Multimodal Large Language Models (MLLMs) largely lag human-level performance on abstract visual reasoning (AVR), which requires models to infer latent rules from visual question sets and generalize them to novel scenarios. Most AVR benchmarks are constrained to narrow and repetitive 2D patterns, involving relatively simple spatial relationships and assessing limited dimensions of reasoning ability. Drawing inspiration from real-world paper folding challenges, we propose Paper Folding Puzzles (PFP), a rigorously designed benchmark specifically developed to assess spatial reasoning capabilities. It comprises 150K visual question-answering samples across five diverse tasks, ranging from basic 2D geometric reasoning to 3D spatial understanding. The developed benchmark dataset can be employed to assess core spatial reasoning abilities essential to human cognition, encompassing fundamental symmetry reasoning and 3D spatial comprehension. Furthermore, we conduct a comprehensive evaluation of 18 leading MLLMs (both closed- and open-source variants) on the PFP benchmark to assess their spatial reasoning capabilities. Our findings show that most MLLMs achieve near-chance performance on FPF, exhibiting substantial performance gaps (>30%) relative to human baselines across all tasks. This highlights a critical research gap in improving spatial reasoning capabilities of MLLMs.

Learning discriminative point-wise features is critical for partially overlapping point cloud registration. In recent years, the integration of a Transformer into point cloud feature representation has demonstrated remarkable success, which typically involves a self-attention module to learn intra-point-cloud features, followed by a cross-attention module for feature exchange between input point clouds. Transformer models mainly benefit from the use of self-attention to capture the global correlations in feature space. However, the global correlations involved in self-attention may not only result in a significant amount of redundant computational overhead but also introduce feature ambiguities, especially in low-overlap scenarios. This is because overlapping regions of point clouds typically do not span a wide range but are rather concentrated around a localized area. Therefore, the correlations with an extensive range of non-overlapping points are ineffective and may degrade the discriminability of features. To address this issue, we present a E fficient P rior- E mbedded A ttention L earning model ( E fficientPEAL). By incorporating overlap prior to the learning process, the point clouds are divided into two parts. One part includes points lying in the putative overlapping region and the other includes points located in the putative non-overlapping region. Then, EfficientPEAL performs localized attention with the putative overlapping points. The proposed attention module significantly reduces the computational complexity of the model while achieving competitive performance. Extensive experiments on 3DMatch/3DLoMatch, ScanNet, and KITTI datasets demonstrate its effectiveness.

Typically, relief generation from an input 3D scene is limited to either bas-relief or high-relief modeling. This paper presents a novel unified scheme for synthesizing reliefs guided by the geometric texture richness of 3D scenes; it can generate both basand high-reliefs. The type of relief and compression coefficient can be specified according to the user’s artistic needs. We use an energy minimization function to obtain the surface reliefs, which contains a geometry preservation term and an edge constraint term. An edge relief measure determined by geometric texture richness and edge z -depth is utilized to achieve a balance between these two terms. During relief generation, the geometry preservation term keeps local surface detail in the original scenes, while the edge constraint term maintains regions of the original models with rich geometric texture. Elsewhere, in highreliefs, the edge constraint term also preserves depth discontinuities in the higher parts of the original scenes. The energy function can be discretized to obtain a sparse linear system. The reliefs are obtained by solving it by an iterative process. Finally, we apply non-linear compression to the relief to meet the user’s artistic needs. Experimental results show the method’s effectiveness for generating both bas- and high-reliefs for complex 3D scenes in a unified manner.

This paper presents SymmSketch—a system for creating symmetric 3D free-form shapes from 2D sketches. The reconstruction task usually separates a 3D symmetric shape into two types of shape components, that is, the self-symmetric shape component and the mutual-symmetric shape components. Each type can be created in an intuitive manner. Using a uniform symmetry plane, the user first draws 2D sketch lines for each shape component on a sketching plane. The z -depth information of the hand-drawn input sketches can be calculated using their property of mirror symmetry to generate 3D construction curves. In order to provide more freedom for controlling the local geometric features of the reconstructed free-form shapes (e.g., non-circular cross-sections), our modeling system creates each shape component from four construction curves. Using one pair of symmetric curves and one pair of general curves, an improved cross-sectional surface blending scheme is applied to generate a parametric surface for each component. The final symmetric free-form shape is progressively created, and is represented by 3D triangular mesh. Experimental results illustrate that our system can generate complex symmetric free-form shapes effectively and conveniently.

In the area of 3D digital engineering and 3D digital geometry processing, shape simplification is an important task to reduce their requirement of large memory and high time complexity. By incorporating the content-aware visual salience measure of a polygonal mesh into simplification operation, a novel feature-aware shape simplification approach is presented in this paper. Owing to the robust extraction of relief heights on 3D highly detailed meshes, our visual salience measure is defined by a center-surround operator on Gaussian-weighted relief heights in a scale-dependent manner. Guided by our visual salience map, the feature-aware shape simplification algorithm can be performed by weighting the high-dimensional feature space quadric error metric of vertex pair contractions with the weight map derived from our visual salience map. The weighted quadric error metric is calculated in a six-dimensional feature space by combining the position and normal information of mesh vertices. Experimental results demonstrate that our visual salience guided shape simplification scheme can adaptively and effectively re-sample the underlying models in a feature-aware manner, which can account for the visually salient features of the complex shapes and thus yield better visual fidelity.

In the literature of industrial designing and digital entertainment, the resizing of 3D complex models is a popular and useful operation. One of the key issues in model resizing is that some visually salient features of the underlying model should be preserved as much as possible. Based on the surface deformation scheme, a novel visual saliency guided content-aware model resizing approach is presented in this paper. Firstly, the edge sensitivity measure is determined by edge saliency measure and slippage value. Owing to the edge sensitivity, a quadratic energy function can thus be constructed to guide salient feature-preserving model resizing. Finally, the original model can be non-homogeneously scaled according to the per-edge scales solved by iteratively minimizing the quadratic energy function. Our visual saliency guided model resizing scheme can be benefit not only for the global resizing procedure but also for the local resizing operation. The experimental results demonstrate that our proposed model resizing scheme can effectively preserve the visually salient features of the underlying model in a content-aware manner.

Shape simplification and re-sampling of underlying point-sampled surfaces under user-defined error bounds is an important and challenging issue. Based on the regular triangulation of the Gaussian sphere and the surface normals mapping onto the Gaussian sphere, a Gaussian sphere based re-sampling scheme is presented that generates a non-uniformly curvature-aware simplification of the given point-sampled model. Owing to the theoretical analysis of shape isophotic error metric for did that Gaussian sphere based sampling, the proposed simplification scheme provides a convenient way to control the re-sampling results under a user-specified error metric bound. The novel algorithm has been implemented and demonstrated on several examples.