A large number of 3D spectral descriptors have been proposed in the literature, which act as an essential component for 3D deformable shape matching and related applications. An outstanding descriptor should have desirable natures including high-level descriptive capacity, cheap storage, and robustness to a set of nuisances. It is, however, unclear which descriptors are more suitable for a particular application. This paper fills the gap by comprehensively evaluating nine state-of-the-art spectral descriptors on ten popular deformable shape datasets as well as perturbations such as mesh discretization, geometric noise, scale transformation, non-isometric setting, partiality, and topological noise. Our evaluated terms for a spectral descriptor cover four major concerns, i.e., distinctiveness, robustness, compactness, and computational efficiency. In the end, we present a summary of the overall performance and several interesting findings that can serve as guidance for the following researchers to construct a new spectral descriptor and choose an appropriate spectral feature in a particular application.

Traditional deep functional map frameworks are widely used for 3D shape matching; however, many methods fail to adaptively capture the relevant frequency information required for functional map estimation in complex scenarios, leading to poor performance, especially under significant deformations. To address these challenges, we propose a novel unsupervised learning-based framework, Deep Frequency Awareness Functional Maps (DFAFM), specifically designed to tackle diverse shape-matching problems. Our approach introduces the Spectral Filter Operator Preservation constraint, which ensures the preservation of critical frequency information. These constraints promote frequency awareness by learning a set of spectral filters and incorporating them as a loss function to jointly supervise the functional maps, pointwise maps, and spectral filters. The spectral filters are constructed using orthonormal Jacobi polynomials with learnable coefficients, enabling adaptive and efficient frequency representation. Furthermore, we propose a refinement strategy that leverages the learned spectral filters and constraints to enhance the accuracy of the final pointwise map. Extensive experiments conducted on multiple benchmark datasets demonstrate that our method outperforms state-of-the-art approaches, particularly in challenging scenarios involving non-isometric deformations and inconsistent topology.

Shape descriptors are extensively used in shape analysis tasks such as shape correspondence, segmentation and retrieval, just to name a few. Their performances significantly determine the efficiency and effectiveness of subsequent applications. For this problem, we propose a novel powerful descriptor called Anisotropic Fractional Spectral Manifold Wavelet Descriptor (AFSMWD), built upon an extended manifold signal processing tool named Anisotropic Fractional Spectral Manifold Wavelet (AFSMW), which is also presented for the first time in this paper. The novelty of AFSMW is integrating the fractional theory into the common anisotropic spectral manifold wavelet. Compared to the existing wavelets, it provides one more new parameter, namely, the fractional order, to balance or enhance the transform coefficients among different shape vertices, enabling more flexible local shape analysis and more hidden shape structural information explored. Due to the advantages of this added parameter and the capability of analyzing shape features from multiple scales and orientations, the AFSMW allows us to construct the powerful descriptor AFSMWD just using the AFSMW transform coefficients of a very simple function. The proposed descriptor appears to be especially localizable, discriminative, and robust to noises. Extensive experiments have demonstrated that our descriptor has outperformed the state-of-the-art descriptors, nearly achieving 22% improvements to the most related work ASMWD and 69% to the recent popular work WEDS on the FAUST dataset. Its superiorities are also announced in some challenging occasions such as shapes with large deformation or topological partiality.

This paper introduces a novel image stylization method with the wireframe structure. Firstly, we divide the input image into multiple square cells of uniform size. The position of the highest and lowest points within each cell is determined and recorded by modeling the relationship between the cell height and grayscale values. Secondly, for each row of cells in the image, the highest and lowest points are sequentially connected with the highest and lower points of adjacent cells, respectively, forming an irregular wireframe envelope structure. Finally, black is filled within the envelope, producing a stylized grayscale image characterized by pronounced grayscale variations. Moreover, this method can be extended to color image stylization through color selection and filling techniques. Experimental results across various images demonstrate the effectiveness and practicality of this approach. The method is simple, efficient, and capable of producing high-quality results automatically in a short time. It offers a fresh perspective on image stylization and has potential applications in areas such as 3D printing, illustration design, and blind creation.