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Tableware objects such as plates, bowls, and cups are usually textureless, uniform in color, and vary widely in shape, making it difficult to apply conventional pose estimation methods that rely on texture cues or object-specific CAD models. These limitations present a significant obstacle to robotic manipulation in restaurant environments, where reliable six-degree-of-freedom (6-DoF) pose estimation is essential for autonomous grasping and collection. To address this problem, we propose a model-free and texture-free 6-DoF pose estimation framework based on a transformer encoder architecture. This method uses only geometry-based features extracted from depth images, including surface vertices and rim normals, which provide strong structural priors. The pipeline begins with object detection and segmentation using a pretrained video foundation model, followed by the generation of uniformly partitioned grids from depth data. For each grid cell, centroid positions, and surface normals are computed and processed by a transformer-based model that jointly predicts object rotation and translation. Experiments with ten types of tableware demonstrate that the method achieves an average rotational error of 3.53 degrees and a translational error of 13.56 mm. Real-world deployment on a mobile robot platform with a manipulator further validated its ability to autonomously recognize and collect tableware, highlighting the practicality of the proposed geometry-driven approach for service robotics.

There are six possible solutions for the surface normal vectors obtained from polarization information during 3D reconstruction. To resolve the ambiguity of surface normal vectors, scholars have introduced additional information, such as shading information. However, this makes the 3D reconstruction task too burdensome. Therefore, in order to make the 3D reconstruction more generally applicable, this paper proposes a complete framework to reconstruct the surface of an object using only polarized images. To solve the ambiguity problem of surface normal vectors, a jump-compensated U-shaped generative adversarial network (RU-Gan) based on jump compensation is designed for fusing six surface normal vectors. Among them, jump compensation is proposed in the encoder and decoder parts, and the content loss function is reconstructed, among other approaches. For the problem that the reflective region of the original image will cause the estimated normal vector to deviate from the true normal vector, a specular reflection model is proposed to optimize the dataset, thus reducing the reflective region. Experiments show that the estimated normal vector obtained in this paper improves the accuracy by about 20° compared with the previous conventional work, and improves the accuracy by about 1.5° compared with the recent neural network model, which means the neural network model proposed in this paper is more suitable for the normal vector estimation task. Furthermore, the object surface reconstruction framework proposed in this paper has the characteristics of simple implementation conditions and high accuracy of reconstructed texture.

This paper presents a stereo camera-based head-eye calibration method that aims to find the globally optimal transformation between a robot’s head and its eye. This method is highly intuitive and simple, so it can be used in a vision system for humanoid robots without any complex procedures. To achieve this, we introduce an extended minimum variance approach for head-eye calibration using surface normal vectors instead of 3D point sets. The presented method considers both positional and orientational error variances between visual measurements and kinematic data in head-eye calibration. Experiments using both synthetic and real data show the accuracy and efficiency of the proposed method.

This paper presents a method for measuring the spatial distribution of surface normal vectors with high angular accuracy. The measured data are visualized using a color-mapping technique and represented as normal maps, which are commonly used in computer graphics. Reliable methods for evaluating material surface properties have long been sought in industrial applications where visual assessments of reflective properties are still widely employed, particularly in appearance-critical fields. Motivated by this need, we introduce an imaging-based technique for measuring the high-resolution spatial distribution of surface normal vectors from specular reflection. A dedicated measurement apparatus was developed to capture surface normal vectors at 1024 × 1024 sampling points with a spatial resolution of 0.02 × 0.02 mm and an angular resolution of approximately 0.1°. Using this apparatus, normal maps were obtained for various materials, including plastic, ceramic tile, inkjet paper, and aluminum sheets. The spatial distribution of surface normal vectors reflects surface roughness, which strongly influences perceived texture. The resulting normal maps enable not only quantitative surface analysis for industrial inspection but also the physical reproduction of gloss in computer graphics.

To automatically measure the surface profile of a cylindrical workpiece, a high-precision multi-beam optical method is proposed in this paper. First, some successive images for the cylindrical workpiece’s surface are acquired by a multi-beam angle sensor under different light directions. Then, the light directions are estimated based on the feature regions in the images to calculate surface normal vectors. Finally, according to the relationship of the surface normal vector and the vertical section of the workpiece’s surface, a depth map is reconstructed to achieve the curvature surface, which can be employed to measure the curvature radius of the cylindrical workpiece’s surface. Experimental results indicate that the proposed measurement method can achieve good measurement precision with a mean error of the curvature radius of a workpiece’s surface of 0.89% at a reasonable speed of 10.226 s, which is superior to some existing methods.

Surface normal vectors provide cues about the local geometric features of the scene which are utilized in many computer vision and computer graphics applications. Thus, the estimation of surface normals by utilizing structured range sensor data is an important research field. Thereupon, we propose a learning-free algorithm to estimate the surface normal vectors from depth maps. Our simple yet effective method relies on computations carried out in scale-space. Our main idea is to estimate the surface normals which cannot be properly computed in the finest scale from the coarser scales. Our method can estimate the surface normals even for images included in datasets that have challenging characteristics such as noisy real-world data or significantly large planar regions that either have a small or no gradient change. We analyze our algorithm’s performance by utilizing five benchmarks, namely, the MIT-Berkeley Intrinsic Images dataset, the New Tsukuba Dataset, the SceneNet RGB-D dataset, the IID-NORD dataset, and the NYU Depth Dataset V2, and by using two different evaluation strategies. According to the experimental results, our method can estimate surface normals efficiently without requiring neither complex computations nor huge amounts of data.

In medical imaging or computational biology, it is required to reconstruct a surface from contours in cross sections for visualization and further processing. We propose a method to generate a surface which is smooth enough and exactly passes through contours in each cross section. For smoothness, we first define an energy of the surface using the gradient of the normal vector. Then, we express the surface using a level set function and assign values of level set function on each cross section to make the surface exactly passing through contours. Finally, we get an energy minimization problem with constraints, which can be solved using the augmented Lagrangian method and the alternating direction method. The solution of the minimization problem is the surface which we look for. Implementation of the algorithm and numerical experiments are presented.

In this paper, we propose a method of exploring the surface geometry of an unknown object by touch. The method is based on the idea that a three-dimensional surface geometry can be reconstructed from two principal curvatures of the object which are estimated from three concurrent curves. First, the process to minimize the number of contact points is addressed for the approximation of an arbitrary curve, which uses normal vectors at the contact points. Then, an algorithm for reconstructing a three-dimensional local surface from four contact points, two of which can be used to compute a normal curvature, is presented. Lastly, our method is applied to cylindrical, spherical and planar objects in simulation and experiments for validation.

Topographic data sets are often composed of terrain samples arranged in irregular meshes. Many gradient estimation methods require the data to be arranged in a regular mesh; irregular meshes present a difficulty for them. This paper presents a novel method of estimating surface gradients from irregularly spaced inputs. The method is derived using directional derivatives and is shown to be a generalization of traditional finite difference methods. Analytical tests were used to evaluate the method, which was shown to be accurate and robust.[PUBLICATION ABSTRACT]

We confirm a well-known conjecture that the round sphere is the only compact, embedded self-similar shrinking solution of mean curvature flow in ℝ3 with genus 0. More generally, we show that the only properly embedded self-similar shrinkers in ℝ3 with vanishing intersection form are the sphere, the cylinder, and the plane. This answers two questions posed by T. Ilmanen.