Set Of Unorganized Points Research Articles

Efficient image restoration with style-guided context cluster and interaction

Recently, convolutional neural networks (CNNs) and vision transformers (ViTs) have emerged as powerful tools for image restoration (IR). Nonetheless, they encountered some limitations due to their characteristics, such as CNNs sacrificing global reception and ViTs requiring large memory and graphics resources. To address these limitations and explore an alternative approach for improved IR performance, we propose two clustering-based frameworks for general IR tasks, which are style-guided context cluster U-Net (SCoC-UNet) and style-guided clustered point interaction U-Net (SCPI-UNet). The SCoC-UNet adopts a U-shaped architecture, comprising position embedding, Encoder, Decoder, and reconstruction block. Specifically, the input low-quality image is viewed as a set of unorganized points, each of which is first given location information by the continuous relative position embedding method. These points are then fed into a symmetric Encoder and Decoder which utilize style-guided context cluster (SCoC) blocks to extract potential context features and high-frequency information. Although SCoC-UNet has obtained decent performance for image restoration, its SCoC block can only capture connectivity at points within the same cluster, which may ignore long-range dependencies in different clusters. To address this issue, we further propose a SCPI-UNet based on SCoC-UNet, which leverages a style-guided clustered point interaction (SCPI) block in place of the SCoC block. The SCPI block utilizes a cross-attention mechanism to establish the connections of feature points between different clusters. Extensive experimental results demonstrate that the proposed SCoC-UNet and SCPI-UNet can handle several typical IR tasks (i.e., JPEG compression artifact reduction, image denoising, and super-resolution) and achieve superior quantitative and qualitative performance over some state-of-the-art methods.

Norest-Net: Normal Estimation Neural Network for 3-D Noisy Point Clouds.

The widely deployed ways to capture a set of unorganized points, e.g., merged laser scans, fusion of depth images, and structure-from- x , usually yield a 3-D noisy point cloud. Accurate normal estimation for the noisy point cloud makes a crucial contribution to the success of various applications. However, the existing normal estimation wisdoms strive to meet a conflicting goal of simultaneously performing normal filtering and preserving surface features, which inevitably leads to inaccurate estimation results. We propose a normal estimation neural network (Norest-Net), which regards normal filtering and feature preservation as two separate tasks, so that each one is specialized rather than traded off. For full noise removal, we present a normal filtering network (NF-Net) branch by learning from the noisy height map descriptor (HMD) of each point to the ground-truth (GT) point normal; for surface feature recovery, we construct a normal refinement network (NR-Net) branch by learning from the bilaterally defiltered point normal descriptor (B-DPND) to the GT point normal. Moreover, NR-Net is detachable to be incorporated into the existing normal estimation methods to boost their performances. Norest-Net shows clear improvements over the state of the arts in both feature preservation and noise robustness on synthetic and real-world captured point clouds.

Reconstruction of Curve Networks from Unorganized Spatial Points

Curve network reconstruction from a set of unorganized points is an important problem in reverse engineering and computer graphics. In this paper, we propose an automatic method to extract curve segments and reconstruct curve networks from unorganized spatial points. Our proposed method divides reconstruction of curve networks into two steps: 1) detecting nodes of curve segments and 2) reconstructing curve segments. For detection of nodes of curve segments, we present a principal component analysis-based algorithm to obtain candidate nodes from unorganized spatial points and a Euclidean distance-based iterative algorithm to remove peripheral nodes and find the actual nodes. For reconstruction of curve segments, we propose an extraction algorithm to obtain the points on each of curve segments. We present quite a number of examples which use our proposed method to reconstruct curve networks from unorganized spatial points. The results demonstrate the effectiveness of our proposed method and its advantages of good automation and high reconstruction efficiency.

Sparse-to-Dense Multi-Encoder Shape Completion of Unstructured Point Cloud

Unstructured point clouds are a representative shape representation of real-world scenes in 3D vision and graphics. Incompletion inevitably arises, due to the way the set of unorganized points is captured, e.g., as fusion of depth images, merged laser scans, or structure-from-x. In this paper, an end-to-end sparse-to-dense multi-encoder neural network (termed an SDME-Net) is proposed for uniformly completing an unstructured point cloud with its shape details preserved. Unlike most existing learning-based shape completion methods that are enforced on the representations of 2D images and 3D voxelization of point clouds, and require priors of the underlying shape's structures, topologies and annotations, the SDME-Net is implemented on the incomplete and even noisy point cloud without any transformation, and makes no specific assumptions about the incompletion distribution and geometry features in the input. Specifically, the defective point cloud is completed and optimized in a sparse-to-dense manner of two-stages. In the first stage, we generate a sparse but complete point cloud based on a bistratal PointNet, and in the second stage, we yield a dense and high-fidelity point cloud by encoding and decoding the sparse result in the first stage using PointNet++. Meanwhile, we combine the distance loss and repulsion loss to generate more uniformly distributed output point clouds closer to the ground-truth counterparts. Qualitative and quantitative experiments on the public ShapeNet dataset illustrate that our approach outperforms the state-of-art learning-based point cloud shape completion methods in terms of real structure recovery, uniformity, and noise/partiality robustness.

Towards globally optimal normal orientations for thin surfaces

Globally unified normal orientations for unorganized point set are essential for reconstruction, rendering, texture mapping etc. Although there is a large body of literature on dealing with various difficult cases to get consistent normal orientation, effective approaches are not available yet to handle a point cloud with thin surfaces, to our best knowledge. The difficulty lies in that thin structure doesn’t have a strong coherence between locations of surface points and their normal orientations. In this paper, we propose a novel approach for computing globally optimal normal orientations to facilitate high-quality surface reconstruction from a point cloud with thin structures. The key idea is to generate an uniform particle set constrained on an offset surface that is topologically identical to the real target surface and further use the particle set to compute and refine the normal vector at each primitive point. Our strategy for inferring the globally consistent orientation is much different from the conventional paradigm that computes unoriented normal vectors and then re-orients them coherently. Experimental results on natural and man-made models with noise and thin parts show that our algorithm outperforms existing approaches on normal consistence and is able to produce a desirable global optimal normal orientations with which a structurally sound thin shape can be finally reconstructed by the well known screened Poisson reconstruction approach.

FITTING A POINT CLOUD TO A 3D POLYHEDRAL SURFACE

Abstract. The ability to measure parameters of large-scale objects in a contactless fashion has a tremendous potential in a number of industrial applications. However, this problem is usually associated with an ambiguous task to compare two data sets specified in two different co-ordinate systems. This paper deals with the study of fitting a set of unorganized points to a polyhedral surface. The developed approach uses Principal Component Analysis (PCA) and Stretched grid method (SGM) to substitute a non-linear problem solution with several linear steps. The squared distance (SD) is a general criterion to control the process of convergence of a set of points to a target surface. The described numerical experiment concerns the remote measurement of a large-scale aerial in the form of a frame with a parabolic shape. The experiment shows that the fitting process of a point cloud to a target surface converges in several linear steps. The method is applicable to the geometry remote measurement of large-scale objects in a contactless fashion.

Virtual Camera Movement with Particle Swarm Optimization and Local Regression

Manually placing and animating virtual camera in a dynamic virtual environment to generate computer animation is a complex and time-consuming process. For this reason, this paper proposes a method to take the sequential shot by gameplay, to determine the best camera placement candidates as an unorganized point set, to reconstruct a curve by the point set using local regression technique and to generate smooth camera movement based on those curves. Finally, the paper presents the application of this algorithm and it analyzes a number of problems in different dynamic virtual environments.

Reconstruction of curves from point clouds using fuzzy logic and ant colony optimization

A new approach based on fuzzy logic and ant colony optimization is presented for the reconstruction of curves from a set of unorganized points. Fuzzy clustering is used to reduce the number of points to cluster centres. Ant colony optimization is used to construct a travelling salesman path which is a closed curve. Extra edges are deleted and new edges are added using the fuzzy membership function. The algorithm presented in this paper has been used for reconstructing open as well as closed curves. The results obtained for multiple and self-intersecting curves are also good. Various examples for open, closed, multiple and intersecting curves with complicated shapes are shown to illustrate the significance of the presented algorithm.

Point morphology

We introduce a complete morphological analysis framework for 3D point clouds. Starting from an unorganized point set sampling a surface, we propose morphological operators in the form of projections, allowing to sample erosions, dilations, closings and openings of an object without any explicit mesh structure. Our framework supports structuring elements with arbitrary shape, accounts robustly for geometric and morphological sharp features, remains efficient at large scales and comes together with a specific adaptive sampler. Based on this meshless framework, we propose applications which benefit from the non-linear nature of morphological analysis and can be expressed as simple sequences of our operators, including medial axis sampling, hysteresis shape filtering and geometry-preserving topological simplification.

Scalable Curvature-based Feature Detection for Unorganized 3D Point Sets

Scalable Curvature-based Feature Detection for Unorganized 3D Point Sets

An Efficient Algorithm for Determining an Aesthetic Shape Connecting Unorganized 2D Points

AbstractWe present anefficient algorithm for determining an aesthetically pleasing shape boundary connecting all the points in a given unorganized set of 2D points, with no other information than point coordinates. By posing shape construction as a minimisation problem which follows the Gestalt laws, our desired shape is non‐intersecting, interpolates all points and minimizes a criterion related to these laws. The basis for our algorithm is an initial graph, an extension of the Euclidean minimum spanning tree but with no leaf nodes, called as the minimum boundary complex . and can be expressed similarly by parametrizing a topological constraint. A close approximation of , termed can be computed fast using a greedy algorithm. is then transformed into a closed interpolating boundary in two steps to satisfy ’s topological and minimization requirements. Computing exactly is an NP (Non‐Polynomial)‐hard problem, whereas is computed in linearithmic time. We present many examples showing considerable improvement over previous techniques, especially for shapes with sharp corners. Source code is available online.

Simple computation of reaction–diffusion processes on point clouds

The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.

SURFACE RECONSTRUCTION FROM SCATTERED POINT DATA ON OCTREE

In this paper, we propose a very efficient method which reconstructs the high resolution surface from a set of unorganized points. Our method is based on the level set method using adaptive octree. We start with the surface reconstruction model proposed in [20]. In [20], they introduced a very fast and efficient method which is different from the previous methods using the level set method. Most existing methods[21, 22] employed the time evolving process from an initial surface to point cloud. But in [20], they considered the surface reconstruction process as an elliptic problem in the narrow band including point cloud. So they could obtain very speedy method because they didn't have to limit the time evolution step by the finite speed of propagation. However, they implemented that model just on the uniform grid. So they still have the weakness that it needs so much memories because of being fulfilled only on the uniform grid. Their algorithm basically solves a large linear system of which size is the same as the number of the grid in a narrow band. Besides, it is not easy to make the width of band narrow enough since the decision of band width depends on the distribution of point data. After all, as far as it is implemented on the uniform grid, it is almost impossible to generate the surface on the high resolution because the memory requirement increases geometrically. We resolve it by adapting octree data structure[12, 11] to our problem and by introducing a new redistancing algorithm which is different from the existing one[19].

Point set morphological filtering and semantic spatial configuration modeling: Application to microscopic image and bio-structure analysis

High-level spatial relation and configuration modeling issues are gaining momentum in the image analysis and pattern recognition fields. In particular, it is deemed important whenever one needs to mine high-content images or large scale image databases in a more expressive way than a purely statistically one. Continuing previous efforts to incorporate structural analysis by developing specific efficient morphological tools performing on mesh representations like Delaunay triangulations, we propose to formalize spatial relation modeling techniques dedicated to unorganized point sets. We provide an original mesh lattice framework which is more convenient for structural representations of large image data by means of interest point sets and their morphological analysis. The set of designed numerical operators is based on a specific dilation operator that makes it possible to handle concepts like “between” or “left of” over sparse representations of image data such as graphs. Based on this new theoretical framework for reasoning about images, we are able to process high-level queries over large histopathological images, knowing that digitized histopathology is a new challenge in the field of bio-imaging due to the high-content nature and large size of these images.

Point Cloud Merging for Complete 3D Surface Reconstruction

This article addresses the problem of reconstructing 3D surfaces from unorganized point sets (also known as point clouds). Thisissue is common to many different areas of science and engineering, including computer graphics and computer vision. Unorganizedpoint sets can be acquired in different ways, e.g., using laser scanners, computer tomography, magnetic resonance imaging, multicameravision systems, etc. This paper presents a method for point cloud merging that allows calculating the initial rotation andtranslation between point clouds of different viewing angles. By tracking the marker's position, scanning and point cloud registrationcan be done in real time and with high accuracy. Ill. 7, bibl. 11 (in English; abstracts in English and Lithuanian).http://dx.doi.org/10.5755/j01.eee.113.7.616

Bipartite Polar Classification for Surface Reconstruction

In this paper, we propose bipartite polar classification to augment an input unorganized point set ℘ with two disjoint groups of points distributed around the ambient space of ℘ to assist the task of surface reconstruction. The goal of bipartite polar classification is to obtain a space partitioning of ℘ by assigning pairs of Voronoi poles into two mutually invisible sets lying in the opposite sides of ℘ through direct point set visibility examination. Based on the observation that a pair of Voronoi poles are mutually invisible, spatial classification is accomplished by carving away visible exterior poles with their counterparts simultaneously determined as interior ones. By examining the conflicts of mutual invisibility, holes or boundaries can also be effectively detected, resulting in a hole-aware space carving technique. With the classified poles, the task of surface reconstruction can be facilitated by more robust surface normal estimation with global consistent orientation and off-surface point specification for variational implicit surface reconstruction. We demonstrate the ability of the bipartite polar classification to achieve robust and efficient space carving on unorganized point clouds with holes and complex topology and show its application to surface reconstruction.

A SURVEY ON METHODS FOR RECONSTRUCTING SURFACES FROM UNORGANIZED POINT SETS / PAVIRŠIŲ REKONSTRUKCIJOS IŠ NESTRUKTŪRIZUOTŲ TAŠKŲ RINKINIŲ METODŲ APŽVALGA

This paper addresses the issue of reconstructing and visualizing surfaces from unorganized point sets. These can be acquired using different techniques, such as 3D-laser scanning, computerized tomography, magnetic resonance imaging and multi-camera imaging. The problem of reconstructing surfaces from their unorganized point sets is common for many diverse areas, including computer graphics, computer vision, computational geometry or reverse engineering. The paper presents three alternative methods that all use variations in complementary cones to triangulate and reconstruct the tested 3D surfaces. The article evaluates and contrasts three alternatives.

Wavelet frame based surface reconstruction from unorganized points

Applications of wavelet frames to image restoration problems (e.g. image deblurring and inpainting) have been successful due to their redundancy and capability of sparsely approximating piecewise smooth functions like images (see e.g. [13,14,8]). However, wavelet frames have not yet been used for surface reconstruction problems. Recently in [6], connections between one of the wavelet frame based image restoration model [8,28,48] and variational models (e.g. the ROF model [45]) were rigorously established. Such connections not only grant new insights to wavelet frame based image restorations, it also case a geometric explanation to wavelet frame based approaches. This leads us to a wavelet frame based model, as well as a fast algorithm, to reconstruct implicit surfaces from unorganized point sets in R^3. We will demonstrate the effectiveness of the proposed model using several commonly used examples.

Multi-level partition of unity algebraic point set surfaces

We present a multi-level partition of unity algebraic set surfaces (MPU-APSS) for surface reconstruction which can be represented by either a projection or in an implicit form. An algebraic point set surface (APSS) defines a smooth surface from a set of unorganized points using local moving least-squares (MLS) fitting of algebraic spheres. However, due to the local nature, APSS does not work well for geometry editing and modeling. Instead, our method builds an implicit approximation function for the scattered point set based on the partition of unity approach. By using an octree subdivision strategy, we first adaptively construct local algebraic spheres for the point set, and then apply weighting functions to blend together these local shape functions. Finally, we compute an error-controlled approximation of the signed distance function from the surface. In addition, we present an efficient projection operator which makes our representation suitable for point set filtering and dynamic point resampling. We demonstrate the effectiveness of our unified approach for both surface reconstruction and geometry modeling such as surface completion.

Variational surface reconstruction based on Delaunay triangulation and graph cut

AbstractA novel method for surface reconstruction from an unorganized point set is presented. An energy functional based on a weighted minimal surface model is proposed for surface reconstruction, which is efficiently minimized by graph cut methods. By solving the minimization problem on the graph dual to a Delaunay‐based tetrahedral mesh, the advantages of explicit and implicit methods for surface reconstruction are well integrated. A triangular surface mesh homeomorphic to the original surface can be extracted directly from the tetrahedral mesh provided a sufficient sampling density exists. Difficult cases involving undersampling, non‐uniformity, noises and topological complexities can be handled effectively as well. Furthermore, for the first time, multi‐phase surface reconstruction is realized based on the graph cut methods. Various examples are included for demonstrating the efficiency and effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.