A Minimalist Approach to Type-Agnostic Detection of Quadrics in Point Clouds

This paper proposes a segmentation-free, automatic and efficient procedure to detect general geometric quadric forms in point clouds, where clutter and occlusions are inevitable. Our everyday world is dominated by man-made objects which are designed using 3D primitives (such as planes, cones, spheres, cylinders, etc.). These objects are also omnipresent in industrial environments. This gives rise to the possibility of abstracting 3D scenes through primitives, thereby positions these geometric forms as an integral part of perception and high level 3D scene understanding. As opposed to state-of-the-art, where a tailored algorithm treats each primitive type separately, we propose to encapsulate all types in a single robust detection procedure. At the center of our approach lies a closed form 3D quadric fit, operating in both primal & dual spaces and requiring as low as 4 oriented-points. Around this fit, we design a novel, local null-space voting strategy to reduce the 4-point case to 3. Voting is coupled with the famous RANSAC and makes our algorithm orders of magnitude faster than its conventional counterparts. This is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes. Results on synthetic and real datasets support the validity of our method.Comment: Accepted for publication at CVPR 201

Generic Primitive Detection in Point Clouds Using Novel Minimal Quadric Fits

We present a novel and effective method for detecting 3D primitives in cluttered, unorganized point clouds, without axillary segmentation or type specification. We consider the quadric surfaces for encapsulating the basic building blocks of our environments - planes, spheres, ellipsoids, cones or cylinders, in a unified fashion. Moreover, quadrics allow us to model higher degree of freedom shapes, such as hyperboloids or paraboloids that could be used in non-rigid settings. We begin by contributing two novel quadric fits targeting 3D point sets that are endowed with tangent space information. Based upon the idea of aligning the quadric gradients with the surface normals, our first formulation is exact and requires as low as four oriented points. The second fit approximates the first, and reduces the computational effort. We theoretically analyze these fits with rigor, and give algebraic and geometric arguments. Next, by re-parameterizing the solution, we devise a new local Hough voting scheme on the null-space coefficients that is combined with RANSAC, reducing the complexity from $O(N^4)$ to $O(N^3)$ (three points). To the best of our knowledge, this is the first method capable of performing a generic cross-type multi-object primitive detection in difficult scenes without segmentation. Our extensive qualitative and quantitative results show that our method is efficient and flexible, as well as being accurate.Comment: Submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence (T-PAMI). arXiv admin note: substantial text overlap with arXiv:1803.0719

Superquadrics for segmentation and modeling range data

We present a novel approach to reliable and efficient recovery of part-descriptions in terms of superquadric models from range data. We show that superquadrics can directly be recovered from unsegmented data, thus avoiding any presegmentation steps (e.g., in terms of surfaces). The approach is based on the recover-andselect paradigm. We present several experiments on real and synthetic range images, where we demonstrate the stability of the results with respect to viewpoint and noise

QuadricsNet: Learning Concise Representation for Geometric Primitives in Point Clouds

This paper presents a novel framework to learn a concise geometric primitive representation for 3D point clouds. Different from representing each type of primitive individually, we focus on the challenging problem of how to achieve a concise and uniform representation robustly. We employ quadrics to represent diverse primitives with only 10 parameters and propose the first end-to-end learning-based framework, namely QuadricsNet, to parse quadrics in point clouds. The relationships between quadrics mathematical formulation and geometric attributes, including the type, scale and pose, are insightfully integrated for effective supervision of QuaidricsNet. Besides, a novel pattern-comprehensive dataset with quadrics segments and objects is collected for training and evaluation. Experiments demonstrate the effectiveness of our concise representation and the robustness of QuadricsNet. Our code is available at \url{https://github.com/MichaelWu99-lab/QuadricsNet}Comment: Submitted to ICRA 2024. 7 page

Reverse engineering for industrial-environment cad models

International audienceIndustrial-environment CAD models are commonly represented by triangular meshes, which do not preserve original information about implicit surfaces used during design. The reverse-engineering algorithms presented in this paper focus on reconstructing implicit information, recovering original data. We propose two different approaches, a numerical one and an original topological approach. We explore specificities found in CAD meshes to achieve high effectiveness, reconstructing 90% of information from massive models (with millions of triangles) after few minutes of processing

Quadric tracing : a geometric method for accelerated sphere tracing of implicit surfaces

Sphere tracing is a common raytracing technique used for rendering implicit surfaces defined by a signed distance function (SDF). However, these distance functions are often expensive to compute, prohibiting several real-time applications despite recent efforts to accelerate it. This paper presents a method to precompute a slightly augmented distance field that hugely accelerates rendering. This novel method called quadric tracing supports two configurations: (i) accelerating raytracing without losing precision, so the original SDF is still needed; (ii) entirely replacing the SDF and tracing an interpolated surface. Quadric tracing can offer 20% to 100% speedup in rendering static scenes and thereby amortizing the slowdown caused by the complexity of the geometry

Fitting of Analytic Surfaces to Noisy Point Clouds

Fitting -continuous or superior surfaces to a set of points sampled on a 2-manifold is central to reverse engi- neering, computer aided geometric modeling, entertaining, modeling of art heritage, etc -- This article addresses the fit- ting of analytic (ellipsoid, cones, cylinders) surfaces in general position in -- Currently, the state of the art presents limitations in 1) automatically finding an initial guess for the analytic surface F sought, and 2) economically estimat- ing the geometric distance between a point of and the analytic surface SF -- These issues are central in estimating an analytic surface which minimizes its accumulated distances to the point set -- In response to this situation, this article presents and tests novel user-independent strategies for addressing aspects 1) and 2) above, for cylinders, cones and ellipsoids -- A conjecture for the calculation of the distance point-ellipsoid is also proposed -- Our strategies produce good initial guesses for F and fast fitting error estimation for F, leading to an agile and robust optimization algorithm -- Ongoing work addresses the fitting of free-form parametric surfaces to

Fitting quadrics with a Bayesian prior

Quadrics are a compact mathematical formulation for a range of primitive surfaces. A problem arises when there are not enough data-points to compute the model but knowledge of the shape is available. This paper presents a method for fitting a quadric with a Bayesian prior. We use a matrix normal prior in order to favour ellipsoids on ambiguous data. The results show the algorithm to cope well when there are few points in the point cloud, competing with contemporary techniques in the area

Surface and Volumetric Segmentation of Complex 3-D Objects Using Parametric Shape Models

The problem of part definition, description, and decomposition is central to the shape recognition systems. In this dissertation, we develop an integrated framework for segmenting dense range data of complex 3-D scenes into their constituent parts in terms of surface and volumetric primitives. Unlike previous approaches, we use geometric properties derived from surface, as well as volumetric models, to recover structured descriptions of complex objects without a priori domain knowledge or stored models. To recover shape descriptions, we use bi-quadric models for surface representation and superquadric models for object-centered volumetric representation. The surface segmentation uses a novel approach of searching for the best piecewise description of the image in terms of bi-quadric (z = f(x,y)) models. It is used to generate the region adjacency graphs, to localize surface discontinuities, and to derive global shape properties of the surfaces. A superquadric model is recovered for the entire data set and residuals are computed to evaluate the fit. The goodness-of-fit value based on the inside-outside function, and the mean-squared distance of data from the model provide quantitative evaluation of the model. The qualitative evaluation criteria check the local consistency of the model in the form of residual maps of overestimated and underestimated data regions. The control structure invokes the models in a systematic manner, evaluates the intermediate descriptions, and integrates them to achieve final segmentation. Superquadric and bi-quadric models are recovered in parallel to incorporate the best of the coarse-to-fine and fine-to-coarse segmentation strategies. The model evaluation criteria determine the dimensionality of the scene, and decide whether to terminate the procedure, or selectively refine the segmentation by following a global-to-local part segmentation approach. The control module generates hypotheses about superquadric models at clusters of underestimated data and performs controlled extrapolation of the part-model by shrinking the global model. As the global model shrinks and the local models grow, they are evaluated and tested for termination or further segmentation. We present results on real range images of scenes of varying complexity, including objects with occluding parts, and scenes where surface segmentation is not sufficient to guide the volumetric segmentation. We analyze the issue of segmentation of complex scenes thoroughly by studying the effect of missing data on volumetric model recovery, generating object-centered descriptions, and presenting a complete set of criteria for the evaluation of the superquadric models. We conclude by discussing the applications of our approach in data reduction, 3-D object recognition, geometric modeling, automatic model generation. object manipulation, and active vision