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A data structure for the 3d Hough transform for plane detection
Abstract
The Hough Transform is a well-known method for detection of parametrized objects. It is the de facto standard for detecting lines and circles in 2-dimensional data sets. For 3D it has attained little attention so far. Apart from computation costs, the main problem lies in the representation of the accumulator: Usual implementations favor geometrical objects with certain parameters due to uneven sampling of the parameter space. In this paper we present a novel approach to design the accumulator focusing on achieving the same size for each cell. The proposed accumulator is compared to previously known designs.
... La méthode a été appliquée à la détection de formes 3D comme les sphères ( [3]), les plans ( [188,31,30]) ou encore les cylindres ( [153]). Des auteurs ont proposé d'appliquer plusieurs transformées successives en dimension faible plutôt qu'une seule en dimension élevée, comme par exemple dans [153] pour la détection de cylindres. ...
Dans le cadre de cette thèse, nous nous intéressons à plusieurs problématiques liées au traitement de données 3D. La première concerne la détection et le suivi de personnes dans des séquences d'images de profondeur. Nous proposons une amélioration d'une méthode existante basée sur une étape de segmentation, puis de suivi des personnes. La deuxième problématique abordée est la détection et la modélisation de têtes dans un nuage de points 3D. Pour cela, nous adoptons une approche probabiliste basée sur un nouveau modèle de mélange sphérique. La dernière application traitée est liée à la restauration d'images de profondeur présentant des données manquantes. Nous proposons pour cela d'utiliser une méthode d'approximation de surface par Dm-splines d'interpolation avec changements d'échelle pour approximer et restaurer les données. Les résultats présentés illustrent l'efficacité des algorithmes développés.
... One of the most popular and powerful methods for detecting parametric shapes in 2D images is the Hough transform (HT), first introduced in [4] for line detection. During the last decades, many HT-based methods have been widely proposed for 2D detection of circles, ellipses and also arbitrary shapes [5], but only recently has the HT been applied to a 3D scene, mainly for plane detection6789. The popularity of this method stems from the simplicity and generality of the conversion of features extracted from the image space into a set of votes collected in a parametric space, which is easier to analyze. ...
Three-dimensional object recognition on range data and 3D point clouds is becoming more important nowadays. Since many real objects have a shape that could be approximated by simple primitives, robust pattern recognition can be used to search for primitive models. For example, the Hough transform is a well-known technique which is largely adopted in 2D image space. In this paper, we systematically analyze different probabilistic/randomized Hough transform algorithms for spherical object detection in dense point clouds. In particular, we study and compare four variants which are characterized by the number of points drawn together for surface computation into the parametric space and we formally discuss their models. We also propose a new method that combines the advantages of both single-point and multi-point approaches for a faster and more accurate detection. The methods are tested on synthetic and real datasets.
... The main problem is to determine the most suitable surface description for a given set of points. Using the Hough transformation is a possible approach to solve this problem [19], but it is computationally expensive compared to mesh-based methods. ...
In this paper we present an approach to introduce semantics into a SLAM-generated 3D point cloud map from 3D laser scans of an office environment. For semantic classification we propose to first reconstruct surface planes in the point cloud. Using an OWL-DL ontology, we automatically analyze relations between surface planes in a cluster to generate hypotheses for present objects. To check these hypotheses we surface sample appropriate CAD models and use standard ICP to fit the scan data with the model of the hypothesized object. The final result is a hybrid semantic map, in which all identified objects have been replaced by their corresponding CAD models.
... Most shape based approaches use feature descriptors to detect instances of predefined objects, e.g., [6]. Other approaches use Hough transformations to detect planar surfaces in 3D laser scans [2]. Mesh based approaches create triangle meshes to approximate the scanned surfaces. ...
This paper presents a novel approach to create polygonal maps from 3D point cloud data. The gained map is augmented with an interpretation of the scene. Our procedure produces accurate maps of indoor environments fast and reliably. These maps are successfully used by different robots with varying sensor configurations for reliable self localization.
... III. DESIRED POINTS BY PLANE EXTRACTION Planes are extracted from the point clouds using the randomized Hough Transform as described in [2] or similar plane detection techniques. Each plane i is represented using the Hesse normal form, i.e. by a unit normal n i and a distance from the origin ρ i . ...
Plane detection is an important step in the reconstruction of 3D models of buildings from point clouds. The results of plane detection methods based on the region growing approach mainly depend on the choice of seed points. In this study, we introduce a novel region growing-based method for plane detection in unorganized point clouds. Our method uses the Iterative Closest Point (ICP) algorithm to extract reliable seeds. To enhance the performance and the quality of the results, we used voxel grids representation of the point clouds in the growing process. The classification of the candidate planes is improved by using the number of voxel cells covering accumulated segments. The method is deterministic, runs in O(nlog(n)), and does not take into account the orientation of the point clouds. The results of plane detection using the proposed method on a benchmark consisting of 9 point clouds of buildings show a better precision of extracted planes compared to those obtained with 3-D KHT and PCL-RANSAC. Although slower than 3-D KHT, our method requires an execution time (3 x times) shorter than PCL-RANSAC.
CAD mesh models have been widely employed in current CAD/CAM systems, where it is quite useful to recognize the features of the CAD mesh models. The first step of feature recognition is to segment the CAD mesh model into meaningful parts. Although there are lots of mesh segmentation methods in literature, the majority of them are not suitable to CAD mesh models. In this paper, we design a mesh segmentation method based on clustering, dedicated to the CAD mesh model. Specifically, by the agglomerative clustering method, the given CAD mesh model is first clustered into the sparse and dense triangle regions. Furthermore, the sparse triangle region is separated into planar regions, cylindrical regions, and conical regions by the Gauss map of the triangular faces and Hough transformation; the dense triangle region is also segmented by the mean shift operation performed on the mean curvature field defined on the mesh faces. Lots of empirical results demonstrate the effectiveness and efficiency of the CAD mesh segmentation method in this paper.
A new unified system application for the production audit in an aerospace industry is presented in this paper which comprises two key application tools such as (a) 3D PAMT (production audit measurement tool) and (b) 3D PACT (production audit compare tool). In spite of the facts that above functionalities are modular wise independent, commonly they are related in terms of assisting the production audit task. 3D PAMT facilitates the verification of manufactured parts to be within a pre-defined threshold range using a calibrated stereo camera with the safety test engineer interaction in order to select the matching disparity points. The distance between datum points with or without reference to a planar reference surface model can be obtained. We describe the system flow, plus validate the technique via a number of experimental datasets. 3D PACT allows the identification of discrepancies between a computed 3D point cloud model and the corresponding digital mock-up point cloud model. Usually, the computer aided geometry model is built before an actual installation. This knowledge about the components of an installation assembly is available as semantic information in an extendable markup language (XML) format of the CATIA model. We have provided an use case study of a sample assembly with components such as cube, pyramid, rectangular prism and triangular prism. The proposed cost-effective and robust framework for 3D measurement audit and model comparison is based on the input available from a digital camera and the semantic metadata knowledge available from geometry models which can be used for verification tasks.
This paper presents HSM3D, an algorithm for global rigid 6DOF alignment of 3D point clouds. The algorithm works by projecting the two input sets into the Radon/Hough domain, whose properties allow to decompose the 6DOF search into a series of fast one-dimensional cross-correlations. No planes or other particular features must be present in the input data, and the algorithm is provably complete in the case of noise-free input. The algorithm has been experimentally validated on publicly available data sets.
We propose a method to identify planar regions in volume data using a specialized version of the discrete Radon transform
operating on a structured or unstructured grid. The algorithm uses an efficient discretization scheme for the parameter space
to obtain a running time of
O(N (TlogT))\mathcal O(N (T\log T))
, where T is the number of cells and N is the number of plane normals in the discretized parameter space.
We apply our algorithm in an industrial setting and perform experiments with real-world data generated by topology optimization
algorithms, where the planar regions represent portions of a mechanical part that can be built using steel plate.
This patent relates to a method and means for recognizing a complex
pattern in a picture. The picture is divided into framelets, each framelet being
sized so that any segment of the complex pattern therewithin is essentially a
straight line. Each framelet is scanned to produce an electrical pulse for each
point scanned on the segment therewithin. Each of the electrical pulses of each
segment is then transformed into a separate strnight line to form a plane
transform in a pictorial display. Each line in the plane transform of a segment
is positioned laterally so that a point on the line midway between the top and
the bottom of the pictorial display occurs at a distance from the left edge of
the pictorial display equal to the distance of the generating point in the
segment from the left edge of the framelet. Each line in the plane transform of
a segment is inclined in the pictorial display at an angle to the vertical whose
tangent is proportional to the vertical displacement of the generating point in
the segment from the center of the framelet. The coordinate position of the
point of intersection of the lines in the pictorial display for each segment is
determined and recorded. The sum total of said recorded coordinate positions
being representative of the complex pattern. (AEC)
A new method is proposed for curve detection. For a curve with n parameters, instead of transforming one pixel into a hypersurface of the n-D parameter space as the HT and its variants do, we randomly pick n pixels and map them into one point in the parameter space. In comparison with the HT and its variants, our new method has the advantages of small storage, high speed, infinite parameter space and arbitrarily high resolution. The preliminary experiments have shown that the new method is quite effective.
The Hough Transform for straight line detection is considered. It is shown that if just a small subset of the edge points in the image, selected at random, is used as input for the Hough Transform, the performance is often only slightly impaired, thus the execution time can be considerably shortened. The performance of the resulting “Probabilistic Hough Transform” is analysed. The analysis is supported by experimental evidence.
Abstract In this paper we present an automatic algorithm to detect basic shapes in unorganized point clouds. The algorithm decomposes the point cloud into a concise, hybrid structure of inherent shapes and a set of remaining points. Each detected shape serves as a proxy for a set of corresponding points. Our method is based on random sampling and detects planes, spheres, cylinders, cones and tori. For models with surfaces composed of these basic shapes only, for example, CAD models, we automatically obtain a representation solely consisting of shape proxies. We demonstrate that the algorithm is robust even in the presence of many outliers and a high degree of noise. The proposed method scales well with respect to the size of the input point cloud and the number and size of the shapes within the data. Even point sets with several millions of samples are robustly decomposed within less than a minute. Moreover, the algorithm is conceptually simple and easy to implement. Application areas include measurement of physical parameters, scan registration, surface compression, hybrid rendering, shape classification, meshing, simplification, approximation and reverse engineering.
Hough has proposed an interesting and computationally efficient procedure for detecting lines in pictures. This paper points out that the use of angle-radius rather than slope-intercept parameters simplifies the computation further. It also shows how the method can be used for more general curve fitting, and gives alternative interpretations that explain the source of its efficiency.
A new paradigm, Random Sample Consensus (RANSAC), for fitting a model to experimental data is introduced. RANSAC is capable of interpreting/smoothing data containing a significant percentage of gross errors, and is thus ideally suited for applications in automated image analysis where interpretation is based on the data provided by error-prone feature detectors. The authors describe the application of RANSAC to the Location Determination Problem (LDP): given an image depicting a set of landmarks with known locations, determine that point in space from which the image was obtained. In response to a RANSAC requirement, new results are derived on the minimum number of landmarks needed to obtain a solution, and algorithms are presented for computing these minimum-landmark solutions in closed form. These results provide the basis for an automatic system that can solve the LDP under difficult viewing and analysis conditions. Implementation details and computational examples are also presented
This paper addresses the issue of 3D mesh indexation by using shape descriptors (SDs) under constraints of geometric and topological invariance. A new shape descriptor, the canonical 3D Hough transform descriptor (C3DHTD) is here proposed. Intrinsically topologically stable, the C3DHTD is not invariant to geometric transformations. Nevertheless, we show mathematically how the C3DHTD can be optimally associated (in terms of compactness of representation and computational complexity) with a spatial alignment procedure which leads to a geometric invariant behavior. Experiments carried out upon the categorized MPEG-7 3D model database objectively show that the C3DHTD outperforms both the MPEG-7 3D SD and classic EGIs descriptor.
A Probabilistic Hough Transform Efficient RANSAC for Point-Cloud Shape Detection
- N Kiryati
- Y Eldar
- A Bruckstein
- R Schnabel
- R Wahl
- R L Klein
- E Oja
- P Kultanen
Kiryati, N., Eldar, Y., and Bruckstein, A. (1991). A Probabilistic Hough Transform. Pattern Recognit., 24(4), 303–316. Schnabel, R., Wahl, R., and Klein, R. (2007). Efficient RANSAC for Point-Cloud Shape Detection. Comput. Graphics Forum. Xu, L., Oja, E., and Kultanen, P. (1990). A new Curve Detection Method: Randomized Hough Transform (RHT). Pattern Recognit
Deforming Scans for Improving the Map Quality Using Plane Extraction and Thin Plate Splines
- D Borrmann
- J Elseberg
Borrmann, D. and Elseberg, J. (2009). Deforming Scans for Improving the Map Quality Using Plane Extraction and Thin Plate
Splines. Master's thesis, Univ. Osnabrück.