Bounds on the k-neighborhood for locally uniform sampled surfaces

Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view

Bounds on the k-neighborhood for locally uniform sampled surfaces

Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view

Segmentation-based multi-scale edge extraction to measure the persistence of features in unorganized point clouds

Edge extraction has attracted a lot of attention in computer vision. The accuracy of extracting edges in point clouds can be a significant asset for a variety of engineering scenarios. To address these issues, we propose a segmentation-based multi-scale edge extraction technique. In this approach, different regions of a point cloud are segmented by a global analysis according to the geodesic distance. Afterwards, a multi-scale operator is defined according to local neighborhoods. Thereupon, by applying this operator at multiple scales of the point cloud, the persistence of features is determined. We illustrate the proposed method by computing a feature weight that measures the likelihood of a point to be an edge, then detects the edge points based on that value at both global and local scales. Moreover, we evaluate quantitatively and qualitatively our method. Experimental results show that the proposed approach achieves a superior accuracy. Furthermore, we demonstrate the robustness of our approach in noisier real-world datasets.Peer ReviewedPostprint (author's final draft

NeurSF: Neural Shading Field for Image Harmonization

Image harmonization aims at adjusting the appearance of the foreground to make it more compatible with the background. Due to a lack of understanding of the background illumination direction, existing works are incapable of generating a realistic foreground shading. In this paper, we decompose the image harmonization into two sub-problems: 1) illumination estimation of background images and 2) rendering of foreground objects. Before solving these two sub-problems, we first learn a direction-aware illumination descriptor via a neural rendering framework, of which the key is a Shading Module that decomposes the shading field into multiple shading components given depth information. Then we design a Background Illumination Estimation Module to extract the direction-aware illumination descriptor from the background. Finally, the illumination descriptor is used in conjunction with the neural rendering framework to generate the harmonized foreground image containing a novel harmonized shading. Moreover, we construct a photo-realistic synthetic image harmonization dataset that contains numerous shading variations by image-based lighting. Extensive experiments on this dataset demonstrate the effectiveness of the proposed method. Our dataset and code will be made publicly available

Normal Transformer: Extracting Surface Geometry from LiDAR Points Enhanced by Visual Semantics

High-quality estimation of surface normal can help reduce ambiguity in many geometry understanding problems, such as collision avoidance and occlusion inference. This paper presents a technique for estimating the normal from 3D point clouds and 2D colour images. We have developed a transformer neural network that learns to utilise the hybrid information of visual semantic and 3D geometric data, as well as effective learning strategies. Compared to existing methods, the information fusion of the proposed method is more effective, which is supported by experiments. We have also built a simulation environment of outdoor traffic scenes in a 3D rendering engine to obtain annotated data to train the normal estimator. The model trained on synthetic data is tested on the real scenes in the KITTI dataset. And subsequent tasks built upon the estimated normal directions in the KITTI dataset show that the proposed estimator has advantage over existing methods