Building Polygonal Maps from Laser Range Data

Transcription

1 ECAI Int. Cognitive Robotics Worksho, Valencia, Sain, August 2004 Building Polygonal Mas from Laser Range Data Longin Jan Latecki and Rolf Lakaemer and Xinyu Sun and Diedrich Wolter Abstract. This aer resents a new aroach to the roblem of building a global ma from laser range data, utilizing shae based object recognition techniques originally develoed for tasks in comuter vision. In contrast to classical aroaches, the erceived environment is reresented by olygonal curves (olylines), ossibly containing rich shae information yet consisting of a relatively small number of vertices. The main task, besides segmentation of the raw scan oint data into olylines and denoising, is to find corresonding environmental features in consecutive scans to merge the olylinedata to a global ma. The corresondence roblem is solved using shae similarity between the olylines. The aroach does not require any odometry data and is robust to discontinuities in robot osition, e.g., when the robot slis. Since higher order objects in the form of olylines and their shae similarity are resent in our aroach, it rovides a link between the necessary low-level and the desired high-level information in robot navigation. The resented integration of satial arrangement information, illustrates the fact that high level satial information can be easily integrated in our framework. 1 INTRODUCTION The roblems of self-localization and robot maing are of high imortance to the field of mobile robotics. Robot maing describes the rocess of acquiring satial models of hysical environments through mobile robots. Self-localization is the method of determining the robot s osition with the robot s internal satial reresentation. The central method required is a matching of sensor data, which - in the tyical case of a laser range finder as the robot s sensor - is called scan matching. Whenever a robot needs to coe with unknown or changing environments, localization and maing have to be carried out simultaneously, this technique is called SLAM (Simultaneous Localization and Maing). To attack the roblem of maing and/or localization, mainly statistical techniques are used (Thrun [15], Dissanayake et al. [3]), e.g., the extended Kalman filter, a linear recursive estimator for systems described by non-linear rocess models and/or observation models, are the basis for most current SLAM algorithms. Bayesian rules build the foundation of the models emloyed. For localization, often artially observable Markov decision rocesses (POMDP) are utilized. The robot s internal geometric reresentation forms the basis for these techniques. It is build ato of the ercetual data read from the laser range finder (LRF). Tyically, either the lanar location of reflection oints read from the LRF is used directly as the geometric reresentation, or simle features in the form of line segments Temle University, Philadelhia, USA, latecki@temle.edu lakamer@temle.edu xysun@euclid.math.temle.edu University of Bremen, Bremen, Germany dwolter@informatik.unibremen.de or corner oints are extracted (Cox [2]; Gutmann and Schlegel [5]; Gutmann [7]; Röfer [14]). Although robot maing and localization techniques are very sohisticated they do not yield the desired erformance. We observe that these systems use only a very rimitive geometric reresentation. As the internal geometric reresentation is a foundation for the sohisticated techniques in localization and maing, shortcomings on the level of the geometric reresentation affect the overall erformance. The main goal of this aer is the introduction of an elaborate and cognitively motivated geometric reresentation and a reasoning formalism for robot maing. A successful geometric reresentation must result in a much more comact reresentation than uninterruted ercetual data, but must neither discard valuable information nor imly any loss of generality. We claim that the reresentation roosed in this aer, namely olygonal curves or olylines, reresenting arts of object surfaces being obtained from segmented scans, fulfills these demands. The relation among the objects is based on shae similarity and on qualitative arrangement information. Reresenting the assable sace exlicitly by means of shae is not only adequate for maing alications but also hels to bridge the ga from metric information needed to toological knowledge due to the object centered ersective offered. Moreover, an object-centered reresentation is a crucial building block in dealing with changing environments, as such a reresentation allows us to searate the artial changes from the unchanged arts. In this aer we focus on incremental building of the object reresentation. There exist aroaches to ma building that aly more sohisticated geometric method to scan data, e.g., Forsberg et al. [4] and Jensfelt and Christensen [9]. However, they focus on extraction of linear structures only, why we not only consider extraction of olygonal structures but also on similarity of olygonal structures. The similarity of olygonal structures is a driving force of our aroach. 2 MAP BUILDING PROCESS Ma Building is the rocess of memorizing erceived objects and features the robot has assed by, merging corresonding objects in consecutive scans of the local environment. The robot s internal satial reresentation is referred to as a ma, in the case of a feature based satial reresentation it is commonly referred to as a feature ma [15]. A key challenge in ma building is to match a local sensor reading against the global ma. Multile roblems occur, e.g., the noise of the data erceived must be filtered in a way to obtain the required features, and the corresondence between erceived objects must be found on the basis of the filtered (visual) features, since additional information, i.e., odometry, has roven to be inaccurate. This excludes the ossibility of simly suerimosing consecutive scans on to of one another, as can be seen in the examle shown in Figure 1(a). It shows the effects of accumulated errors in rotation and distance measure, because the geometrical roerties of the envi-

2 ronment indicated by the LRF urely interreted in connection with odometry increasingly differ from reality, resulting in large dislacements of the erceived objects and block-like reresentations in the global ma. Odometry is designed to record the distance the robot has traveled and the rotational angle the robot has turned with resect to the starting osition. However, odometry makes unreliable recording on a large scale. Using alignment based on shae similarity, we can construct a significantly better ma by correcting the errors of the odometry or even discarding the recording of the odometry comletely. The alignment is comuted using stable objects in the ma to calculate the current osition of the robot. Assuming that some objects in two consecutive scans are not moving, we align the stationary objects in the second scan to the corresonding objects in the first scan. The robot s movement and its osition defining the global osition of the scanned environment is achieved by the resulting movement and rotational angle comuted by the alignment. An examle global ma comuted using our alignment algorithm is shown in Figure 1(c). The scans are aligned iteratively, then suerimosed on each other without any information from the odometry. The row scan data alignment based on robot s odometry is shown in Figure 1(a). The quality of the ma in (c) is much better, and the objects can be easily identified. To have a fair comarison, the ma in (c) should be comared to the ma in (b). The ma (b) is obtained from (a) with a simle algorithm that corrects significant rotation errors of the odometry by finding rotation angles that maximize the roximity of long lines and rotated according the scans accordingly. Although the imrovement from (b) to (c) is significant, we can still find some fuzziness in certain areas of (c). This is due to the nature of the erceived data, which introduces noise in several ways: 1. Scanning an object with a fractal or nonrigid shae. An examle of such can be a lant in any office building. The locations of the scan oints on such objects are mostly random, and the recordings of the scan oints are not going to rovide us useful osition information, even if the robot is not moving. 2. Scanning objects too far away. Scanning objects far away inevitably will create more error than scanning objects close by, due to uneven ground or other movement/vibration effects. Aligning all objects in the scans, the error introduced by this defective data will accumulate and roagate. 3. Scanning moving objects. Objects are aligned under the assumtion that only the robot moves, being the only source of change of the distance between them. But once there is a moving object in the scan, such an assumtion is no longer true, and the alignment will not be reliable, esecially when the moving object is near the scanner. In the following we will address these roblems, and discuss their solutions in our framework. One shortcoming of the recursive alignment rocess is that when errors occur, they will not be corrected nor eliminated. In fact, they are most likely to be accumulated and roagated as show in Figure 1(c). Another drawback is that each scan still exists indeendently of the others, i.e., we are not creating a global ma comosed of objects in the common sense of the word, but comosed of a set of unrelated olylines. Hundreds of laser scans are rinted on aer and human eyes can easily identify objects from the rintout, but these scans cannot be used by robot localization because these objects are not resent in the internal robot reresentation. Hence a rocess is needed that can deal with these roblems, and that can create a global ma comosed of just a few objects. We roose such a rocess that we call merging in this aer. In order to describe it, we need to introduce some notation. A global ma is built iteratively as the robot moves. We denote the scan and the global ma at time by and resectively. Each scan and the global ma is comosed of olylines. We assume that the range data is maed to locations of reflection oints in the Euclidean lane, using a local coordinate system. These oints are segmented into individual olylines with a simle heuristic: Traversing the reflection oints following the order of the LRF, an object transition is said to be resent wherever two consecutive oints are further aart than a given distance threshold (20 cm in the case of our examle ma). The recise choice of the threshold is not crucial as subsequent rocessing accounts for differences. The obtained olygonal objects are further simlified to reduce the influence of noise (Section 3.1). We aly discrete curve evolution (DCE, described below) followed by least square fitting of line segments to obtain the simlified olyline objects. To create the global ma, we start with the first global ma being equal to the first scan. Assuming we have created the global ma at time, we use and to create in the following stes: We extract a virtual scan from the global ma. is the art of the global ma to which the revious scan was merged. The virtual scan is a corrected version of the actual scan. The noise correction was achieved by merging in the revious ste of to the global ma. We use shae similarity (described in Section 3) to find the corresondence between objects in and, which can be a manyto-many corresondence. Since is art of the global ma, we obtain the corresondence between and arts of the global ma. We align olylines in to the corresonding olylines in. We reeatedly aly the least squares method to find the otimal translation and rotation. The main difference in comarison to the standard aroaches is that the corresonding oints are limited to olylines with similar shae. Thus, we greatly reduce the roblem of local minimum. This allows us to align to even if the robot dislacment is large (see Figure 3). Finally, we merge the aligned scan to to create. Merging an aligned new scan to the global ma adds newly detected olylines in the surrounding area to the global ma while not discarding the existing olylines no longer seen by the robot. The goal is to roduce a global ma comosed of a few olylines. The details of merging are resented in Section 4. Reeating this rocedure iteratively for each new scan, we are able to create a global ma that remembers all the objects and features along the ath the robot has traveled. The result can be seen in Figure 1(d), which dislays the final global ma as a set of olylines. We used exactly the same raw inut data for all four mas in Figure 1. This feature-based aroach yields a comact reresentation, and most imortantly, it reresents the robot s surroundings by a single set of non-overlaing olylines that can be easily recognized and comared using shae similarity. 3 STRUCTURAL REPRESENTATION OF SHAPE A first ste in the resented aroach is to extract shae information from data acquired by a laser range finder (LRF). Polygonal lines, termed olylines, serve in our aroach as a fundamental building 2

3 (a) (b) t (c) (d) Figure 1. (a) A global ma built using the information from odometry only. (b) A global ma with significant rotation errors corrected. (c) A global ma built using the roosed alignment only. (d) A real global ma built using the roosed merging aroach. 3

4 K block. They already cature more context than other features tyically emloyed in scan matching aroaches (e.g., simle line segments or even uninterreted data). The richness of erceivable shaes in a regular indoor scenario yields a more reliable matching than other feature-based aroaches, as mixus in determining features are more unlikely to occur. At the same time, we are able to construct a comact reresentation for an arbitrary environment. However, we exloit even more context information than reresented by a single olyline considering shae as a structure of olylines. This allows us with basically no extra effort to coe with environments dislaying mostly simle shaes. 3.1 Grouing and Simlification of Polylines Polylines extracted from raw scan data still carry all the information (and noise) retrieved by the sensor. To make the reresentation more comact and to cancel out noise, we emloy a technique called Discrete Curve Evolution (DCE) introduced by Latecki & Lakämer [11, 12] which achieves these goals without losing valuable shae information. DCE is a context-sensitive rocess that roceeds iteratively. Though the rocess is context-sensitive, it is based on a local relevance measure for a vertex and its two neighbor vertices 5 : Hereby, denotes the Euclidean distance. The rocess of DCE is very simle and roceeds in a straightforward manner. The least relevant vertex is removed until this relevance measure exceeds a given threshold, thereby defining the level of olygon simlification. Consequently, as no relevance measure is assigned to end-oints, they remain fixed. The choice of a secific simlification threshold is not crucial, refer to Figure 2 for results. Imlementation of DCE can benefit from the observation that a olyline can be reresented simultaneously as a double-linked list and a self-balancing tree which reflects the order of relevance measures. Thus, the overall comlexity is "!#. Proceeding this way we obtain a cyclic, ordered vector of olylines. 3.2 Similarity of Polylines Matching scans against the global ma within the context of a shae based reresentation is naturally based on shae matching. This somehow revives a notion in Lu and Milos fundamental work [13] scan matching is similar to model-based shae matching that so far has not received much attention. In the resented aroach we adot a shae matching originated from comuter vision that has roven successful in the context of shae retrieval [12]. It may easily be adated to our needs. The roerty of invariance to change of scale as often desired in comuter vision aroaches is not adequate in our domain and must be excluded. To comute the similarity measure between two olygonal curves, we establish the best ossible corresondence of maximal convex arcs, where a convex arc is a left- or right-arcuated arc. To achieve this, we first decomose the olygonal curves into maximal subarcs that are likewise bent. Since a simle one-to-one comarison of maximal arcs of two olylines is of little use, due to the fact that the curves may consist of a different number of such arcs and even similar shaes may have different small features, we allow for 1-to-1, 1- to-many, and many-to-1 corresondences of maximal arcs. The main $ Context is resected in the course of simlification as vertices neighborhood changes. idea here is that we have at least on one of the contours a maximal convex arc that corresonds to a art of the other contour comosed of adjacent maximal arcs. The best corresondence, i.e., the one yielding the lowest similarity measure, can be comuted using dynamic rogramming, where the similarity of the corresonding visual arts is as defined below. Using dynamic rogramming, the similarity between corresonding arts is comuted and aggregated. The comutation is described extensively in [12]. The similarity induced from the otimal corresondence of olylines % and & will be denoted % &'. Basic similarity of arcs is defined in tangent sace, a multi-valued ste function reresenting angular directions of line-segments only. This reresentation was reviously used in comuter vision, in articular in [1]. Denoting the maing function by (, the similarity gets defined as follows: *) % &'+,.-/ % -0 1 &' 2 (43 65 ( ;:7< 5 where -/ % denotes the arc length of%, and the whole integral is over arc length. The constant8 3;:7 is chosen to minimize the integral (c. [12]). Obviously, the similarity measure is a rather a dissimilarity measure as the identical curves yield=, the lowest ossible measure. This measure differs from the original work in that it is affected by an absolute change of size rather than a relative one (c. [12]). It should be noted that this measure is based on shae information only, neither the arcs osition nor orientation are considered. This is ossible due to the large context information of olylines; osition and orientation will be accounted for when comuting the actual matching. 3.3 Matching of Polylines Comuting the actual matching of two structural shae reresentations extracted from scan and ma is erformed by finding the best corresondence of olylines which resects the cyclic order. We must also take into account that (a) not all olylines may get matched as the features visibility changes and (b) that due to segmentation noise (c. section 3.1) it is not necessarily a one-to-one corresondence. Furthermore, any corresondence of olylines induces an alignment of the olylines which constraints the scan s origin. For examle, matching a olyline erceived in front of the robot to a olyline that is based on the estimated osition of the robot to its right, the robot must have turned right. Hence, we demand all induced alignments to be alike. To enable efficient comutation of the matching, an estimation of the induced alignment is required. It can either be derived from odometry (if available) or simly reflect the assumtion that the robot has not moved. We stress that we do not use any odometry data in our aroach.? Let us assume that >.???DC?FE and >.?? E C0G E are two?h cyclic? ordered E vectors of olylines. Denoting corresondence of and I by relation J, the task can be formulated as minimization as follows.?h L"M N*O : N M GQPSR6T,U >? > EI ;V%XW 6Y.J Z? > [? > E \ min Hereby,% denotes a enalty for not matching a olyline. This is necessary, as not establishing any corresondence would otherwise yield the lowest ossible similarity =. The similarity measure is comosed of the shae similarity measure resented in Section 3.2 and the alignment measure considering the difference between the alignment induced by the corresonding olylines and the estimated one. 4

5 (a) (b) (c) (d) (e) (f) Figure 2. The rocess of extracting olygonal features from a scan. Raw scan oints (a) are groued to olylines (b), then simlification by means of DCE is erformed. Figures (c) to (f) show various simlification levels (1,5,10, and 15 resectively) highlighting that the recise choice the simlification level is not critical for shae information obtained. The grid denotes 1 meter distance. Considering alignments becomes necessary when many featureless shaes, e.g., chairs legs, need to be tracked. We use an adequate extension of the dynamic rogramming scheme to comute the best corresondence. The extension regards the ability to detect even 1-to-many and many-to-1 corresondences of olylines and results in a linear extra effort such that the overall comlexity is. Observe that is very low, it was around 10 for our examle ma, since this is the number of olylines in a scan. The outlined matching is owerful enough to track shaes even if no odometry information is available and the robot has traveled a remarkable distance between two consecutive scans. Figure 3 shows the olyline corresondence comuted by our method, where the corresonding olylines from two different scans are connected by dashed lines. As can be observed, aroaches based on the nearest oint rule fail in this case. Figure 3. Exemlary results of the shae based matching for two scans (green and blue olylines; the grid denotes 1m distance). 4 MERGING Merging an aligned new scan to the global ma adds newly detected features in the surrounding area to the global ma while not discarding the existing features no longer seen by the robot. It roduces a global ma comosed of olylines. It is common that ortions of the same object may be erceived as several indeendent objects in a single scan. Such a henomenon can haen when there is another object blocking the view, or simly because of the angle and the distance from which the object is viewed. During the merging rocess, we need to accurately identify objects in each scan, look for their corresonding objects in the existing global ma, calculate the udated osition of the object, remove moving objects, remove areas where there are objects with nonrigid shae, and more imortantly, merge several objects into a single object whenever ossible. The main idea of the resented merging rocess is to simulate the robot laser scanner to merge the aligned scan to the global ma. As outut we obtain an udated global ma. The simulated laser rays emanate from the current robot ose and follow the arameters of the robot scan device. This means for our data that the and cover the angle of "=. If a ray intersects a olyline in, we select the closest intersection oint to the robot ose, which is called a simulated scan oint (ss). We are creating at most 361 sss. Furthermore, we add all end oints of olylines in to the list of newly created scan oints with roer ordering (since we know between which scan rays they lie). From each ss in, we find the closest oint on. If the distance from to is below a certain threshold, then we take a weighted average of the two oints to create a new oint simulated rays move counter-clockwise in stes of =@ for the new global ma. We use a larger weight for the oint in, since we have more confidence about its osition. If the closet oint cannot be found within a certain distance, the ss will be a new oint on the new global ma. Since we want every olyline vertex in a global ma to have a corresonding oint in the new global ma, we have the following rule. If two consecutive sss and have two corresonding closest oints and in, and there is a vertex between and, we create a new ss in that is the closest oint 5

6 to in the art of between and. Then we take a weighted average of the two oints and to create a new oint for the new global ma. This ste is illustrated in Figure 4. L v 1 g1 sv L s2 s1 2 g2 Figure 4. is a vertex of a olyline of the global ma. is between the closest oints and to two consecutive simulated scan oints (sss) and on olyline in. In such case, we create a new ss in the scan as the closest oint to on a olyline of the scan. Then we take a weighted average of the two oints and to create a new oint for the new global ma. The next ste is to create a set of ordered olylines from the newly created oints (ncs) in the global ma. The following facts guide this rocess: 1. All ncs in the global ma are ordered. They either inherited their order from the simulated scan rays or where sorted in between two sss (who inherited their order from the simulated scan rays). 2. All consecutive ncs whose redecessors belonged to the same olyline either in or in are classified as belonging to the same olyline. 3. The arts of olylines in that are not redecessors of any ncs are integrated in as searate olylines. First we connect all consecutive (in scan order) ncs in the new global ma that belong to the same olyline. We further merge consecutive olylines and to a single olyline if the last vertex of and the first vertex of had redecessors in the same olyline either in or in. The motivation for this ste is that the olyline is likely to reresent a single object in (created from and ), since whenever two consecutive oints are in the same object either in or in, they can be classified as belonging to the same object. This rule imlies that searate ortions of the same object will be connected if they are ever detected as oints of the same object. The only excetion to this rule is a bifurcation, which may be caused by dynamic object, e.g., a moving door. To resolve bifurcations, we create two disjoint olylines in a global ma. The created olylines in the new global ma may not be roerly ordered. A olyline is roerly ordered if the order of its vertices is constant with the arc length distance to its first vertex i.e., vertex roceeds if the arc length distances satisfy / *. We aly recursively the following simle rule to obtain roerly ordered olylines: Let 4 be three consecutive vertices in a olyline Y, if the inner angle at is less then a certain threshold (which is = in our case), then vertex is removed. This rule not only makes olylines roerly ordered, but also removes scan artifacts due to sensor noise or due to objects with fine shae features like lants. This rule is justified by the fact that shar inner angles cannot be created by three consecutive laser rays unless they hit an object with fine shae. For objects with fine shae, we obtain a dense sequence of shar inner angles. Since this rule would remove them comletely, these kind of objects requires a secial treatment. Such objects have different reflections atters for different scans, thus, their shae may change from scan to scan. These object are not considered in the merging rocess, but they are laced on the global ma after merging. To (temorarily) remove objects, we use a bounding box around them, called eraser box, to erase the areas where the erceived data is highly unreliable. We create an eraser box in a scan by creating a bounding rectangle containing all consecutive vertices Y in each olyline of with inner angles that are less than =. If such a shar angle is san by three consecutive scan oints, it is very unlikely that these oints result from scan readings of a real object with a stable shae. Thus, such shar angles indicate either noisy readings or an object with fuzzy shae, like lants. The rocessing of eraser boxes is comosed of three main stes: (1) for each scan we identify eraser boxes, (2) we transfer the eraser boxes to the global ma, and (3) we merge overlaing eraser boxes in the global ma to a single eraser box that contain them. We need these three stes, because the data in a small area may aear to be reliable in a given scan, but aears highly unreliable in most of the other scans. Thus, we mark the whole area unreliable regardless of the quality of any single scan. The data inside the eraser boxes on the global ma is not used for further iterations of building the global ma. In order to create stable global mas, we can only merge erceived stationary objects, i.e., we need to detect moving objects and remove them from actual scans before merging. To remove moving objects, we use the result of shae matching to identify corresonding objects in scan and, say is matched to. We can also easily remember in the rocess of merging that is merged into the object in. Since and reresent the same real object, their distance after alignment should be very small. If this is not the case, the object is moving, in which case we need to backtrack to its first aearance in the scans, remove it, and redo the merging rocess again to remove any unwanted effects it may have caused. Finally, we aly DCE and least square fitting to create a new set of simlified olylines. An examle result is shown in Fig. 1(d). 5 CONCLUSIONS We have resented a comrehensive geometric model for robot maing based on shae information. Shae matching has been tailored to the domain of scan matching. The matching is owerful enough to disregard ose information and coe with significantly differing scans. This imroves erformance of today s scan matching aroaches dramatically. In this aer we concentrate on solving geometric roblems related to global ma building, and do not include any statistical methods, to demonstrate the ower of the roosed geometric aroach. However, we are aware that statistical methods are needed to guarantee robust erformance. A suitable extension of our aroach to include statistical methods will be resented in a searate aer. 6

7 ACKNOWLEDGEMENTS This work was suorted in art by the National Science Foundation under grant INT and the grant from Temle University Office of the Vice President for Research and Graduate Studies. It was carried out in collaboration with the SFB/TR 8 Satial Cognition, roject R3 [Q-Shae] suort by the Deutsche Forschungsgemeinschaft (DFG). All suort is gratefully acknowledged. REFERENCES [1] M. Arkin, L. P. Chew, D. P. Huttenlocher, K. Kedem, and J. S. B. Mitchell (1991). An efficiently comutable metric for comaring olygonal shaes. IEEE Trans. PAMI, 13: [2] Cox, I.J., Blanche An exeriment in Guidance and Navigation of an Autonomous Robot Vehicle. IEEE Transaction on Robotics and Automation 7:2, , [3] Dissanayake, G.,Durrant-Whyte, H., and Bailey, T., A comutationally efficient solution to the simultaneous localization and ma building (SLAM) roblem. ICRA 2000 Worksho on Mobile Robot Navigation and Maing, [4] J. Forsberg, U. Larsson, and A. Wernersson. Mobile Robot Navigation using the Range-Weighted Hough Transform. IEEE Robotics and Automation Magazine 21, , [5] Gutmann, J.-S., Schlegel, C., AMOS: Comarison of Scan Matching Aroaches for Self-Localization in Indoor Environments. 1st Euromicro Worksho on Advanced Mobile Robots (Eurobot), [6] Gutmann, J.-S. and Konolige, K., Incremental Maing of Large Cyclic Environments. Int. Symosium on Comutational Intelligence in Robotics and Automation (CIRA 99), Monterey, [7] Gutmann, J.-S., Robuste Navigation mobiler System, PhD thesis, University of Freiburg, Germany, [8] D. Hähnel, D. Schulz, and W. Burgard. Ma Building with Mobile Robots in Poulated Environments, Int. Conf. on Int. Robots and Systems (IROS), [9] P. Jensfelt and H. I. Christensen. Pose Tracking Using Laser Scanning and Minimalistic Environmental Models, IEEE Trans. on Robotics and Automation, [10] B. Kuiers. The Satial Semantic Hierarchy, Artificial Intelligence 119, , [11] L. J. Latecki and R. Lakämer (1999). Convexity Rule for Shae Decomosition Based on Discrete Contour Evolution. Comuter Vision and Image Understanding 73: [12] L. J. Latecki and R. Lakämer (2000). Shae Similarity Measure Based on Corresondence of Visual Parts. IEEE Trans. Pattern Analysis and Machine Intelligence 22: [13] Lu, F., Milios, E. (1997). Robot Pose Estimation in Unknown Environments by Matching 2D Range Scans. Journal of Intelligent and Robotic Systems 18: [14] Röfer, T., Using Histogram Correlation to Create Consistent Laser Scan Mas. IEEE Int. Conf. on Robotics Systems (IROS). Lausanne, Switzerland, , [15] Thrun, S. (2002). Robot Maing: A Survey, In Lakemeyer, G. and Nebel, B. (eds.): Exloring Artificial Intelligence in the New Millenium, Morgan Kaufmann,