MorphOPC: Advancing Mask Optimization with Multi-scale Hierarchical Morphological Learning

Chen Wang; Gi-joon Nam; Hua Xiang; Jinjun Xiong; Lei Zhuang; Ruiyang Qin; Yuting Hu

arxiv: 2605.12528 · v1 · pith:4KALGOSHnew · submitted 2026-04-13 · 💻 cs.CV · cs.AI· cs.AR

MorphOPC: Advancing Mask Optimization with Multi-scale Hierarchical Morphological Learning

Yuting Hu , Lei Zhuang , Chen Wang , Ruiyang Qin , Hua Xiang , Gi-joon Nam , Jinjun Xiong This is my paper

Pith reviewed 2026-05-14 21:10 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.AR

keywords optical proximity correctionmask optimizationmorphological operationsmulti-scale neural networkslithographygenerative modelssemiconductor manufacturing

0 comments

The pith

A neural model learns optimal photomasks by sequencing morphological operations on local layout features.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tries to establish that reformulating mask generation as a sequence of morphological operations on local features of the circuit layout enables a multi-scale hierarchical neural network to learn the geometric transformations required for optical proximity correction. Standard encoder-decoder models often miss these transformations and produce suboptimal masks, so the new approach builds specialized modules to handle dilation, erosion and similar shape adjustments at different scales. If the claim holds, the result is a faster machine-learning surrogate for traditional OPC that delivers higher pattern fidelity on the wafer and lower manufacturing costs. A reader would care because shrinking feature sizes in chips make accurate pattern transfer harder, and better OPC directly affects yield and production speed in semiconductor fabrication.

Core claim

MorphOPC formulates mask generation as a sequence of morphological operations on local layout features and introduces a multi-scale hierarchical model with neural morphological modules to learn the transformations from target layouts to optimal masks.

What carries the argument

Multi-scale hierarchical architecture whose neural morphological modules apply sequences of shape operations such as dilation and erosion to local layout features.

If this is right

Higher printing fidelity than prior methods on edge-based OPC and ILT benchmarks for both metal and via layers.
Lower manufacturing cost while maintaining or improving pattern accuracy.
Scalable performance across multiple layout types without requiring full physical simulation at every step.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same morphological-module idea could be tested on other inverse problems such as source-mask optimization or resist modeling.
Hybrid systems that feed the neural output into a fast lithography simulator might close any remaining accuracy gap.
If the learned operations prove robust, they could reduce reliance on hand-crafted correction rules in production flows.

Load-bearing premise

The premise that the needed mask corrections can be expressed and learned as sequences of basic shape-expanding and shape-shrinking operations applied to parts of the layout pattern.

What would settle it

A test on a new set of benchmarks with smaller feature sizes or different layer types in which MorphOPC produces lower printing fidelity than the current best methods.

Figures

Figures reproduced from arXiv: 2605.12528 by Chen Wang, Gi-joon Nam, Hua Xiang, Jinjun Xiong, Lei Zhuang, Ruiyang Qin, Yuting Hu.

**Figure 2.** Figure 2: Illustration of MorphOPC architecture. can be interpreted as the compositional result of a sequence of different dilation and erosion operations applied to the local target features. Through appropriate combinations of dilation and erosion, morphological operators can capture and manipulate structural patterns that are highly relevant to mask optimization. This structural bias makes morphology particularl… view at source ↗

**Figure 3.** Figure 3: Views of morphological outputs relative to the input [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Test result visualization. Rows correspond to ten test cases from (a) the ICCAD 2013 benchmark, and (b) the MaskOpt [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Average running time on ICCAD 2013 benchmark. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

read the original abstract

As feature sizes shrink to the nanometer scale, accurately transferring circuit patterns from photomasks to silicon wafers becomes increasingly challenging. Optical proximity correction (OPC) is widely used to ensure pattern fidelity and manufacturability. Recent generative mask optimization models based on encoder-decoder architecture can synthesize near-optimal masks, serving as fast machine learning (ML) surrogates for traditional OPC. However, these models often fail to capture the geometric transformations from target layouts to mask patterns, leading to suboptimal quality. In this work, we formulate mask generation as a sequence of morphological operations on local layout features and propose \textit{MorphOPC}, a multi-scale hierarchical model with neural morphological modules to learn these transformations. Experiments on edge-based OPC and ILT benchmarks across metal and via layers show that \textit{MorphOPC} consistently outperforms state-of-the-art methods, achieving higher printing fidelity and lower manufacturing cost, demonstrating strong potential for scalable mask optimization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

MorphOPC swaps standard encoder-decoder setups for multi-scale neural morphological modules to model mask generation as learned geometric operations, and the benchmarks show steady gains over prior generative OPC work.

read the letter

The new piece is the explicit framing of mask optimization as a stack of morphological operations on local layout features, handled by a hierarchical neural architecture instead of generic generative models. That choice targets the geometric transformations that the abstract says encoder-decoder approaches miss, and the paper tests it directly on edge-based OPC and ILT tasks for metal and via layers. The reported results are consistent outperformance in printing fidelity and manufacturing cost, which is the practical payoff in nanometer lithography. The empirical setup looks clean on the surface: external benchmarks, no obvious self-fitting, and a clear claim that the morphological modules capture the needed transformations better. Credit to the authors for keeping the evaluation focused on standard OPC metrics rather than inventing new ones. The soft spot is the level of detail available so far. The abstract does not spell out the exact module design, the scale hierarchy, or the ablation controls that would show whether the morphological formulation is doing the heavy lifting or whether the gains come from training tricks and capacity. Without those, it is hard to judge how robust the improvement is when the layout distribution shifts. The central assumption—that local morphological steps suffice to learn the full target-to-mask mapping—holds up in the reported numbers but would benefit from more dissection in the full text. This is a paper for the computational lithography crowd and for groups applying structured ML to manufacturing constraints. A reader already working on OPC or ILT will pick up a concrete architecture and fresh numbers to compare against. It is coherent on its own terms and the claims are falsifiable on the same benchmarks, so it clears the bar for a serious referee. I would send it out rather than desk-reject, with the expectation that the authors supply the missing ablations and implementation specifics.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes MorphOPC, a multi-scale hierarchical model that formulates mask generation for optical proximity correction (OPC) as a sequence of morphological operations on local layout features. Neural morphological modules are introduced to learn geometric transformations from target layouts to optimal masks. Experiments on edge-based OPC and ILT benchmarks across metal and via layers are reported to show consistent outperformance over state-of-the-art methods in printing fidelity and manufacturing cost.

Significance. If the reported outperformance holds under detailed scrutiny, the work offers a structured inductive bias via morphological operations that could improve upon standard encoder-decoder architectures for mask optimization, potentially enabling faster and more accurate surrogates for traditional OPC in nanometer-scale lithography. The evaluation on standard benchmarks for both metal and via layers provides a reasonable testbed, and the modeling choice of hierarchical morphological modules is a clear contribution worth exploring further.

major comments (2)

[Experiments] Experiments section: the central claim of consistent outperformance on benchmarks is load-bearing for the paper's contribution, yet the description provides no quantitative tables, specific baseline methods (e.g., which encoder-decoder or ILT solvers), exact metric definitions for printing fidelity and manufacturing cost, or ablation results isolating the multi-scale hierarchy and neural morphological modules. Without these, it is impossible to verify robustness against post-hoc choices or benchmark construction details.
[Method] Method section on neural morphological modules: the formulation assumes these modules can accurately capture required geometric transformations, but no details are given on differentiability of the morphological operations, the precise multi-scale fusion mechanism, or any constraints on receptive fields that would ensure the hierarchy actually learns scale-specific features rather than defaulting to generic convolutions.

minor comments (2)

[Abstract] Abstract: the phrase 'lower manufacturing cost' is used without a parenthetical definition or reference to the specific cost model; adding this would improve clarity for readers unfamiliar with OPC metrics.
[Introduction] Notation: the term 'neural morphological modules' is introduced without an explicit equation or diagram reference in the initial description; a short formal definition or pointer to the relevant figure would aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comments point by point below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Experiments] Experiments section: the central claim of consistent outperformance on benchmarks is load-bearing for the paper's contribution, yet the description provides no quantitative tables, specific baseline methods (e.g., which encoder-decoder or ILT solvers), exact metric definitions for printing fidelity and manufacturing cost, or ablation results isolating the multi-scale hierarchy and neural morphological modules. Without these, it is impossible to verify robustness against post-hoc choices or benchmark construction details.

Authors: We agree that the experiments section requires more detailed quantitative support. In the revised manuscript, we will add comprehensive tables reporting results on the edge-based OPC and ILT benchmarks for both metal and via layers. We will explicitly list the baseline methods (including specific encoder-decoder architectures and ILT solvers), provide exact metric definitions (e.g., edge placement error for printing fidelity and process variation band area for manufacturing cost), and include ablation studies isolating the multi-scale hierarchy and neural morphological modules. These additions will enable direct verification of the outperformance claims. revision: yes
Referee: [Method] Method section on neural morphological modules: the formulation assumes these modules can accurately capture required geometric transformations, but no details are given on differentiability of the morphological operations, the precise multi-scale fusion mechanism, or any constraints on receptive fields that would ensure the hierarchy actually learns scale-specific features rather than defaulting to generic convolutions.

Authors: We acknowledge the need for greater technical detail. In the revised method section, we will specify that differentiability is achieved via soft morphological approximations with continuous relaxations for erosion and dilation operations. We will describe the multi-scale fusion mechanism as a hierarchical aggregation using progressive upsampling and feature concatenation across scales. We will also detail the receptive field constraints, where each level employs dilated convolutions with scale-specific kernel sizes to enforce learning of geometric transformations at distinct resolutions rather than generic convolutions. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents MorphOPC as an empirical neural architecture for mask optimization, formulating the task as learning morphological operations via multi-scale modules and validating via experiments on standard OPC/ILT benchmarks. No equations, derivations, or self-citations are shown that reduce the central claims to fitted inputs or prior self-referential results by construction. The approach is self-contained against external benchmarks with no load-bearing self-definition or prediction-by-fit.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review based on abstract only; the central claim rests on the domain assumption that morphological operations suffice to model layout-to-mask transformations and that the neural modules can learn them from data.

axioms (1)

domain assumption Mask generation can be formulated as a sequence of morphological operations on local layout features
Explicitly stated in the abstract as the modeling choice for the problem.

invented entities (1)

Neural morphological modules no independent evidence
purpose: To learn geometric transformations in a hierarchical multi-scale manner
New component introduced in the proposed MorphOPC model

pith-pipeline@v0.9.0 · 5472 in / 1218 out tokens · 29676 ms · 2026-05-14T21:10:11.949768+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

35 extracted references · 35 canonical work pages

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[1] [1]

Ahmed Awad, Atsushi Takahashi, Satoshi Tanaka, and Chikaaki Kodama. 2014. A fast process variation and pattern fidelity aware mask optimization algorithm. In2014 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, 238–245

work page 2014

[2] [2]

Shayak Banerjee, Zhuo Li, and Sani R Nassif. 2013. ICCAD-2013 CAD contest in mask optimization and benchmark suite. In2013 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, 271–274

work page 2013

[3] [3]

Hu Cao, Yueyue Wang, Joy Chen, Dongsheng Jiang, Xiaopeng Zhang, Qi Tian, and Manning Wang. 2022. Swin-unet: Unet-like pure transformer for medical image segmentation. InEuropean conference on computer vision. Springer, 205– 218

work page 2022

[4] [4]

Guojin Chen, Wanli Chen, Yuzhe Ma, Haoyu Yang, and Bei Yu. 2020. DAMO: Deep agile mask optimization for full chip scale. InProceedings of the 39th International Conference on Computer-Aided Design. 1–9

work page 2020

[5] [5]

Guojin Chen, Haoyu Yang, Haoxing Mark Ren, Bei Yu, and David Z Pan. 2024. Differentiable edge-based opc. InProceedings of the 43rd IEEE/ACM International Conference on Computer-Aided Design. 1–9

work page 2024

[6] [6]

GL-T Chiu and Jane M Shaw. 1997. Optical lithography: introduction.IBM Journal of Research and Development41, 1.2 (1997), 3–6

work page 1997

[7] [7]

Puneet Gupta, Fook-Luen Heng, and Mark A Lavin. 2004. Merits of cellwise model-based OPC. InDesign and Process Integration for Microelectronic Manufac- turing II, Vol. 5379. SPIE, 182–189

work page 2004

[8] [8]

Robert M Haralick, Stanley R Sternberg, and Xinhua Zhuang. 1987. Image analysis using mathematical morphology.IEEE transactions on pattern analysis and machine intelligence4 (1987), 532–550

work page 1987

[9] [9]

Yuting Hu, Lei Zhuang, Hua Xiang, Jinjun Xiong, and Gi-Joon Nam. 2025. MaskOpt: A Large-Scale Mask Optimization Dataset to Advance AI in Integrated Circuit Manufacturing.arXiv preprint arXiv:2512.20655(2025)

work page arXiv 2025

[10] [10]

Ningning Jia and Edmund Y Lam. 2010. Machine learning for inverse lithography: using stochastic gradient descent for robustphotomask synthesis.Journal of Optics12, 4 (2010), 045601

work page 2010

[11] [11]

Bentian Jiang, Lixin Liu, Yuzhe Ma, Hang Zhang, Bei Yu, and Evangeline FY Young

work page

[12] [12]

InProceedings of the 39th International Conference on Computer-Aided Design

Neural-ILT: Migrating ILT to neural networks for mask printability and complexity co-optimization. InProceedings of the 39th International Conference on Computer-Aided Design. 1–9

work page

[13] [13]

Jian Kuang, Wing-Kai Chow, and Evangeline FY Young. 2015. A robust approach for process variation aware mask optimization. In2015 Design, Automation & Test in Europe Conference & Exhibition (DATE). IEEE, 1591–1594

work page 2015

[14] [14]

Xiaoxiao Liang, Yikang Ouyang, Haoyu Yang, Bei Yu, and Yuzhe Ma. 2024. RL- OPC: Mask Optimization With Deep Reinforcement Learning.IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems43, 1 (2024), 340–351. doi:10.1109/TCAD.2023.3309745

work page doi:10.1109/tcad.2023.3309745 2024

[15] [15]

Xu Ma and Gonzalo R Arce. 2011. Pixel-based OPC optimization based on conjugate gradients.Optics express19, 3 (2011), 2165–2180

work page 2011

[16] [16]

2008.Fundamental principles of optical lithography: the science of microfabrication

Chris Mack. 2008.Fundamental principles of optical lithography: the science of microfabrication. John Wiley & Sons

work page 2008

[17] [17]

2013.Mathematical morphology: from theory to applications

Laurent Najman and Hugues Talbot. 2013.Mathematical morphology: from theory to applications. John Wiley & Sons

work page 2013

[18] [18]

David M Pawlowski, Liang Deng, and Martin DF Wong. 2007. Fast and accurate OPC for standard-cell layouts. In2007 Asia and South Pacific Design Automation Conference. IEEE, 7–12

work page 2007

[19] [19]

Amyn Poonawala and Peyman Milanfar. 2007. Mask design for optical mi- crolithography—an inverse imaging problem.IEEE Transactions on Image Pro- cessing16, 3 (2007), 774–788

work page 2007

[20] [20]

Jiacheng Ruan, Jincheng Li, and Suncheng Xiang. 2024. Vm-unet: Vision mamba unet for medical image segmentation.ACM Transactions on Multimedia Comput- ing, Communications and Applications(2024)

work page 2024

[21] [21]

2017.Image processing and mathematical morphology: fundamentals and applications

Frank Y Shih. 2017.Image processing and mathematical morphology: fundamentals and applications. CRC press

work page 2017

[22] [22]

Frank Y Shih and Owen Robert Mitchell. 2002. Threshold decomposition of gray-scale morphology into binary morphology.IEEE Transactions on Pattern Analysis and Machine Intelligence11, 1 (2002), 31–42

work page 2002

[23] [23]

Frank Y Shih, Yucong Shen, and Xin Zhong. 2019. Development of deep learn- ing framework for mathematical morphology.International Journal of Pattern Recognition and Artificial Intelligence33, 06 (2019), 1954024

work page 2019

[24] [24]

Huang-Chia Shih and En-Rui Liu. 2016. Automatic reference color selection for adaptive mathematical morphology and application in image segmentation. IEEE transactions on Image Processing25, 10 (2016), 4665–4676

work page 2016

[25] [25]

Alexander Starikov. 2003. Design and Process Integration for Microelectronic Manufacturing II: 26-28 February 2003, Santa Clara, California, USA. SPIE- International Society for Optical Engineering

work page 2003

[26] [26]

Shuyuan Sun, Fan Yang, Bei Yu, Li Shang, and Xuan Zeng. 2023. Efficient ILT via multi-level lithography simulation. In2023 60th ACM/IEEE design automation conference (DAC). IEEE, 1–6

work page 2023

[27] [27]

Kevin Trebing, Tomasz Sta`nczyk, and Siamak Mehrkanoon. 2021. SmaAt-UNet: Precipitation nowcasting using a small attention-UNet architecture.Pattern Recognition Letters145 (2021), 178–186

work page 2021

[28] [28]

Haoyu Yang, Shuhe Li, Yuzhe Ma, Bei Yu, and Evangeline FY Young. 2018. GAN- OPC: Mask optimization with lithography-guided generative adversarial nets. In Proceedings of the 55th Annual Design Automation Conference. 1–6

work page 2018

[29] [29]

Haoyu Yang, Zongyi Li, Kumara Sastry, Saumyadip Mukhopadhyay, Anima Anandkumar, Brucek Khailany, Vivek Singh, and Haoxing Ren. 2022. Large scale mask optimization via convolutional fourier neural operator and litho-guided self training.arXiv preprint arXiv:2207.04056(2022)

work page arXiv 2022

[30] [30]

Haoyu Yang and Haoxing Ren. 2025. Gpu-accelerated inverse lithography to- wards high quality curvy mask generation. InProceedings of the 2025 International Symposium on Physical Design. 42–50

work page 2025

[31] [31]

Yixin Yang, Kexuan Liu, Yunhui Gao, Chen Wang, and Liangcai Cao. 2025. Ad- vancements and challenges in inverse lithography technology: a review of arti- ficial intelligence-based approaches.Light: Science & Applications14, 1 (2025), 250

work page 2025

[32] [32]

Frederic Zana and J-C Klein. 2001. Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation.IEEE transactions on image processing10, 7 (2001), 1010–1019

work page 2001

[33] [33]

Weiguo Zhang, Dan Shi, and Xiaoqiang Yang. 2015. An improved edge detection algorithm based on mathematical morphology and directional wavelet transform. In2015 8th International Congress on Image and Signal Processing (CISP). IEEE, 335–339

work page 2015

[34] [34]

Su Zheng, Yuzhe Ma, Bei Yu, and Martin DF Wong. 2024. EMOGen: Enhancing mask optimization via pattern generation. InProceedings of the 61st ACM/IEEE Design Automation Conference. 1–6

work page 2024

[35] [35]

Su Zheng, Haoyu Yang, Binwu Zhu, Bei Yu, and Martin Wong. 2023. Lithobench: Benchmarking ai computational lithography for semiconductor manufacturing. Advances in Neural Information Processing Systems36 (2023), 30243–30254. 9

work page 2023