantities defined for each point in the volume: the volume density σ and the(directional) color c .
In addition, the volume has compact support and the boundaries of the volumeare encoded by t n and t f .
[Equation]
The transparency T ( t ) is derived from the volume density as explained below.
The function T ( t )denotes the accumulated transmittance along the ray from t n to t
[Equation]
and T ( t ) is a monotonic decreasing function with a starting value of T ( t n ) = 1 .
The product
T ( t ) σ ( r ( t )) can be regarded as a weighting function w ( t ) in the volume rendering equation as in
Eq.
In order to involve a signed distance functions f , we have to define a function Ψ to transform asigned distance function so that it can be used to compute the density related terms in the renderingequation.
One way is to directly model a density function σ ( r ( t ))
=
Ψ ( f ( r ( t )))
as proposed by
VOLSDF [30].
Taking this approach, a sampling method is required to satisfy an error bound of thesampling to make it less than an error threshold by gradually reducing the scale parameter.
Anotherway is to model the weighting function w (( t ))
=
Ψ ( f ( r ( t )))
as proposed by NeuS.
The NeuS papershowcases a complex derivation to get the expression for the density function σ .
We rethink this problem to obtain a simplified derivation by focusing on transparency instead of theweighting function and also a better understanding of the problem, as follows:
[Equation]
An interesting observation is that the derivative of the transparency function T ′ ( t ) is the negativeweighting function.
The weighting function has the property of having a maximum on the surface.
We take the derivative of the weighting function and set it to 0 to find the extrema (maxima), asfollows.
[Equation]
Assuming a planar surface and a single ray-plane intersection, we can see that the extremum point,denoted as t s , of the weighting function w ( t ) will also be the extremum point of the derivative ofthe transparency function T ′ ( t ) .
The point t s is expected to be the intersection of the ray and thesurface.
Therefore, we consider defining the transparency function directly as T ( t ) =
Ψ ( f ( r ( t ))) .
If the transparency function is designed in such a way that its derivative T ′ ( t ) reaches a minimumon the surface, it follows that the weighting function has a maximum on the surface.
Therefore, onecan directly model a transparency function under the condition that its derivative has a minimum onthe surface.
This is conceptually simpler than modeling the weighting function w ( t ) as proposed by
NeuS. We compute the derivative of Ψ ( f ( r ( t ))) as follows.
[Equation]
5) where ∇ f ( r ( t )) ·
d is the product of the surface normal and the ray direction, which is a constantin case of a planar surface and a single ray-plane intersection.
The signed distance function is zeroon the surface.
Hence Ψ ′ has an extremum at f = 0 .
This also means Ψ has the steepest slope atthe surface of the shape.
On the other hand, the signed distance function is positive outside of the object, and negative when entering the interior of the object.
We generally assume that t =
t n isoutside so that the signed distance starts positive and decays to a negative value along a ray, which is amonotonic decreasing function.
According to the characteristics of transparency T ( t ) =
Ψ ( f ( r ( t ))) ,the transparency starts at 1 at t = t n and is a monotonic decreasing function to 0 inside the object.
This inverse property results in the Ψ function being a monotonic increasing function from 0 to 1.
Therefore, we have our design criteria for Ψ : Ψ should be a monotonic increasing function from 0 to1, with the steepest slope at 0.
A very intuitive idea to satisfy this criteria is to use a sigmoid function and normalize the functionto have an output in the interval [0 , 1] .
We simply use the logistic sigmoid function proposed by
NeuS [28] for a fair comparison.
However, our idea is more general and other sigmoid functionscould be used.
Our designed transparency function is as follows,
[Equation]
where Ψ s is the logistic sigmoid function with parameter s controlling the slope of the function.
Notethat the parameter s is also the standard deviation of the function Ψ ′ s .
We will use this fact later whendiscussing the adaptive version of the framework.
Given the differentiable transparency function T ( t ) , the volume density σ can be easily calculatedfollowing Eq. 3.
[Equation]
3.2 Implicit displacement field without 3D supervision
In order to enable a multi-scale fitting framework, we propose to model the signed distance functionas a combination of a base distance function and a displacement function [32, 15] along the normal ofthe base distance function.
The implicit displacement function is an additional implicit function.
Thereason for this design is that it is difficult for a single implicit function to learn low-frequency andhigh-frequency information at the same time.
The implicit displacement function can complementthe base implicit function, so that it is easier to learn high-frequency information.
Compared with the task of learning implicit functions from point clouds, reconstructing 3D shapesfrom multiple images makes it more difficult to learn high-frequency content.
We propose to useneural networks to learn frequencies at multiple scales, and to gradually increase the frequencycontent in a coarse-to-fine manner.
Suppose f is the combined implicit function that represents the surface we want to obtain.
Thefunction f b is the base implicit function that represents the base surface.
Following the work [32], thedisplacement implicit function f d ′ is used to map the point x b on the base surface to the surface pointx along the normal n b and vice versa f d is used to map the point x on the base surface to the surfacepoint x b along the normal n b , thus f d ′ ( x b ) = f d ( x ) .
Because of the nature of implicit functions, therelationship between the two functions can be expressed as follows,
[Equation]
where x b = ∇ f b ( x b ) ∥∇ f b ( x b ) ∥ , is the normal of x b on the base surface.
To compute the expression forthe implicit function f , we bring the formula x b = x − f d ′ ( x b ) n b into the Eq.
(8) and obtain theexpression for the combined implicit function:
[Equation]
Therefore, we can use the base implicit function and the displacement implicit function to representthe combined implicit function.
However, two challenges arise.
First, the Eq. 9 is only satisfied ifthe point x is on the surface.
Second, the normal at the point x b is difficult to estimate when onlyknowing the position x .
We rely on two assumption to solve the problem.
One assumption is that thisdeformation can be applied to all iso-surfaces, i.e. f b ( x b ) = f
( x b + f d ′ ( x b ) n b ) = c .
In this waythe equation is assumed to be valid for all points in the volume and not only on the surface.
Anotherassumption is that x b and x are not too far away, thus n b can be replaced with normal n on the point x in the Eq.
We control the magnitude of the implicit displacement function using a displacementconstraint 4 Ψ ′ s ( f b ) .
To precisely control the frequency, we use positional encoding to encode the base implicit functionand the displacement implicit function separately.
We would like to note some differences to [32].
We use positional encoding instead of Siren [26], so that the frequency can be explicitly controlled bya coarse-to-fine strategy better than simply using two Siren networks with two different frequencylevels.
This is useful when 3D supervision is not given.
The details are shown in the supplementary.
Positional encoding decomposes the input position x into multiple selected frequency bands.
[Equation]
where each component consists of a sin and a cos function with different frequency.
[Equation]
Directly learning high-frequency positional encoding makes the network susceptible to noise, becausewrongly learned high-frequencies hinder the learning of low frequencies.
This problem is lesspronounced if 3D supervision is available, however high-frequency information of images is easilyintroduced into the surface generation as noise.
We use the coarse-to-fine strategy proposed by Park etal.
[22] to gradually increase the frequency of the positional encoding.
[Equation]
where α ∈ [0 , 1] is the parameter to control the frequency information involved.
In each iteration, αis increased by 1 /n max until it touches 1, where n max is the maximum number of iterations.
We utilize two kinds of positional encoding γ ( x , α b ) , γ ( x , α d ) with different parameter α b andα d .
We set α b = 0 .
5 α d and only control α d for simplicity.
We also use two MLP functions
MLP b , MLP d for fitting the base and displacement functions.
[Equation]
where n = ∇ f b ( x ) ∥∇ f b ( x ) ∥ that can be computed by the gradient of MLP b and Ψ ′ s ( f b )
=
Ψ ′ s ( MLP b ( γ ( x , α b ))) .
The s of the displacement constraint should be clamped during training.
We show how to control the adaptive s in the supplemental materials.
We bring this implicit function into Eq.
(6) for calculating the transparency so that the radiance (color)ˆ C s of images can be computed by the volume rendering equation.
To train the network, we employ the loss function
L =
L rad + L reg , which includes the radianceloss and the Eikonal regularization loss of the signed distance functions.
For the regularization loss,we constrain both the base implicit function and the detailed implicit function.
[Equation]
3.3 Modeling an adaptivate transparency function
In previous subsections, the transparency function is defined as sigmoid function that is controlledby a scale s .
This parameter controls the slope of the sigmoid function and it is also the standarddeviation of the derivative.
We can also say that it controls the smoothness of the function.
When s islarge, the value of the sigmoid function drops sharply as the position moves away from the surface.
On the contrary, the value decreases smoothly when s is small.
However, choosing a single parameters per iteration gives the same behavior at all spatial locations in the volume.
Since two signed distance functions need to be reconstructed, especially after the high frequency issuperimposed, it is easy to have a situation where the Eikonal equation is not satisfied, that is, thenorm of the gradient of the SDF is not 1 in some positions.
Even with the regularization loss, it isimpossible to avoid this problem.
We propose to use the norm of the gradient of the signed distance field to weight the parameter s ina spatially varying manner.
We increase s when the norm of the gradient along the ray direction islarger than 1.
This means that when the norm of the gradient is greater than 1, the implicit functionchanges more drastically and this indicates a region that should be improved.
Making s larger incertain regions, requires the distance function to be more precise and it magnifies errors due to anincorrect distance function, especially near the surface.
In order to modify the scale s adaptively, wepropose the following equation:
[Equation]
where ∇ f is the gradient of the signed distance function, and K is the number of sampling points, ω iis the normalized Ψ ′ s ( f i ) as the weight and K (cid:80)
[Equation]
While this method can be used to control the transparency function, it can also be used in thehierarchical sampling stage proposed by standard NeRF.
By locally increasing s , more samples willbe generated near the surface where the signed distance values change more rapidly.
This mechanismalso helps to optimization to focus on these regions in the volume.
Experiments
Baselines.
We compare to the following three state-of-the-art baselines: (1)NeuS [28] is the mostrelevant baseline for our work.
We consider it to be the best published method.
(2)VolSDF [30] isconcurrent work to NeuS.
We consider it to be the second best published method.
Overall it alsoperforms very well.
(3)NeRF focuses on image synthesis and is included for completeness.
NeRFis not really a surface reconstruction method and does not reconstruct high quality surfaces, butit is very good in image-based metrics.
We use a threshold of 25 (as proposed by NeuS [28]) toextract surfaces for the comparisons.
For all three methods, we use the default parameters and thenumber of iterations recommended in their respective papers.
We do not include older methods in thecomparison, such as UNISURF [21] or IDR [31], because NeuS and VolSDF have better results.
Datasets.
We conduct experiments on the DTU dataset [11].
We follow previous work and choosethe same 15 models for comparison.
DTU is a multi-view stereo dataset.
Each scene consists of49 or 64 views with 1600 × 1200 resolution.
We further choose 9 challenging scenes from otherdatasets: 6 scenes from the NeRF-synthetic dataset [18] and 3 scenes from BlendedMVS [29](CC-
License).
The image resolution of NeRF synthetic dataset [18] is 800 × 800 and 100 views areprovided for each scene.
The dataset contains objects with very obvious detailed and sharp features,such as the Lego and Microphone scene.
We chose this dataset for the analysis of reconstructions ofhigh-frequency details.
The BlendedMVS dataset is similar to the DTU dataset, but with a richerbackground.
This dataset provides image resolution of 768 × 576.
We also select models withhigh-frequency details or sharp features which are difficult to reconstruct.
In all three datasets, groundtruth surfaces and camera poses are provided.
Evaluation metrics.
To evaluate the quality of the reconstruction, we follow previous work and used
Chamfer distance (lower values are better) and PSNR (higher values are better).
For the DTU dataset,we use the official evaluation protocol, which means computing the mean of accuracy (distance fromthe reconstructed surface to the ground truth surface) and completeness (distance from the groundtruth surface to the reconstructed surface).
For DTU and BlendedMVS, the background is not part ofthe ground truth surface.
Therefore, we remove the background for computing the Chamfer distance,following previous work.
The NeRF-synthetic dataset [18] has no background, so we only removedisconnected parts for all competing methods.
Implementation details.
We use MLPs to model two signed distance functions f b and f d .
Each MLPconsists of 8 layers.
Related work like NeuS [28] and IDR [31] also use MLPs with 8 layers.
We adopt
Adam optimizer with learning rate 5 e − 4 for the network training using NVIDIA TITAN A100 40GBgraphics cards.
For adaptive sampling, we first uniformly sample 64 points on the ray, then calculatethe SDF and its gradient at these points.
We utilize the Eq.
15 to calculate the gain of the s parameter,and then adaptively update the weight according to the gain and sample an additional 64 points. For
[Table] the coarse-to-fine strategy, we observe that using α 0 d = 0 at the beginning for surface reconstructionproduces smoothed results.
We utilize α 0 d = 0 .
5 and α 0 b = 0 .
5 α 0 d = 0 .
25 for both signed distancefunctions.
We set L = 16 for the parameter of the frequency band of positional encoding.
We includecode URL for reference (https://github.com/Anonymous-Authors-Hub/Improved-surfaces.git).
Forother parameter settings, please see the supplemental materials.
Comparison.
In table 1, we show quantitative results with other competitors on 15 scenes of the
DTU dataset [11].
The values shown in the upper part of the table measure the fidelity of the surfacereconstruction, the Chamfer distance.
The numbers indicate that our method significantly outperforms
NeRF.
In most scenes, our method is better than VolSDF and NeuS so that the overall average distanceis also improved.
In the lower part of the table we show the PSNR values.
It can be seen that our
PSNR surpasses all other methods.
We further compare the visual quality achieved by differentmethods.
As shown in Fig.
3, our method can reconstruct high-frequency details.
For example, thewindows have better geometric details, and the feathers of the bird are more distinct.
Most of the scenes in the DTU dataset have smooth surfaces, and high-frequency details are notobvious.
We selected 9 challenging models from the NeRF-synthetic dataset [18] and BlendedMVSdataset [29], which have more high-frequency details.
For example, the Lego model has unevenrepeating bumps, and the power cord of the Mic model has a very thin structure (Fig. 1).
The robotmodel has richer edge and corner features (Fig.
3 second row).
As shown in Table 2, the gap betweenour surface reconstruction quality and that of all other methods widens.
This shows that our methodis especially advantageous for surface reconstructions with high-frequency information.
We canalso observe that NeRF is very good in the image-based metric (PSNR) while performing poorly inthe surface reconstruction metric (Chamfer distance).
This observation is consistent with previouswork.
Compared with the NeRF-Synthetic dataset, the BlendedBMS dataset has a more complexbackground, this also restricts the performance of NeRF to a certain extent.
Besides outperforming [Table] [Table] other baselines in terms of quantitative error, we also achieve better results in terms of qualitativevisual effects.
As shown in Fig.
1, our method can more accurately reconstruct the details of each
Lego block and even some of the tiny holes that are not reconstructed by any other method.
For the
Robot scene, our method can reconstruct more accurate facial contours and sharper horns.
Finally,for the Mic model, our method can clearly reconstruct the power cord, while other methods will messup this structure.
Ablation study.
We verify the influence of different modules on the reconstruction results, includingthe coarse-to-fine module, the implicit displacement function module, and the position-adaptive scontrol module.
In Table 3, “Base ”refers to the baseline method, which is NeuS. "H" means we usehigh-frequency positional encoding.
Here we set L=16 to represent high frequencies. "
C2F" refersto the coarse-to-fine optimization strategy.
We set the initial α to 0.5.
"IDF" represents using theimplicit displacement function in reconstruction.
For each dataset, we chose the mean of the threescenes as the quantitative metric.
From the results of the BlendedMVS dataset, we can observe thatthe divergence of network training can be prevented based on the coarse-to-fine strategy.
From the DTU and NeRF-synthetic datasets, introducing high-frequency directly can easily lead to overfittingon these datasets.
This means that an increase in PSNR cannot guarantee the improvement of thefidelity of surface reconstruction.
Although the coarse-to-fine module can alleviate this mismatchto some degree, it is difficult to further improve the performance.
However, adding the implicitdisplacement function component improves the fidelity of the surface reconstruction and PSNR at thesame time.
During reconstruction, the network with adaptive s can help to improve the reconstructquality upon more complex scenes.
Conclusion
We introduce a new method for multi-view surface reconstruction with high-frequency details.
Wepropose a new derivation to explain the relationship between signed distance and transparency andpropose a class of functions that can be used.
By decomposing the signed distance field into acombination of two independent implicit functions, and using adaptive scale constraints to focus onoptimizing the regions where the implicit function distribution is not ideal, a more refined surfacecan be reconstructed compared to previous work.
The experimental results show that the methodoutperforms the current state of the art in terms of quantitative reconstruction quality and visualinspection.
A current limitation is that this method needs to optimize an additional implicit function,so it requires more computational resources and creates additional coding complexity.
In addition,due to the lack of 3D supervision, we still observe overfitting to the ground truth radiance to someextent.
An interesting direction for future work is to explore reconstruction of scenes under differentlighting modalities.
Finally, we do not expect negative social impacts that will be directly linked toour research.
Negative social impacts of surface reconstruction in general are possible though.
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