Nature-inspired cellular surfaces ( e.g. , Triply Periodic Minimal Surfaces or TPMS) are known as a versatile source of architected material designs for various applications ( e.g. , tissue engineering, mechanical engineering) due to their exceptional geometric and mechanical attributes. However, finding effective geometric modeling methods for those cellular surfaces remains one of the field’s longstanding, fundamental, open research problems. While different strategies, such as parametric, implicit, and boundary methods, have been successfully developed to mimic and approximate those intricate surfaces with nodal coordinates, these mainstream existing approaches can only generate limited types of cellular surfaces due to either topological complexity ( i.e. , high genus) or a limited set of identified functions ( e.g. , implicit functions). Fundamentally, current methods lack a mechanism to approximate complex periodic surfaces using a compact, interpretable basis. Just as Fourier transforms decompose signals into sine waves, our goal is to decompose cellular structures into weighted mixtures of analytic primitives. Thus, in this work, we leverage a deep learning model by introducing a hybrid generative parameterization framework that learns a compact, global representation for 3D Signed Distance fields (SDFs) by projecting complex geometries onto a learned basis of analytic primitives. Our model has employed a 3D convolutional encoder to extract latent features from input SDF volumes and decodes them into physically interpretable parameters, including fill-fraction factors, periodicity exponents, and soft mixture weights, over a list of complex SDF candidate functions. Such a design enables the model to perform spectral approximation of complex structural motifs directly in function space. We evaluated our model on four datasets of synthetic cellular surfaces and TPMS, and our method shows high-fidelity reconstructions. Furthermore, we demonstrate that our neural inference method achieves a ∼ 636x speedup compared to direct parameter optimization, enabling real-time design exploration. Our parametric approach offers an efficient and interpretable parameterization pipeline for CPCS, facilitating downstream tasks in simulation, design optimization, and digital manufacturing of cellular materials. • A novel hybrid implicit representation for complex periodic geometries is proposed. • The model combines a library of analytic primitives with a dual-encoder neural network. • It predicts physically interpretable parameters like fill-fraction, periodicity, and mixture weights. • Achieves high-fidelity reconstruction of complex Cubic Periodic Cellular Surfaces(CPCS). • Demonstrates strong performance on diverse datasets, including Triply Periodic Minimal Surfaces (TPMS).

This paper proposes a sample-wise triple-parametric deep learning framework (TPDLF) for 2D curve parameterization. The proposed framework integrates Bézier, B-spline, and Non-Uniform Rational B-spline (NURBS) curve formulations within a unified neural network architecture, enabling the reconstruction of smooth and closed 2D curves such as real-world airfoil and synthetic Superformula shapes (with n -fold symmetry). An encoder compresses the input curve shape into a latent space, while three distinct decoders untangle the latent space by inferring corresponding governing parameters for each parameterization ( i.e. , Bézier/B-spline/NURBS). The corresponding reconstruction modules are then deployed to ensure smooth curve generation using the governing parameters inferred from the three decoders. The learned governing parameters not only facilitate curve reconstruction but also provide interpretable insights into the underlying geometric structure, reflected by our adjustable post-processing—an interactive graphic user interface (GUI) has been developed to enable manipulating the inferred governing parameters ( e.g. , control points and weights) both manually and precisely for fine-tuning the raw input 2D curve into specified target parameterization (Bézier/B-spline/NURBS) in real-time. The proposed framework demonstrates the effectiveness of combining classical parametric shape modeling with modern deep-learning techniques for advancing shape synthesis and analysis. • Integrating Bézier, B-spline, and NURBS parameterizations within one network. • Ensuring smooth, accurate, closed-curve generation with basis-function layers. • Providing users with real-time, graphical control over inferred parameters. • Sidestepping adversarial training instability and producing interpretable parameters.

Images and videos shot in low light are often accompanied by severe image degradation, such as color noise, chromatic aberrations and loss of details. Most existing convolutional neural network (CNN)-based low-light enhancement methods focus on decomposing the image into illumination and reflection parts via the Retinex model, but these methods often fail to adequately consider controlling noise during enhancement and perform poorly in the face of complex lighting environments. In this letter, we propose a powerful Vision Transformer-based Generative Adversarial Network (Transformer-GAN) for enhancing low-light images. Transformer-GAN consists of two subnets as follows: (1) the feature extraction is achieved by an iterative multi-branch network in the feature extraction subnet, and (2) the enhancement is completed in the image reconstruction subnet. The innovative core works are multi-head multi-covariance self-attention (MHMCA) and Light feature-forward module structures (LFFM) in Transformer-GAN. Experiments demonstrate that our method outperforms state-of-the-art low-light enhancement methods on popular low-light datasets.