FEATURE-BASED REGISTRATION OF RANGE IMAGES IN DOMESTIC ENVIRONMENTS

Transcription

1 FEATURE-BASED REGISTRATION OF RANGE IMAGES IN DOMESTIC ENVIRONMENTS Michael Wünstel, Thomas Röfer Technologie-Zentrum Informatik (TZI) Universität Bremen Postfach , D Bremen {wuenstel, Abstract Keywords: Registration is an important step to combine pictures that are taken either from different perspectives (multi-viewpoint), at different points in time (multi-temporal) or even from diverse sensors (multi-modal). The result is a single image that contains the combined information of all original images. We use D range data taken by a laser range scanner. During recording occlusions can leave some of the objects scanned incompletely. Thus it is the task of the registration to produce images which give the most complete view of the scene possible. An algorithm often used for the registration of range images is the ICP algorithm [7]. This point-based algorithm only uses local information, and it has the advantage that it is universally applicable. The drawbacks are that its very time consuming, it may converge in a local minimum, and the result cannot be evaluated absolutely. Therefore, for our domestic scenario we present an approach that first detects certain global features of the room and then uses their semantic and spatial information to register the range images. Thus this approach has the advantage that its tendency to get stuck in a local minimum is reduced and the overall performance is increased. Registration, Matching, Range Image, ICP, Feature Extraction 1. Introduction The algorithm most frequently used for 3-D point cloud registration is the ICP-Algorithm. In each step it determines the quality of the match and calculates a better rigid transformation T between the two data sets if possible. There exist various variations of the algorithm. An extensive comparison of the algorithms can be found in Rusinkiewicz and Levoy [7]. Their categorization is done concerning the main steps of the algorithm: The selection of the

2 2 points used, the matching of points, the weighting of corresponding points followed by a rejection of bad pairs, and the minimization of the energy function based on the chosen error metric. Therefore the possible variations are quite large and run from probabilistic oriented approaches [4] to numerical oriented approaches [5]. In Dallay and Flynn [2] several variants of the ICP-Algorithm have been tested and also the basic limitations of the algorithm are presented. As the calculation, especially of the nearest neighbors, is very computing-time expensive, and the algorithm may converge to a local minimum we show an alternative that uses the knowledge of extracted features to match the data sets. We show the mode of action within domestic environments. Thereby we extract the walls of a room (vertical planes), identify their relations, and use this knowledge to match the original range images. We get a good measurement to evaluate the registration not only by a number but by the relation of semanticbased features. 2. The Algorithms In this section we present our implementation of the Levenberg Marquardt- ICP (LM-ICP) algorithm which is based on the work of Fitzgibbon [3]. To overcome some problems of the generally applicable ICP algorithm as mentioned above we point out our feature-based matching method inspired by the work of Stamos and Leordeanu [10]. They extract planar regions and linear features at the areas of intersection to use them for registration. Our approach presented here is the extension of the work of Röfer [6] from 2-D (matching line segments) to 3-D (matching planes, namely walls). The LM-ICP-Algorithm The matching of planes is based on Fitzgibbon s ICP-Algorithm [3] and will be presented in more detail. The fundamental ICP-Algorithm mainly consists of an energy function that represents the fitness of the match between two data sets, and it has to be minimized. The value of the energy function is the weighted sum of the squared distances between the points in data set A and their nearest neighbors in data set B: B E(a) = w( m φ(i) T (a, n i ) ) 2 i=1

3 Feature-Based Registration ofrange Images in DomesticEnvironments 3 where: a m i n i φ(i) w parameters of the rigid transformation T from data set B to A point i of data set A point i of data set B index of the nearest point in data set A to point n i weighting function: identical, if the distance is below a certain threshold, constant otherwise The optimization consists of a main loop in which a new rigid transformation T is calculated and the quality of the match is evaluated through the energy function in every optimization step. This is repeated until a termination condition is achieved (either the progress per iteration step falls below a certain threshold or a maximal number of iterations is reached). In our implementation of the ICP-Algorithm we homogenize the points in a way that every point within a set of points has a minimum distance to its neighboring point. This prevents the algorithm from emphasizing regions with a high point density. To speed up the search for the nearest point of n i in the reference data set A we parse the points into a Kd-tree [1]. The search for the nearest neighbor is the most time consuming task in our implementation. The weight of a pair of points is given by their distance if the distance is below a certain threshold and has a constant value otherwise. The threshold is reduced in each minimization step until a minimal value is reached. Therefore points that are further away loose weight for the registration. No pairs are rejected. We either use the Euclidean distance or the Manhattan distance as an error metric. For the calculation of the new values we apply the Levenberg-Marquardt algorithm. Besides the energy function we use the difference quotient as an approximation for the derivation needed. That means that for every parameter two values of the energy function have to be calculated. As a starting position we transform the center of gravity of data set B into data set A. Our Approach: Feature-Based Registration As already mentioned the ICP-Algorithm is a powerful instrument for point registration although it has some drawbacks. The quality of a match can be evaluated numerically. Nevertheless the overall success is partly dependent on more or less random parameters such as the starting position. Therefore newer approaches try to extract features from the range data that can be used for matching [8]. That is a substantively difficult task as usually the registration is a preprocessing step, and therefore only a limited number of features of the sub-scene are available. In our domain, domestic environments, the room itself supplies such features. We extract the walls and analyze the relations between them. The algorithm is inspired by the work of [10] and [6]. The plane detection algorithm we use is based on the work of [9]. For every point it calculates

4 4 the normal vector and the point projected to the fitted plane from a neighboring region of this point. The neighboring points do not have to be calculated as they are given directly through the ordering of the scanning process. To calculate the plane we use SVD (Singular Value Decomposition). As a result we get the normal vector of the plane and the nearest point to the origin point on the plane. The normal vector is only taken if the corresponding singular value is below a certain local threshold. The potential planes are then calculated using a region-growing algorithm where again a co-planarity of neighboring values has to be achieved. The last step of the plane detection consists of a global comparison of the local normals with the average normal of the plane candidate. This enables us to sort out, for example, continuously curved surfaces. After having calculated the planes the actual registration algorithm can be started. Figure 1 shows the overview of the feature-based (FB) algorithm. It consists of three main parts. In the preprocessing step the walls are extracted and they are ordered spatially. In each data set the ordered two-element subsets are calculated. In the registration step, for every pair of the subsets calculated previously the transformation between the data set A and B is determined. Therefore the data sets are aligned with regard to the first walls of each data set (step 1) and afterwards moved parallel to these walls until the other walls are overlapping (step 2). In the last step, the winning registration is selected. The quality of a match is calculated from the number of center points of the data set B lying within a certain distance (0.05m) to a wall of data set A. To additionally be able to rate scans with the same number of matching walls, the overall sum of the distances is calculated. 3. Experiments and Results To perform our experiments we use the range data of an office scene. We will first apply the LM-ICP algorithm to the data and afterwards the FB algorithm. The data sets consist of two scans that were scanned from two different positions. The scene consists of the entrance area of an office with a book shelf, a cupboard, a door and a chair. The figures 2a and 2b show the scene from two different perspectives together with the scanning equipment. Figure 3 shows the two data sets before the registration process. For the ICP-based algorithm the centers of gravity of the two data sets are aligned afterwards. The result of the LM-ICP algorithm can be seen in figure 4. Figure 8 shows the planes detected for the range image resulting from the right position. Only planes larger than a certain threshold are taken into consideration. Here only neighboring information is used to fulfill the planarity condition. For the registration algorithm the condition has to be strengthened.

5 Feature-Based Registration ofrange Images in DomesticEnvironments 5 Figure 1. FB Registration Algorithm Figure 2a. Left view of the scene Figure 2b. Right view of the scene The figures 5 and 6 show the intermediate results of our feature-based matching algorithm. In the first step (figure 5) the two corresponding planes W Ai and W Bs are aligned (brighter walls on the right). In the second step (figure 6) the data set B is translated along W Ai in a way that W Aj and W Bt are congruent (brighter walls on the top). The black coordinate plane indicates the particular place and orientation of the scanning system. Figure 7 shows the final result of the best match. As the algorithm is based on the position of two corresponding wall pairs it is ambiguous in a sense that there exist more than one set that describes the right transformation.

6 6 Figure 3. Starting formation with homogenized point density Result of the LM-ICP Algo- Figure 4. rithm Figure 5. FB Matching, Step 1 Figure 6. FB Matching, Step 2 Figure 7. algorithm Result of the feature-based Planes detected (right posi- Figure 8. tion)

7 Feature-Based Registration ofrange Images in DomesticEnvironments 7 4. Conclusion and Outlook We have presented an approach that bases the registration on the recognition of robust domestic features namely vertical planes predominately the walls. In contrast to the common point-based ICP-algorithm this method is not using point correspondences but spatial relations of semantic features. For the future we have planned to incorporate even more semantic information such as the positions of certain furniture. Furthermore strategies for the fast handling of several scans simultaneously have to be investigated. Acknowledgments This project is supported by the Deutsche Forschungsgemeinschaft, DFG, through interdisciplinary Transregional Collaborative Research Center Spatial Cognition: Reasoning, Action, Interaction. References [1] J. Andreas Bærentzen. jab/ [2] Gerald Dalley and Patrick J. Flynn. Range image registration: A software platform and empirical evaluation. In Danielle C. Young, editor, Proceedings of the Third International Conference on 3-D Digital Imaging and Modeling (3DIM-01), pages , Quebec City, Canada, IEEE Computer Society, Los Alamitos, CA. [3] A. W. Fitzgibbon. Robust Registration of 2D and 3D Point Sets. In Proceedings of the British Machine Vision Conference, pages , [4] Dirk Hähnel and Wolfram Burgard. Probabilistic Matching for 3D Scan Registration. In Fachtagung ROBOTIK 2002, [5] P. Neugebauer. Geometrical cloning of 3D objects via simultaneous registration of multiple range images. In Proceedings of the 1997 International Conference on Shape Modeling and Application (SMI-97), pages , Los Alamitos, CA, IEEE Computer Society. [6] T. Röfer. Using histogram correlation to create consistent laser scan maps. In IEEE International Conference on Robotics Systems (IROS-2002), pages , [7] Szymon Rusinkiewicz and Marc Levoy. Efficient variants of the ICP algorithm. In Danielle C. Young, editor, Proceedings of the Third International Conference on 3-D Digital Imaging and Modeling (3DIM-01), pages , Quebec City, Canada, IEEE Computer Society, Los Alamitos, CA. [8] Nikolaus Schön. Feature evaluation for surface registration. Annual Report 32, University Erlangen-Nürnberg, [9] I. Stamos and P. Allen. 3-D Model Construction using Range and Image Data. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR- 00), pages , Los Alamitos, IEEE. [10] Ioannis Stamos and Marius Leordeanu. Automated feature-based range registration of urban scenes of large scale. In International Conference of Computer Vision and Pattern Recognition, volume 2, pages , 2003.