NAB: Neural Adaptive Binning for Sparse-View CT reconstruction
Authors: Wangduo Xie
Matthew B. Blaschko
Venue: ICLR 2026 Poster (2026)
Keywords: Binning
Rotation
Reconstruction
Computed Tomography
Primary area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
TL;DR: We propose Neural Adaptive Binning (NAB) method, a novel CT reconstruction algorithm that integrates shape priors via learnable binning-based coordinate encoding, achieving accurate CT reconstruction from sparse views.

Abstract: Computed Tomography (CT) plays a vital role in inspecting the internal structures of industrial objects. Furthermore, achieving high-quality CT reconstruction from sparse views is essential for reducing production costs. While classic implicit neural networks have shown promising results for sparse reconstruction, they are unable to leverage shape priors of objects. Motivated by the observation that numerous industrial objects exhibit rectangular structures, we propose a novel \textbf{N}eural \textbf{A}daptive \textbf{B}inning (\textbf{NAB}) method that effectively integrates rectangular priors into the reconstruction process. Specifically, our approach first maps coordinate space into a binned  vector space. This mapping relies on an innovative binning mechanism based on differences between shifted hyperbolic tangent functions, with our extension enabling rotations around the input-plane normal vector. The resulting representations are then processed by a neural network to predict CT attenuation coefficients. This design enables end-to-end optimization of the encoding parameters---including position, size, steepness, and rotation---via gradient flow from the projection data, thus enhancing reconstruction accuracy. By adjusting the smoothness of the binning function, NAB can generalize to objects with more complex geometries. This research provides a new perspective on integrating shape priors into neural network-based reconstruction. Extensive experiments demonstrate that NAB achieves superior performance on two industrial datasets. It also maintains robust on medical datasets when the binning function is extended to more general expression. The code is available at \url{https://github.com/Wangduo-Xie/NAB_CT_reconstruction}.

Published as a conference paper at ICLR 2026
NAB: NEURAL ADAPTIVE BINNING FOR SPARSE- VIEW CT RECONSTRUCTION
Wangduo Xie, Matthew B. Blaschko
Center for Processing Speech and Images Department of ESAT
KU Leuven
(wangduo. xie, matthew. matthew. bwwschkoo)sssattttt...... .ww.eatt..kluuee....
ABSTRACT
Computed Tomography (CT) plays a vital role inspecting the internal struc- tures of industrial objects. Furthermore, achieving high-quality CT reconstruc- tion from sparse views is essential for reducing production costs. While classic implicit neural networks have shown promising results for sparse reconstruction, they are unable to leverage shape priors of objects. Motivated by the observa- tion that numerous industrial objects exhibit rectangular structures, propose novel Neural Adaptive Binning (NAB) method that effectively integrates rectan- gular priors into the reconstruction process. Specifically, our approach first maps coordinate space into binned vector space. This mapping relies on an innova- tive binning mechanism based on differences between shifted hyperbolic tangent functions, with our extension enabling rotations around the input-plane normal vector. The resulting representations are then processed by a neural network predict CT attenuation coefficients. This design enables end-to-end optimization the encoding via gradient flow from the projection data, thus enhancing reconstruction accu- racy. By adjusting the smoothness of the binning function, NAB can generalize perspec-
ceeunetter-nicludinng position, size, steepness, and rotation-
objects with more complex geometries. This research provides tive on integrating shape priors into neural network-based reconstruction. Exten- sive experiments demonstrate that NAB achieves superior performance industrial datasets. It also maintains robust on medical datasets when the bin- ning function is extended to more general expression. The code is available https: nttps://github com www//om/nnnacccceceeccoc Wangduu Xie/NAB Beep:NAB____eeee CTTreccnstructioon
INTRODUCTION
Computed Tomography (CT), as a high-precision non-destructive testing technology, plays an im- portant role in industrial metrology, quality inspection, and medical diagnosis. Although the CT reconstruction accuracy typically improves with more scan views, acquiring additional views in- creases production costs in industrial environment and radiation exposure medical scenario. Consequently, sparse-view CT reconstruction has become key research problem. Moreover, since reconstruction an ioo-po inverse problem, exploring how to perform CT reconstruction fewer views is also crucial for uncovering deeper mathematical structures.
With the advancement of deep learning, supervised learning has been used to construct pairs of sparse views and dense views to learn their correspondence. However, due to the data offset between the training and testing datasets, such methods often suffer from limited generalization ability. To avoid this problem, Implicit Neural Representations (INRs) have been used for self-supervised CT reconstruction by encoding spatial coordinates into Fourier features, which are then mapped to the attenuation coefficient using neural network, relying solely the object's
projection data.
Despite their success in CT reconstruction, INRs struggle to capture the shape prior presented in in- dustrial CT scans and are fundamentally restricted by its limited harmonic representation. In particu- lar, industrial CT often involves man-made objects with predominantly rectangular structures such bricks, brackets, metal plates. This structure serves powerful prior, yet most existing INR
such

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Ground Truhh
SSM
Fouch
0:100
Fpech 10o
Frach M6
088
0.60
Frech 9000
FANR
7,28
16.57
27,49
36.57
38.25
Gronn Touth
SSI4
Epush
0,050 Epoch 10C
0.357 Epech 300
0.845 Epoch 900
0,395 Epoch 29900
0.942
Figure I: Evolution of adaptive binning during training using our self-supervised method on two different samples (16 views). The reconstructed CT images gradually approach the ground truth.
variants fail to leverage it effectively. To address this, we propose a method that explicitly utilizes this shape prior, enabling more accurate reconstruction. Furthermore, by relaxing the assumption of rectangularity, our algorithm can generalize to broader geometries beyond rectangular forms.
Specifically, instead of encoding each coordinate to the random Fourier features, propose novel scheme named neural adaptive binning (NAB). In this approach, each dimension of the feature vector corresponds specific binning operation over the coordinate plane. To construct the binning operation, we first compute the height difference of the shifted hyperbolic tangent function along one axis. We then apply similar procedure in the orthogonal direction. These difference functions, orientated along different directions, are then combined via Hadamard product to form a localized bin. However, since rectangular regions in the real world usually appear in various orientations rather than being strictly axis axis-aligned, we introduce an affine transformation in the input coordinate space before calculating the difference functions. This allows the resulting bin to be rotated differentiable manner, enabling our model to adaptively capture orientation variations.
Due to the differentiabilityy of the hyperbolic tangent funetion, our binning scheme supports not only rigid body transformation but also scaling transformation. Once the encoding is completed, a neu- ral network maps the binning representation to the attenuation coefficient for reconstruction, as shown in Figure TT To further enhance flexibility, we introduce a multi-scale steepness mechanism that generalizes the rectangular binning to smoother, bulge-like binning structures. The extension enables the framework to reconstruct objects with both rectangular and curved geometries. More- over, we analytically derive the upper bound of the distance between our NAB representation and set of binary vectors, and prove that the steepness approaches infinity, the distance converges to zero. The convergence proof builds a theoretical connection between our NAB and the random binning scheme in kernel methods. In summary, our contributions are as follows:
(1) Our work proposes a novel encoding method, Neural Adaptive Binning (NAB), which ex- plicitly models rectangular priors commonly observed in industrial CT scenarios and offers new perspective on shape-aware representation learning.
O (2) We designed differentiable way that adaptively adjusts the size, position, and rotation of each bin, enabling end-to-end optimization of bin parameters alongside the neural network. Furthermore, we propose multi-scale steepness strategy to accommodate both rectangular and curved structures. Through function approximation analysis, we build a bridge between NAB and random hard bins.
(3) We conduct comprehensive ablation studies analyze the impact of different binning com- ponents in NAB, and perform extensive comparative experiments against leading methods, demon- strating the superior performance our approach.
RELATED WORK
Classic CT reconstruction Classical CT reconstruction techniques can be broadly divided into an- alytical and iterative methods. Among them, FBP (Herman) 2009) is the representative of analytical
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methods. Iterative methods mainly composed of SIRT (Gregor & Benson 2008), SART (An- dersen & Kak 1984), and NAG _L (Nesterov 2013 Neubauer 2017). In addition, there are also iterative methods such Wang & Jiang (2004) y Sidky & Pan (2008). Analytical methods faster but prone to artifacts, while iterative methods are slower but have fewer artifacts.
Self-supervised CT reconstruction Due the generalization problem of supervised methods, self- supervised neural networks have broad prospects in the field of CT reconstruction. Their represen- tatives are deep image prior (DIP) (Ulyanov et al. 2018 Baguer et al., 2020) and implicit neural representation (INR) (Tancik et al. 2020; Sitzmann et al. 2020). The classical INR encodes the coordinates as trigonometric functions, which are then combined by neural network to reconstruct the object. This type of method has achieved good performance in rendering (Mildenhall et al.) 2021 and reconstruction (Niemeyer et al. 2020) in natural scenes. And it has gradually become popular in the field of CT reconstruction. For CT reconstruction tasks, most methods directly use
INRs without external priors (Sun et al. 2021 Zang al.) 2021 Rückert al. 2022 Zha et al.]
2022
Wu et al. 2023b Saragadam et al. 2023
Wu al. 2023a Cai al. 2024). There has been
recent works combining external CT data or material priors into INR (Shen et al. 2022 Gu et al.
2023
Shi et al. 2024 Liu et al., 2024 Liu & Bai 2024 Xie al. 2025 Tian al. 2025 How-
ever, these methods overlook the role of coordinate encoding in unsupervised prior acquisition. In addition, when changing the representation from implicit to explicit, some methods use 3D Gaussian Kerbl et al., 2023) for CT reconstruction (Zha et al.] 2024 Li et al., 2025; Yuluo et al.] 2025) in explicit representation. However, 3D Gaussian- methods lack strong fitting ability compared to neural network, resulting in a loss of accuracy. In addition, restricted to the Gaussian form, they cannot model rectangular patterns explicitly.
MOTIVATION
INRs with Random Fourier Coding (RFC) often generate distinctive wave-like artifacts during construction. The issue arises from two main factors. First, RFC is based on random sampling, which prevents the INR from using object's shape prior. Second, the INR is limited certain combinations of harmonics. An INR with RFC is limited to representing functions of the form: (Ytiee al., 2022
Σ ou sin ((w, r) + Φw)
WE H(R)
Among these, H(2) is limited by the RFC frequency matrix Ω =- 100 ..., 2r which is sam- pled once and fixed before INR training. The restriction takes the following form:
H(L)) c
Σ
8t ZA
ssc Kb-1
Intuitively, training an INR can be regarded as making transitions among the functions that can be represented by Equation Consequently, when the object goes beyond the range specified
Cocrdinate
CT Reconstructod Imagee
Spane vector
Shared Natral
forwand opecator A
Netwerke
Loss
Bizning
Sparso
Sinogram
Figure 2: Our method's overall framework.
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by Equation I artifacts are likely to emerge. Moreover, according the Gibbs phenomenon, overshoot in height inevitably occurs near a jump discontinuity point, even as the number of trigono- metric functions in the approximation approaches infinity. Therefore, to better handle rectangular boundaries in industrial objects, and incorporate the shape prior, we abandon the RFC and instead propose method based adaptive binning coding.
METHODOLOGY
4.1 PARALLEL BINNING DESIGN
200
330
100
(a) Differestable y(c)
(b) Dificrentable p(C)
(c) Difiremiable g(C)
Fixed Fourier coding
Differentiable Binning Features g(c); and its generation way in method (subgraph (a), (b), (c)) and Fixed Fourier Feature in classic INR (subgraph (d)). The @ represents Hadamard product, which will act two 256x256 matrices.
Figure 3:
For any coordinate vector с RN in an N-dimensional coordinate system, our objective to construct a differentiable fE that maps to vector representation Ve. with the explicit purpose of leveraging the industrial object's rectangular prior:
Vcc fE(c)
(3)
However, there is no natural differentiable function that can directly express the prior. To circumvent this challenge, we design square waves along N orthogonal directions. Without loss of generality, we illustrate our method with the case of N = 2. The square waves (c), along the r-axis are constructed as the difference between two shifted hyperbolic tangent functions on the same axis:
== <(c)ese ((C)
where:
(c)teft = Lanhh(ks - ui + h.))
1
(5)
(c)riggtt; Lanh(kilte - (am
2 h:))
(6)
where I, denotes z-axis coordinate of and k; controls the steepness of the tanh function. The parameter u; specifies the center the first parallel shift of the lanh function, while Jh, and - correspond to the distance of the second and third parallel displacement, respectively. An instance of square waves, Y(c).. is depicted in subgraph (a) of Figure By duality, we construct another square wave μ(c), along the orthogonal direction (the y-axis):
p(c); p(c)teft. H(C)right.
where:
p(c)teft, Janni(ka vi +++551) u.))
(8)
((Criight = == Saanh(ki - wx)
(9)
where Me represent the c's y-axis coordinate. Similar to the definition of z-axis direction, Us w and - denotes the center and displacement along the y-axis direction.
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To obtain bin of length h, and width w,. centered at (u,, 24), we take the product of the square waves p(c); and ((c), from the two orthogonal directions:
g(c): = ulc)s (c);
(10)
The visualization of g(c); is shown in subgraph (c) of Figure 3 Until now, a rectangular shape can be approximated by combining multiple bins with adaptive translation and scaling; however, this approach yields suboptimal performance when the object contains oblique rectangular regions. Therefore, we propose a novel rotation embedding strategy Section 4.2
4.2 ROTATION TRANSFORMATION
To relax the restriction that bins must be axis-aligned, generalize the bin's representation g(c); by incorporating rotations with arbitrary angle 0,. The rotated representation thus defined as s(c);
g(c) = (f(c)efft. -ic)ri (f(c)teft, (ichee)))..
(11)
where (c))eef,, and (c)righ,, denote the results of rotating (C))eft, and (c)riigt,, along the nor- mal direction of the input coordinate plane, with the rotation center located at (us, vs):
(c))eft = [Lanh( (kinh((((coss(0)) (iin(O))] u4. vi] + h:))
(12)
(Orright =
-sin(fe)]( - ui ye vi] h+))
(13)
2
Figure Appendix illustrates the rotation of (c)right, at different angles. Similarly, the results
of rotating f(c)tefe, and p(c)righe, around (u4, 24) in the same direction are formulated as follows:
a(c)eese, = (tasn((:((sss(()))) (Os, cos(O.)](z== - us Ve - wz]T + +22u00 ww))
(14)
p(c)right, :=
ttanh (A:(ssinn)))) cos((:)][=== - Us Wl - 2/
2 wi))
(15)
By rotating the different components ua(-) and 7(-) to pa()) and 7()). respectively, we effectively
rotate g(c); around (u,, 04) by angle 0;. yielding ((c); (see Equation (1I.. Differentiable angle A, can be learned during self-supervised CT reconstruction. Finally, by introducing the magnification
(height) factor >; for each bin, the fr(ce in Equation 33 is designed as:
fE(C) ( Asg(c)a..,.Ax(((
(16)
4.3 LIMITING APPROXIMATION OF BINNING
Through the above method, every coordinate e is mapped to vector fE(C). When X; = 1.0, (r( lies close the binary vector set S == {(h,, h,,...,, T E 13] Interestingly, the distance converges to 0 as all K; increase. Specifically, for every the distance between fE(C) and S is controlled by a function fais R + IR whose variables are {ke, us, Vs, wi, h4, 0, 1, 2, M.. M..:
min ZES
[[fe(c) 2111 (ake Us Us wc, h4 0,li 1,2,..
(17)
For any given parameters set {u, ves Wi, h1 O,li 1, M.. fass has the properties:
lim faio( (fhi, Us Vi, wi, h, 0z/i = 1, M)) 0.
(18)
By the squeeze theorem, we know that for every e, the following holds:
lim
min ZES
[[((c) 2111 = 0
(19)
When Equation 19) is enforeed, it guarantees that the bin contains the distinct boundary. As result, fF(C) can represent ideal rectangular bins. This can also be viewed as a type of hard binning feature (Rahimi & Recht 2007), albeit in non-random manner.
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4.4 LINK TO NEURAL NETWORKS
For every e E RRA, we employ neural network /net IR- +
IR to map the adaptive binning
features fr((c) E IR to the CT attenuation coefficient coordinate within the object:
Xe fne((fE(c))
(20)
The overall framework of our algorithm is shown in Figure 2 The loss function during training is calculated on the projection domain:
Loss [|A(X) 2
(21)
Where E H represents the object to be optimized by spreading X. E IR' over the entire coordinate grid according to coordinate c. A IR R represents the forward operator, which is controlled by parameters of imaging geometry and machine configuration with V detector pixels and rotations. Y e URx represents the collected sinogram data.
When minimizing Equation (21), the weights and biases of fnet and differentiable parameter set {)e, k,, G,, U4 U2y h2s will 2, .... .M of fE will updated at the same time.
03
153
153
(4) 8 (Dp steep
(bi 8 (Op, staep
(9 (C), steep
(8) (C) steep
Figure 4: Differentiable Binning Features 3(c);'s 's multi-scale variations with changing steepness k;--
4.5 SHAPE GENERALIZATION
Our method mainly designed rectangular regions commonly encountered in industrial CT. However, the proposed binning function, as approximate bump function, is also capable of rep- resenting more complex geometry. For objects comprising both rectangular and noctrectan geometry, the bin is configured using multi-scale steepness approach that incorporates finer steep- ness levels. Specifically, each k; is taken from the set (pI...,Pyy) which includes both large and small steepness, where ness values lead to different smooth variants. These variants provide rich bases for reconstructing objects. We further validate the effectiveness of the multi-scale mechanism Section which involves a dataset containing regions with non-zero curvature.
denotes the number of scales. As shown in Figure different steep-
5 EXPERIMENTS
5.1 DATASET AND IMPLEMENTATION DETAILS
Dataset We extracted slice from calcium carbonate hollow cube (Schoonhoven al. 2024 and rotated it at 19 different angles to create 19 different phantoms. From these, we generated CT pro- jections from 16, 14, and 12 views for each phantom, respectively, which we refer to as the CaCO3 dataset. In addition, 2017) and generate CT projections with the same view configurations as the CaCO3 dataset, forming the Workpieces dataset. All projections were acquired under parallel-beam geometry. In addition to industrial datasets, we also conducted experiments on medical datasets, the results are shown in Appendix Section A.8
sample 10 slices with diverse structures from the Zeiss data (Klacansky)
Implementation Details Our algorithm based on the PyTorel framework, where the optimizer the Adam algorithm with (81, 12) (0.9, 0.999). The initialization strategy and learning rate

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Published as a conference paper at ICLR 2026
setting described in Appendix Section A.4 and Section A.3 scale steepness values are set to {600, j and for Workpieces dataset, they are set to {25, 50, 75). We use ReLU the activation function in method and fix the length of the adaptive binning feature to 456. A four-layer neural network used in our approaches. Our method stops training epoch 29,99 99990, and we report results both epoch 19,990 and 29,990. The differentiability of the operator A in Equation (21) is implemented using Tomosipo (Hendriksen et al. (2021).
For the CaCO;; dataset, the multi-
5.2 PERFORMANCE COMPARISON
Comparison methods Since most competitive reconstruction methods are based on INRs, we pri- marily compare method with them. Specifically, compare INR INR based on random Fourier feature encoding (Tancik et al. 2020), implemented with a four-layer fully connected net- work (FCN) whose width, depth, and activation function identical those of the FCN in method. In addition, the length of the Fourier features the INR, y is set to 456, the same as our bin encoding length. However, the number of parameters in , is 3 x 10 fewer than in our method. To control the parameters' effect performance, introduce another baseline: INR,, which uses 260 neurons in each hidden layer-resulting in x 10 more parameters than our method.
16
Views!
PSNR SSIM
9.65 0.123
16:60:02244
30.06/0.954
31.31/0.949
46.03 7.999
Views!
25.62/0.899
12 Views!
PSNR /
14.02/0.177
70.748 (4) DIP-TV
26.59/ 0.903
34.15/09799
(5) Ground Truth
(b) FBP
(c) SIRT
(c) INR,
(1) Ours
Figure 5: Reconstruction 12, 14, 16 views the CaCO3 dataset. The best numerical result is marked in red, and the second-best result is marked in blue. Zooming in shows that the comparison methods exhibit edge blurring and distortions, while our method maintains sharp boundaries.
We also compared our method with Sirem, which replaces the activation function in the neural net- work of INR, with a sine function. Furthermore, we compared our method with Sireng, which, consistent with (Sitzmann et al. 2020). does not use positional encoding like Random Fourier Cod- ing. Siren, consists of five layers: 456 neurons in the first hidden layer and 260 neurons in the remaining hidden layers, using sine activation functions. In addition, we include comparisons with leading unsupervised methods, including Instant-NGP (Müller et al. 2022, Zhaa et al. 2022), DIP (Uyanov et al. 2018 Baguer et al., 2020). DIP-TV (Liu et al. 2019 which adds an isotropic TV loss to DIP in the image domain, and Wire (Saragadam al. 2023). as well as classical meth- ods FBP, SIRT, and NAG.S.. For deep-learning based comparative methods that rely on implicit representations, report results at 29,990 epochs, which is equal to method's training epochs. However, for DIP and DIP-TV, we adopt an earlier stopping point than 29,990 epochs, since these methods prone overfitting.

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Published as a conference paper at ICLR 2026
Table I: Numerical results of reconstruction the CaCO3 dataset. "Trainable Params" refers the
total number of trainable parameters. The best result is in bold and the second-best is underlined.
view
14-view
12-wiew
Trainable
Methods
PSNRT
SSIM
PSNR
SSIMT
PSNRT
SSIM
Params
FBP
11.74
0.125
10.68
0.109
9.44
0.095
SIRT
15.64
0.201
15.14
0.195
14.75
0.195
NAG_LS
15.99
0.204
15.48
0.197
15.11
0.196
DIP
22.42
0.673
21.69
0.651
20.89
0.563
1.90 10
DIP-TV
24.05
0.783
21.98
0.703
22.40
0.688
1.90
106
Instant-NGP
30.81
0.953
30.03
0.946
27.23
0.911
2.96 106
Wire
23.80
0.785
23.35
0.752
21.96
0.721
2.65 10
Siren
19.82
0.227
18.34
0.193
16.98
0.164
2.49 10
Siren2
19.64
0.210
18.57
0.186
17.67
0.175
2.56 x 10
1NR,
29.01
0.934
27.10
0.891
25.08
0.854
2.49 x 10
INR
27.94
0.901
25.55
0.831
22.82
0.750
2.55 x 10
INRr,
38.89
0.983
37.83
0.970
30.36
0.901
1,25 x 10
Ours (Iter = 19990)
41.52
0.991
36.09
0,945
30.51
0.853
2.52 x 10S
Ours (Iter 29990)
43.61
0.996
40.07
0.977
34.72
0.888
2.52 10
Since the compared methods exhibit limited performance on the CaCO3 dataset, we additionally evaluate INRtg, an INR based on seven-layer FCN in which each hidden layer has 456 neurons. Notably, INR:, has four times more parameters than our method.
Views:
17.1230.173
14
Views:
PSNR: /SIM
13.48 0.0
33.28/
34.94/0.961
PSNR: SSIM
16.11/0.162
27.98 0.797
34,66 0.942
(a) Ground Truth
(b) FBP
INR,
(d) Ours
Figure 6: Reconstruction at 12, 14, 16 sparse views the Workpieces dataset.
Quantitative evaluation For every method, Table reports the average PSNR/SSIM (Appendix Section A.6) on the CaCO, dataset. With the same FCN architecture, replacing random Fourier encoding with our NAB boosts LNR,, by 9.64 dB, 12.97 dB and 14.60 dB under 12, and 16 view settings, respectively. For INRi, although it has more parameters than our method, its performance remains inferior to our method. When INR,, is expanded to INR which has nearly five times as many parameters
model. method still outperforms it by 4.36 dB, 2.24 dB, and 4.72 dB under 12, 14 and views, respectively. Figure showws that, under both the 14 views and 16 views settings, method is better than INR, and INR,, in almost every epoch.
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For the CaCO, dataset, Instant-NGiP achieved the highest performance in the 12 view SSIM metric, however, it exhibited lower PSNR values than our method across all views. The substantial number of trainable parameters and the limited interpretability remain inherent limitations of the Instant- NGP. comparison, our method has fewer parameters and better interpretability.
For the Workpieces dataset, Table summarizes the performance of different methods. shows that our method exceeds , by 5.39 dB, 1.20 dB and 2.92 dB under 12, 14, and 16 views, re- spectively. For INR;, our method outperforms by an average of 2.82 dB across different settings. The performance improvement on this dataset is smaller than that on the CaCO3 dataset, mainly because the Workpieces dataset contains not only rectangular, but also many curved shapes like ares and circles. Even so, our method still achieves the best reconstruction performance with small number of parameters. Meanwhile, we observe performance reversal the 14 view and 16 view settings for DIP, Instant-NGP, 1N and INR;, where the 14 view results are superior to 16 view configuration. We attribute this phenomenon to the consistent orientation of phantoms the Work- pieces dataset, which introduces a coupling effect between the reconstruction algorithms and their orientation sensitivity. In addition, we find that our method achieves competitive performance while requiring 10k fewer training epochs, showing that it works well with fewer iterations.
Table 2: Numerical results of reconstruction on the Workpieces dataset. "Trainable Params" refers to total number of trainable parameters. The best result bold and the second-best is underlined.
16-view
viww
12-view
Trainable
Methods
PSNR
SSIM
PSNR
SSIM
PSNR
SSIM
Params
FBP
18.12
0.198
15.48
0.165
16.61
0.165
SIRT
22.91
0.385
22.68
0.382
21.04
0.347
NAG_LS
23.29
0.381
23.15
0.373
21.37
0.348
DIP
28.28
0.713
29.41
0.704
25.76
0.625
1.90 10
DIP-TV
33.64
0.918
29.89
0.777
28.20
0.786
1.90 X 106
Instant-NGP
31.17
0.904
31.95
0.914
28.38
0.832
2.96 x 10
Wire
28.77
0.834
28.14
0.796
27.29
0.794
2.65 x 10S
Siren
31.56
0.614
30.03
0.541
29.11
0.564
2.49 x 10
Sirenz
32.70
0.700
31.82
0.639
28.89
0.590
2.56 x 10S
INR,
33.34
0.911
34.03
0.912
27.37
0.787
2.49 105
INR,,
33.89
0.929
34.11
0.926
27.80
0.828
2.55 105
Ours (Iter 19990)
35.70
0.926
34.98
0.927
31.85
0.896
2.52 10
Ours (Iter 29990)
36.26
0.938
35.23
0.941
32.76
0.909
2.52 10
PSNR with Mean Standard Deviation views!
PSMR with Mean and Standard Deviation 11.6 viewes
15-
35-
POUR
POUR
15-
B&c
Mi
0.5
0.5
1.0
2.3 Spoch
2.0
25
3.0
0.5
0.5
3.0
2.0
30
Epoch
Figure 7: Avg. PSNR + std. per epoch on the CaCO3 dataset(14 views and 16 views). Our method outperforms INR, and LNRi, in almost every epoch, while using only 20% of INR;," parameters.

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Qualitative evaluation The qualitative evaluation of reconstruction is shown in Figure and Fig- o Since this paper primarily compares the proposed encoding method and Fourier encoding, the visualization includes two representative instances ("INRy" " and "Ours"). For both instances, the neural network is kept unchanged, and only the encoding method switched from Fourier encoding to NAB. For the CaCO, dataset, our method reconstructs sharp edges with minimal artifacts, while the comparison methods all exhibit blurred edges and distortion. The triangular ripple artifacts of the , illustrate its difficulty in reconstructing rectangular areas. The phenomenon reflects the limitations of random Fourier coding compared to our NAB. In addition, we have included visu- alization comparing I, and our method in the Section A.7 For the Workpieces dataset, we can see that our method not only reconstructs straight edges, but also reconstructs edges with non-zero curvature. Furthermore, our method produces fewer artifacts non-edge areas on this dataset.
5.3 ABLATION STUDY
To verify the effectiveness of the different differentiable parts in our method, we conducted an ablation experi- ment as shown in Table Firstly, the results show that the bin's center location {us, f and bin's side length {he, w are the most important parts. If the algorithm makes them fixed, it will result in a 10+ dB performance degradation. Secondly, the bin's 's ability to rotate is the second most important part. Once the rotation ability is disabled, the average PSNR the entire dataset will decrease by 6.11 dB. Thirdly, the loss of the automatic adjustment of steepness will also affect the final perfor- mance, resulting in a 0.7 dB performance degradation. Finally, the trainability of bin height has only a 0.24 dB impact on performance, suggesting that it is nearly compensated by the subsequent neural network.
Table 3: Ablation study the CaCO3 dataset (16 views). "w/o X means that the component "X" is kept frozen (not updated) during reconstruction, with all other components remaining trainable.
Methods
PSNR1
SSIM
w/o Center Location
29.82
0.901
w/o Side Length
30.82
0.787
w/o Bin Rotation
37.50
0.982
w/o Bin Height
43.37
0.996
w/o Steepness
42.91
0.994
Full setting (Ours)
43.61
0.996
CONCLUSION
This paper proposes a novel CT reconstruction method based on neural adaptive binning (NAB). We design the mathematical model of binning as the difference between two shifted hyperbolic tan- gent functions. By embedding rotational transformations into the bin's ' expression and making the bin's parameters differentiable, we generalize the vanilla bin into flexible binning encoding that can adaptively scale, rotate, and shift to appropriate variations. This encoding can not only capture rectangular patterns but also adjust to shapes with non-zero curvature. After the binning representa- tion, the encoding results are further mapped to CT attenuation coefficients via a subsequent neural network. Under the supervision of projection data, our algorithm can calculate the final CT recon- struction in a self-supervised manner. Furthermore, we prove that the mathematical limits of this encoding result in strict coordinate partitioning and have a close relationship with random hard bins. Extensive experiments on two industrial datasets demonstrate that our method effectively leverages shape priors and achieves superior reconstruction performance. In addition, it also performs robustly on medical datasets when the binning function is generalized to smoother formulation.
ACKNOWLEDGMENTS
We acknowledge funding from the Flemish Government (AI Research Program) and the Research Foundation Flanders (FWO) through project number GOG292IN. We acknowledge the EuroHPC Joint Undertaking for awarding the project ID CHPC-BEN-2025B07--5 070 and EHPC-AIF-202SSC0222
EHPC-BEN-2025B 1- access to the EuroHPC supercomputer LEONARDO, hosted by CINECA (Italy) and the LEONARDO consortium. In addition, the resources and services used in this work were partially provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation Flanders (FWO) and the Flemish Government.
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A APPENDIX
A.1 USAGE OF LARGE LANGUAGE MODELS
We used large language model (LLM) polish the writing and, with assistance from the LLM, completed the plot visualizations.
A.2 LIMITATIONS AND FUTURE WORKS
As part of future work, we plan to evaluate the performance of combining random Fourier encoding with the proposed binning-based approach. Furthermore, we aim to explore the convergence be- havior of our method through the lens the neural tangent kernel (NTK) framework (Jacot et al., 2018
This will help derive theoretical results the training dynamics of our method.
A.3 ROTATION VISUALIZATION
This section is supplement to Section 4.2
13
100
653
390
058
625
030
115
4015
1.00
230
168
133
159
208
100
1.0
100
025
-335
025
203
200
157
100
(e) 0.1 x
(0 0:125 X
(g) 0.15 x
do 0:175 X
Figure 8: Rotation results of the two-dimensional hyperbolic tangent function at different angles.
A.4 INITIALIZATION STRATEGY
This section is supplement to Section 5.1 and Section A.8
For the Neural network fnet 's parameters in our method, we use the network initialization strategy from (Shen al. (022), which the same as that used in (Sitzmann et al., 2020). For binning location parameters {ug 4/} and side length parameters (hs, w. we adopt the initialization strategy of (Li et al. 2025). which was originally designed to determine the Gaussian function's center and length. This initialization provides reasonable starting point for location and length parameter.
Unlike (Li et al. 2025), however, our method does not assume a Gaussian formulation. For the initialization of the rotation angle parameters 0,, sample it from normal distribution:
iid ~ N'0, 0.05²), = 1,1,...... M
0,
(22)
For the initialization of the bin height As we sample it from uniform distribution:
X; iid ((,,)), 1), i 1, ..... .M
(23)
For steepness kG we initialize according to the alternately selection strategy:
k; ((( 1) mod T.) 1}, 1,2, ..., M
(24)
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For the CaCO3, dataset, S is set to (600, 800) and L is set to 2. For the Workpieces dataset, S is set to (25,50 50, 75) and L is set to For the Medical-Axice dataset, set to (4, 6, 8, 12, 14, 16, 18, 20) and L is set 8. The M above represents the number of bins. In approach, the CaCO3 dataset and Workpiece dataset. For the Medical-Axial dataset, which is more complex and contains rectangular structures, increase M to 3000.
=4 for
For the initialization of the random Fourier coding in the comparison method, the element in RFC matrix is sampled independently from (O, 4.0%).
A.5 LEARNING RATE SETTING
This section is supplement to Section 5.1 and Section A.8
For the CaCO; dataset, in the case of sparse reconstruction with 14 and 16 views, the learning rate (Ir) for the neural network fnet is set to 8.0 10-4, The same ir (8.0 10-4) is applied to the binning location parameters {u;, 2 and side length { w,). The for the rotation angle 0, and the steepness k; are both set 1.0 10-4, The Ir for bin height X; is set to 1.0 10-5 For sparse reconstruction with 12 views, all learning rates remain the same as in the other view settings, except for the Ir of rotation angle 0, is increased to 4.0 X 10-
For the Workpiece dataset, in sparse reconstruction with 12 views, 14 views and 16 views, the Ir of the neural network neet set to 7.0 10-1 The Ir assigned the binning location parameters {u, v2) } is 8.0 x 10-1 The Ir for the side length parameters (h4, w;} } is 4.0 x 10-1 The lr assigned the rotation angle 0; specified as 8.0 10-4 The (r for the steepness k; 4.0 10TH The ir for the bin height A, is set to 1.0 X 10-5
For the Medical-Axial dataset, in sparse reconstruction with 48 views, the ir of the neural network faet is set to 2.0 x 10-4 The Ir for the binning location parameters [u,, v, } is 4.0 x 10 10-4. The ir for the side length parameters {h,, w;} is 8.0 x 10 The ir assigned the rotation angle 0, is set to 1.0 x 10-4 The Ir for the steepness k; is 4.0 x 10-5, The Ir for the bin height X; is 8.0 10-1
A.6 EVALUATION METRICS
This section is supplement to Section 5.2
PSNR and SSIM widely used evaluate CT image quality in reconstruction and artifact removal (e.g.. Liao et al. 2019 Reed et al. 2021 Shen et al. 2022] Xie & Blaschko, 2023 Liu et al.) 2023).
The PSNR values reported in Table land Table 2 reters the average PSNR (PSNRavg) in CaCO,
dataset and Workpieces dataset respectively. PSNRavg 's specific calculation formula is as follows:
Nabjact
PSNRavg
Σ
PSNR;
(25)
Notject
where:
MAX;
PSNR; == 10 logıo
, 1,2, ... Notject
(26)
H -
Σ W
y=1 (1,(z,
((x,)))
HW
The Notjeet indicates the number of objects to be reconstructed in the corresponding dataset. H and W represent the length and width of the object to be reconstructed, respectively. 1, represents ith objects' ground truth, and L represents the reconstructed result of the jth object.
Similarly, the SSIM values reported in Table and Table refers the average SSIM (SSIMavg) in CaCO3 dataset and Workpiece dataset respectively:
Nobject
SSIMavg =
SSIM;
(27)
Nobject
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The specific calculation formula of SSIM, is as follows (Wang et al. 2004)
(2pr i + (2) 11, + C2) SSIM, (#ī, 1,, + C1) + of + C2)
(28)
where:
Fr the mean values of 7 over the 8th object
Hj,; the mean values 4 over the tth object
i : the variances of I, over the 8th object
i. the variances of I, over the th object
2
r1,; the covariance between I; and i, over the th object
C1. C2 stabilization constants
For any E f1,2, Nobjecth, PSNR, was computed using the function
peak laak.signas signal moise se ratio from the skimage metrics module in the library (Van der Walt et al. 2014). Similarly, SSIM; was computed using the function deructural.simiie
from the same module.
A.7
MORE VISUAL RESULTS ON CACO3 DATASET
This section is supplement to Section 5.2
16
Views:
PSNR / SSIM
38.49 28.49/0.96 0.985
46.03 / 0.999
12 Views:
PSNR SSIM
21.67 0.777 (b) INR
34.15 /.955 (c) Ours
(a) Ground Truth
Figure 9: Reconstruction at 16 and 12 sparse views the CaCOg dataset. The blue arrows show that the comparison method struggles to accurately reconstruct edges and corner points, whereas our method achieves better results. In addition, the comparison method exhibits wavy artifacts.
We performed visual comparison the CaCO3 dataset under two boundary settings (12 and 16 views). As shown above, although the baseline INR,, has four times more parameters than our method, it produces more wavy artifacts and less sharp boundaries and corners.
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With 16 views, IN achieves performance close ours. However, after zooming in to reveal finer details, corner imperfections and wavy artifacts in flat regions remain visible. Although the comparison is not strictly fair (the neural network of INR;, is larger than ours), it still highlights the advantage of our method.
A.8 ROBUSTNESS ON MEDICAL DATASET
This section is supplement to Section 5.1 and Section 5.2
PSNR SSIM
11.34 00382
31.42 0.882
/ 0.920
PSNR / SSIM (6) Ground Truth
11.32/00377 0.377
31.47/0.879
33.02 15.02.0.900
(6) FBP
(c) INR
(d) Ours
Reconstruction at 48 sparse views on the Medical-Axial dataset. The best numerical result marked in red, and the second-best result is marked in blue. When zooming in, we observe that the comparison method RNR exhibits edge blurring and some non-edge areas are distorted by artifacts, whereas our method produces fewer artifacts and yields cleaner boundaries.
Figure 10:
To verify the robustness this work, we constructed a Medical-Axial dataset comprising 40 differ- ent slices, which are derived from the axial plane of the first four lung volumes in the training set of the Medical Segmentation Decathlon (ntonelli et al. 2022). Specifically, the four lung volumes labeled Lung_001, Lung_003, Lung_004, and Lung_ 005 in the raw data. For each volume, extracted 10 slices at 5-slice intervals starting from the 5th slice (i.c., the slices indexed at 5, 10, 15, ... 50). The projection of the Medical-Axial dataset is obtained from parallel-beand geometry with sparse view under 48 different angles.
To compare performance, we use INR based on RFC baseline. For fair comparison, we ensure that the depth, width, activation function of the FCN, the length of the encoded output vector of the encoder, total number of training epochs, and the optimization method are exactly the same those in our method. Because medical data contains more detailed textures than industrial data, we use ten-layer FCN for both the comparative method and our approach. The initialization strategy and learning rate setting described in Section A.4 and Section A.5 For simplicity, we abbreviate the comparative method as INRREC.
Quantitative evaluation For every method, Table 4 reports the average PSNR/SSIM on the dif- ferent sub-datasets (10 slices from sub-dataset Lung 0011, 10 slices from sub-dataset Lung-003 10 slices from sub-dataset A04, and 10 slices from sub-dataset Lung-005 and whole Medical- Axial dataset. We find that replacing random Fourier encoding with our NAB boosts INR by 0.56 dB in whole Medical-A Axial dataset.
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Table 4: Reconstruction results the whole Medical-Axial dataset and different sub-datasets.
Lung 001
Lung 003
Lung 004
Lung 005
Whole dataset
Methods
PSNR
SSIMT
PSNR1
SSIM
PSNR1
SSIM
PSNR1
SSIMI
PSNR
SSIM
INR
31.82
0,890
34.03
0.882
33.71
0.824
31.34
0,877
32.72
0.868
Ours
33.00
0.909
34.49
0.893
34.25
0.834
31.39
0.886
33.28
0.881
Qualitative evaluation The qualitative evaluation of reconstruction is shown in Figure I0] We found that our method achieves good performance even in medical data with complex shapes that do not contain rectangular objects, and our results do not show wave-like artifacts. This demonstrates that our method is robust on medical dataset.
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Reviews:
[{"review_id": "Kzv1akfh1i", "reviewer": "Reviewer_VTfR", "summary": "The paper proposes a new encoding method used in implicit neural representation, which is learnable and can be used for image with simple structure. The experiments show the proposed method is effectively in sparse view CT reconstruction.", "questions": "What’s the performance of the proposed method with full view or less view (such as 8). \n\nHow to select the hyper parameter M.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The self-supervised method can reconstruct the CT image with high quality.\nMathematical limits of the encoding result was given.", "weaknesses": "The proposed method has not evaluated with complex image. Such as medical image or industrial CT image with complex structure.\n\nIf the method can be adapted to 3D image reconstruction.\n\nFor the propose method needs about 30000 iterations. For the industrial scene，the time costs of proposed method is significantly. The comparison of time costs and iteration number with INR (Random Fourier Features) should be given.\n\nComparison with some other method is necessary, such as data-dirven tight frame method、DIP+TV method, also diffusion based SOTA method, DPS.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "244dj6llsa", "reviewer": "Reviewer_4f2T", "summary": "The paper proposes a neural adaptive binning scheme as an alternative to traditional random Fourier feature coordinate encoding. The scheme not only supports rigid body transformations but also achieves scaling transformations, which enables explicit modeling of the rectangular priors commonly encountered in industrial CT scenarios.", "questions": "1. The authors mention that implicit neural representations with random Fourier coding often produce distinctive wave-like artifacts during reconstruction. However, upon comparing the INR results with the proposed method in Figures 5 and 6, the differences in reconstruction outcomes primarily manifest in the internal smoothness rather than at the edges. In practice, such artifacts can often be mitigated through regularization techniques. The authors are requested to clarify the advantages of their proposed method compared to alternative approaches, such as incorporating Total Variation (TV) regularization [1] into the network architecture.\n\n[1] Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-Shape Priors for Image Segmentation. J. Math. Imaging Vis. 64(6): 625-645 (2022)\n\n2. The results in Table 2 appear unusual, as the INR method shows better performance with 14 views than with 16 views. It seems counterintuitive and requires explanation.\n\n3. The reconstruction results of INR in Figure 6 appear excessively smooth. Could this indicate potential overfitting to the training data?\n\n4. The evaluation on medical datasets should be conducted to validate the robustness.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The proposed Neural Adaptive Binning (NAB) method exhibits strong mathematical interpretability, which provides theoretical guarantees for rectangular priors.", "weaknesses": "The numerical results of the proposed method do not demonstrate irreplaceability, as comparable effects could be achieved through regularization techniques. Additionally, there is a lack of validation in specialized application scenarios.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "O2QF6DFxix", "reviewer": "Reviewer_9B2M", "summary": "This work proposes a new reconstruction method based on implicit neural representations (INR), namely NAB, for industrial CT imaging. The main motivation is that most man-made industrial objects are composed of rectangular structures, while existing INR methods fail to exploit such explicit shape priors, leading to suboptimal performance. To address this issue, the proposed NAB introduces a new encoding strategy, where a hyperbolic tangent function is used to form an adaptive binning operation. With this encoding, the shape prior can be implicitly incorporated into the network optimization, resulting in improved reconstruction quality. The experiments also demonstrate the superiority of the proposed NAB over existing INR methods.", "questions": "Overall, this paper is interesting in its idea and motivation, but the current experimental evaluation is somewhat limited. Therefore, I cannot recommend acceptance in the current version. I would be willing to raise my rating if the above concerns can be properly addressed.", "limitations": "", "rating": 4, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The key motivation and idea of this paper are interesting. Incorporating shape priors is a reasonable way to improve the reconstruction accuracy for industrial CT imaging.\n- The proposed encoding strategy (i.e., the adaptive binning operation) is technically sound.\n- The paper is clearly written and easy to follow.", "weaknesses": "My main concern lies in the experimental evaluation:\n- The compared baselines mainly include the random Fourier encoding, but exclude Instant-NGP [1]. To my knowledge, Instant-NGP is much more powerful than random Fourier encoding in various inverse problems, such as CT or MRI.\n- In Table 1, the $INR_{l_1}$ performs worse than $INR_f$, which is a bit strange since the former has more learnable parameters.\n- The random Fourier encoding has two key hyperparameters, the mean and the standard deviation, which strongly affect its learning capacity. However, these hyperparameters are not reported in the paper.\n- From Figures 5 and 6, the objects from the Workpieces dataset have more complex shapes than those from the CaCO3 dataset. However, the improvement achieved by NAB on the Workpieces dataset is relatively small. Does this indicate that NAB does not perform well on more complex objects?\n- In Table 2, the results of $INR_{l_2}$ are missing.\n- In Figures 5 and 6, the qualitative results of the second-best method ($INR_{l_2}$) are also missing.\n\n[1] Müller, Thomas, et al. \"Instant neural graphics primitives with a multiresolution hash encoding.\" ACM transactions on graphics (TOG) 41.4 (2022): 1-15.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "n6brq0ARWP", "reviewer": "Reviewer_J6rB", "summary": "The paper offers a clear shape-aware alternative to RFC-based INRs by constructing trainable, rotated bins that better match industrial rectangular priors. Instead of random Fourier features in INRs, NAB encodes each spatial coordinate via differentiable rectangular bins formed by differences of shifted tanh functions along two axes, with learnable translation, scale, rotation, height, and steepness. A small FCN maps these bin features to attenuation values, and training minimizes projection-domain MSE with a differentiable forward operator. The authors analyze a limiting property showing convergence of the soft bins toward hard binary partitions as steepness increases. Experiments report sizeable PSNR/SSIM gains over DIP, Wire, and several INR variants, plus ablations on bin parameters.", "questions": "- **On initialization of the neural network.**  \n  The appendix states: “For the neural network $f_{\\text{net}}$’s parameters, we use the initialization strategy from (Shen et al., 2022).” This is unclear. In NeRP, initialization encodes temporal similarity of the same object. How is this strategy adapted in the current paper? Please clarify how the initialization is performed here.\n\n- **On relation to 3D Gaussian representations.**  \n  The proposed shape-aware rectangular encoding appears conceptually similar to explicit 3D Gaussian representations, except that rectangles replace Gaussian ellipsoids. Could the authors add **3D Gaussian representation** as a baseline to directly compare their relative performance?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- **Shape-aware coordinate encoding.**  \n  The paper proposes a shape-aware coordinate encoding scheme tailored to the geometric characteristics of industrial components, effectively leveraging rectangular priors common in real-world applications. For non-canonical rectangles, the model introduces learnable rotation parameters to handle arbitrary orientations, providing greater flexibility. The integration of **multi-scale steepness** further extends the representation from sharp-edged rectangles to smooth, bulge-like bins, enhancing expressiveness.\n\n- **Novel prior design for INR tasks.**  \n  Incorporating a shape-aware prior into the coordinate encoding stage of an implicit neural representation (INR) is both meaningful and underexplored. This design introduces a new perspective for geometry-adaptive representation learning and offers potential inspiration for future INR-based industrial CT research.", "weaknesses": "- **Limited dataset diversity and realism.**  \n  The evaluation is conducted on only two simulated datasets—**CaCO₃** and **Workpieces**—both of which are relatively simple. The CaCO₃ dataset lacks geometric complexity, and the Workpieces dataset includes only a small number of slices. It would strengthen the paper to include experiments on more complex real-world components and on real projection data.\n\n- **Narrow baseline selection.**  \n  The comparative baselines are limited to several RFC-based MLP variants. Given that this paper focuses on a specific industrial CT application, it would be more convincing to include comparisons with **advanced INR methods** such as **SIREN** [1] and **InstantNGP** [2], which are now standard benchmarks for implicit representation learning.\n---\nOverall, the paper presents an interesting idea with potential impact. However, the experimental validation is not sufficiently thorough. The choice of baselines lacks persuasiveness, and the datasets used appear overly simplistic. Providing more rigorous and comprehensive experiments would considerably strengthen the paper and make the results more convincing. I would be open to reconsidering my assessment if the authors can present more substantial empirical evidence in a future revision.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)