Geometric Edge Description and Classification in Point Cloud Data with Application to 3D Object Recognition

Geometric Edge Description and Classification in Point Cloud Data with Application to 3D Object Recognition Troels Bo Jørgensen, Anders Glent Buch and Dirk Kraft The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, Campusvej 55, Odense, Denmark Keywords: Edge Detection, Object Recognition, Pose Estimation. Abstract: This paper addresses the detection of geometric edges on 3D shapes. We investigate the use of local point cloud features and cast the edge detection problem as a learning problem. We show how supervised learning techniques can be applied to an existing shape description in terms of local feature descriptors. We apply our approach to several well-known shape descriptors. As an additional contribution, we develop a novel shape descriptor, termed Equivalent Circumference Surface Angle Descriptor or ECSAD, which is particularly suitable for capturing local surface properties near edges. Our proposed descriptor allows for both fast computation and fast processing by having a low dimension, while still producing highly reliable edge detections. Lastly, we use our features in a 3D object recognition application using a well-established benchmark. We show that our edge features allow for significant speedups while achieving state of the art results. 1 INTRODUCTION Edge detection in general is a highly investigated topic in computer vision, mainly due to the possibil- ity of condensing the input observations with a lim- ited loss of information. This is beneficial also for 3D applications, e.g., point cloud enrichment (Gumhold et al., 2001) and pose estimation (Buch et al., 2013a), since it can decrease computation times. For these reasons, 3D edge detection should be fast, and it Figure 1: Left: a scene captured with a laser scanner (Mian should be easy to use for general point clouds, con- et al., 2006). Right: edge detector response using our taining noise and varying sampling densities. A 3D method (red means high confidence). edge detection example is shown in Figure 1. Several other methods have been proposed to tack- led the issue, including (Gumhold et al., 2001; Guy for finding an edge confidence: 1) directly using a cur- and Medioni, 1997; Pauly et al., 2002; Pauly et al., vature estimate produced by our descriptor or 2) us- 2003). These methods tend to rely on complex hand- ing machine learning techniques with labeled training crafted analyses of large local neighborhoods in order data. Finally, we adopt a non-maximum suppression to determine stable edge confidences. For this reasons technique similar to that of Canny for our 3D edges they become computationally expensive. to arrive at a more condensed representation of point We propose to use a staged approach to produce a clouds, which is desirable for matching tasks in e.g., simpler and faster algorithm, as done in 2D by e.g., object recognition applications. Canny (Canny, 1986), but with very different pro- We evaluate both our curvature based and learning cesses since we are dealing with 3D data. We first based edge detectors against several other methods on estimate the edge direction using a local neighbor- point cloud data from multiple sensor modalities. For hood. Then we compute our local ECSAD descriptor these experiments, we have manually annotated both for describing the neighborhood, and then use the de- training and test data, which provides a benchmark for scriptor to refine the edge direction estimate. Based comparing 3D edge detectors, and allows for future on this descriptor we provide two alternative methods extensions. In a final application, we apply our edge Jørgensen T., Buch A. and Kraft D.. 333 Geometric Edge Description and Classification in Point Cloud Data with Application to 3D Object Recognition. DOI: 10.5220/0005196703330340 In Proceedings of the 10th International Conference on Computer Vision Theory and Applications (VISAPP-2015), pages 333-340 ISBN: 978-989-758-089-5 Copyright c 2015 SCITEPRESS (Science and Technology Publications, Lda.) VISAPP2015-InternationalConferenceonComputerVisionTheoryandApplications representation to a 3D object recognition and 6D pose derived an appropriate local shape descriptor, termed estimation system and show how to achieve both high ECSAD, which can be used for detecting edges, either recognition rates and significant speedups during this directly by a curvature estimate produced by the de- process. scriptor or by learning an edge classifier in descriptor This paper is structured as follows. We start by space. To our knowledge, current shape descriptors, relating our work to other methods for edge detection such as e.g., (Johnson and Hebert, 1999; Mian et al., in Section 2. Then we present our descriptor which is 2006; Rusu et al., 2009; Tombari et al., 2010), are used for reliable edge detection in Section 3. We then focused strictly on the task of describing local shape show in Section 4 how any descriptor can be used for patches of arbitrary geometry for use at a later match- learning an edge detector. In Section 5 we present ing stage. a simple edge thinning scheme for point clouds. In Finally, we motivate the use of our edges and asso- Section 6 we provide extensive experiments of vari- ciated descriptors in a 3D object recognition applica- ous edge detectors, and we additionally show how to tion, where we also apply our descriptor for matching, use our features for 3D object recognition. Finally, leading to state of the art recognition performance. we make concluding remarks in Section 7. We note that, similar to our work, the edges detected in (Buch et al., 2013a; Choi et al., 2013) were also applied for object registration, in the latter case based on point pair features, originally proposed by (Drost 2 RELATED WORK et al., 2010). However, the edge detection method of (Choi et al., 2013) is restricted to organized RGB- The majority of edge detectors have been developed D images, and not general 3D shapes, which renders for 2D images, and one of the most common edge de- evaluations against our work impossible. We do, how- tection algorithms is the Canny edge detector (Canny, ever, compare ourselves with the registration algo- 1986), which revolves around semi-global methods in rithm of (Drost et al., 2010). order to capture more salient features. In (Choi et al., 2013), Canny based methods were applied to RGB-D images from a Kinect camera in order to determine geometric and color based edges in organized point 3 LOCAL SURFACE clouds. DESCRIPTOR FOR EDGE Geometric edge detection in general 3D data DETECTION structures has also gained some attention. For in- stance, (Bahnisch¨ et al., 2009; Monga et al., 1991) We have developed a local descriptor focusing on have implemented edge detector in voxel based 3D edge detection and classification, partly to determine images. These methods are largely extensions of the the direction of the edges, and partly to be used in su- Canny detector to 3D, with a few modification to re- pervised learning for edge detection. The descriptor duce computation times. is a vector of relative angles between opposing sides For unorganized point clouds, local point or direc- of the edge, which we have found to provide a good tion information has been exploited to detect edges. description for geometric edges caused by orientation In (Guy and Medioni, 1997) a PCA analysis of the discontinuities. Before descriptor estimation, the in- normals is made in order to determine how much the put point cloud is down-sampled to a uniform resolu- surface varies. The work in (Pauly et al., 2003) pro- tion. The radius of the spherical support (the area that poses to use the curvature estimates at several differ- influences the descriptor) is a free parameter, but we ent scales in order to determine a edge confidence. have consistently used a value of five times the down- Gumhold et al. (Gumhold et al., 2001) propose to use sampling resolution for simplicity. a more complex combination of eigenvalues, eigen- As will be explained in the following, our descrip- vectors and other curvature estimates in order to de- tor uses a spatial decomposition which gives each spa- termine a handcrafted edge confidence. This paper tial bin approximately the same circumference. Con- also proposes to use a minimum spanning tree where trary to other descriptors that use histograms, our uses short branches are removed in order to do edge thin- simple but stable angle measurements. For these rea- ning. A final spline fitting provides a smoother visual sons, we term our descriptor Equivalent Circumfer- representation. ence Surface Angle Descriptors (ECSAD). In this work, we address the detection of 3D edges in unorganized (or unstructured) point clouds. Such Spatial Decomposition. Similar to other local sur- edges often occur at orientation discontinuities where face descriptors, we use a spatial decomposition, two planar surfaces coincide. For this task, we have which is illustrated in Figure 2 by a cross section 334 GeometricEdgeDescriptionandClassificationinPointCloudDatawithApplicationto3DObjectRecognition the correct spatial bin based on its radial and azimuth coordinates relative to the center point. This is done using the direction vector from the center point to the supporting point. The radial component is immedi- ately given by the norm of this vector, while the azimuth component is given by the relative angle between this vector and the x-axis, measured in the tan- Figure 2: Left: visualization of the computed descriptor at gent plane of the normal vector. For each bin, we an edge point with a tangent direction (red) and a surface normal (blue), please see text for a description how these now compute the relative angle between the surface are defined. The spatial bins are intersected by a number of normal and the direction vector to each point in the surface points, and the contents of each bin is visualized by spatial bin. This angle is then averaged over all points the plane patch spanned by these intersecting surface points.

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