Abstract Image triangulation methods, which decompose an image into a series of triangles, are fundamental in artistic creation and image processing. This paper introduces a novel framework that integrates cubic Bézier curves into image triangulation, enabling the precise reconstruction of curved image features. Our developed framework constructs a well‐structured curved triangle mesh, effectively preventing overlaps between curves. A refined energy function, grounded in differentiable rendering, establishes a direct link between mesh geometry and rendering effects and is instrumental in guiding the curved mesh generation. Additionally, we derive an explicit gradient formula with respect to mesh parameters, facilitating the adaptive and efficient optimization of these parameters to fully leverage the capabilities of cubic Bézier curves. Through experimental and comparative analyses with state‐of‐the‐art methods, our approach demonstrates a significant enhancement in both numerical accuracy and visual quality.

Content-based 3D object retrieval is a challenging problem in computer vision and graphics, especially for non-rigid 3D shapes. This article proposes a multiview-based robust point representation approach for 3D non-rigid shape retrieval. First, we propose an efficient local descriptor called the local point histogram, which is robust to non-rigid changes in shape. Second, we encode local point histogram features into high-level point features (HPF) using Fisher vectors. Finally, we present an efficient feature fusion method that can further enhance the performance of 3D non-rigid shape retrieval. We extensively tested our approach on two benchmark 3D non-rigid shape datasets, including the SHREC2015 non-rigid shape and SHREC2015 canonical forms. Our method achieves 98.33% and 90.55% retrieval accuracy on the SHREC2015 non-rigid shape and SHREC2015 canonical forms datasets, surpassing previous state-of-the-art methods by nearly 2% and 7%, respectively. In addition, we further tested our method on the well-known 3D rigid shape dataset ModelNet, and the experimental results demonstrate that our method is also effective for 3D rigid shape retrieval. We also combine the proposed HPF shape features with deep convolutional features for the 3D rigid shape retrieval task, achieving a retrieval performance comparable to the prior state-of-the-art methods, which indicates a strong complementarity between HPF shape features and deep convolutional features.

Plant identification based on leaf images is a widely concerned application field in artificial intelligence and botany. The key problem is extracting robust discriminative features from leaf images and assigning a measure of similarity. This study proposes an effective, robust shape descriptor to identify plant species from images of their leaves, which we call the high-level triangle shape descriptor (HTSD). First, we extract a leaf image's external contour and internal salient point information. We then use triangle features to describe the leaf contour, which we call the contour point based on triangle features (CPTFs). The internal information of the leaf image is based on salient point triangle features (SPTFs). The third step is to apply the Fisher vector to encode the two kinds of point-based local triangle features into the HTSD. Finally, we employ the simple euclidean distance to calculate the dissimilarities between the HTSD characteristics of leaf images. We have extensively evaluated the proposed approach on several public leaf datasets successfully. Experimental results show that our method has superior recognition accuracy, outperforming current state-of-the-art shape-based and deep-learning plant identification approaches.