Low cost characterization of 3D laser scanners

Transcription

1 Low cost characterization of 3D laser scanners Michele Russo *, Giorgia Morlando, Gabriele Guidi Dept. INDACO, Politecnico di Milano, Via Durando 38a, 20158, Milan, Italy ABSTRACT A range camera calibration represents a paramount importance step for being aware of its actual metrological performances and generating reliable point clouds during the 3D acquisition process. Depending on the range camera openness we might have systems pre-calibrated only once by the industrial manufacturer or systems requiring a regular (and mandatory) end-user calibration before any scan session. The system calibration greatly influences the whole geometrical generation process. It permits the choice of appropriate resolution in 3D scan planning and allows to properly interpret the alignment of several range maps trough Iterative Closest Point (ICP), deciding if it succeeded or not. Finally in polygonal model editing, the modification of geometrical features is greatly helped by the awareness about the 3D capturing device performances. These remarks are effective for both triangulation based instruments, like Minolta Vivid 910, ShapeGrabber SG100 and SG1000 evaluated in this paper, and TOF based instruments. This experimental method is based on post processing of the range data produced by acquiring the surface of a precise test object with a 3D laser scanner. In this procedure resolution, accuracy, and precision parameters are obtained sequentially, through the application of a set of simple geometric processing steps, starting from 3D scanner data generated by scanning at different distance a reference plane. The results obtained were compared with industrial manufacturer data in order to verify their quality, and the possible performance degradation respect to a brand new instrument. Keywords: 3D laser scanner, calibration, characterization, precision, accuracy 1. INTRODUCTION The operating parameters of 3D laser scanners determine the way such systems can be properly used for acquiring geometrical data, and implicitly the whole data processing leading to the construction of a 3D polygonal model. Any manufacturer provides a few metrological information generally obtained after the system calibration, and certifies the correctness and completeness of parameters on the instrument datasheet. On the other hand the final user has to know in advance some basic metrological characteristics of his measurement system - like field of view or working distance - in order to have a proper control over its survey project. If unfortunately the metrological parameters of a scanner are different from what the manufacturer declares, or for some reasons are appropriate at the system purchase but change in time, the user may have completely wrong results. Despite a good equipment maintenance is obviously desirable, using a 3D camera without a defined data checking procedure by the metrological point of view may be a jump in the dark, as demonstrated in the literature [1, 2]. This paper describes an experimental method that may help the awareness of the average 3D scanner user. The proposed technique is easily available, requires only simple additional tools and permits to verify the parameters produced by manufacturer, carrying out missed data in datasheets enclosed to range camera. The aim of this experimental method is to define a simple process that can be applied to every range sensor independently of its working principle, obtaining an objective evaluation about system resolution, measurement uncertainly and accuracy. The final result is a table that summarizes the behaviour of a particular range camera in different working conditions (sensor to surface distance, sensor axis to surface normal angle, etc.). This permits to detect possible unreliable outputs, helping the operator to decide when is time to re-calibrate the instrument, allowing in general a better control during the definition of a survey project and a proper post processing over the acquired data. * michele.russo@polimi.it; phone ; fax

2 2. STATE OF THE ART The topic of the paper regards the characteristics that mostly influence the quality of a 3D acquisition: resolution, measurement uncertainly and system accuracy [3]. Normally every country since 1960 has recognised and adopted Le Systeme International d'unites (SI), that permits to define the measurement uncertainly level as required by ISO These set of definitions leave out the field of range cameras, which is not regulated by standards, assigning to the final user the responsibility of guarantying an acceptable level of metrological reliability [4]. A 3D acquisition system calibration consists in extracting internal parameters to define a mathematical model that describe the system behaviour in relation to instrument characteristics like focal length, lens distortions etc. Calibrated instruments deliver better output data because they present a low systematic error and are mainly characterized by a random uncertain error. Accuracy error minimization is related to the calibration process quality; a low level calibration corresponds to a worst accuracy (i.e. a higher residual systematic error). In a triangulation range camera the resolution parameters are related to its local coordinate system, which in general identify the optical axis of the recording camera as the z axis. Horizontal resolution is defined by a sampling grid over the xy plane, whose spatial frequency can t be endlessly increased due to the physical phenomenon of diffraction, that involves mutual interactions between adjacent sampling cells when their spacing is below a defined limit. This is generally different from depth resolution along z axis, influenced also by the camera-to-target distance and the baseline [3]. The equipment precision, defined by the amount of measurement uncertainty, is a random error depending on different factors: the electronic noise produced by sensor reading and signal amplification has a key role, but also optical phenomenon may add their contributions. When an active range sensor is based on laser, the coherent nature of such light source involves interferences between different light contributions backscattered by a diffusive surface, that in general come from slightly different ranges. The superposition of randomly delayed light waves generates the wellknown speckle effect on the laser spot detected by a range sensor, that affects precision too. Due to such nature, measurement uncertainty can t be deterministically measured and rectified by a calibration process as for accuracy. The only feasible approach is to determine the variation of this parameter through a statistical analysis on a population of sample measurements, in order to predict a reasonable value expected for a new measurement. It is so necessary to know in advance the true value of each measured point, in order to calculate an histogram of deviations between true and measured points, whose distribution is usually close to a Gaussian due to the dominant contribution of thermal (electronic) noise. The standard deviation that can be calculated on such population of random values, is the average range error that we can expect over an acquired range map, and it can be used to define the equipment precision. Fig. 1. Schematic representation of a triangulation based range camera with their main components.

3 Accuracy defines the systematic error present on a range map. It only depends on intrinsic characteristics of the instrument and its variation, as uncertainly, is related to the distance from the survey surface and sensor orientation respect to the object. If these external conditions remain unchanged, there is no variation in accuracy error. This kind of error can be minimized by a calibration process, recording the residual parameters obtained at the end of task. For the reason described before, range camera has to be positioned in different location in order to scan a calibrated object from different points of view. A lot of calibrated objects can be found in the market place and presents different levels of price and precision: terrace pyramid-shaped objects, target plates, spheres on rotating table, concentric cylinders, objects composed by inclined planes characterized by angles measured with CMM, flat objects with circular holes. These kind of things are used in metrology field to obtain a particular accuracy in measurement [1], but they are very expensive especially in relation with the dimension of the calibrated object, that have to be consistent with the range camera field of view. Planar object are cheaper than the calibrated ones, they can be easily found and employed from a non qualified user. A rectified plane can be used for the characterization of a range camera if the roughness of its surface is one order of magnitude lower than the smaller dimension that can be deterministically recorded by the instrument. A range camera can achieve 50/100 µm for a single measurement, for this reason the planarity level of the test plane has to be inside the 5/10 µm range. 3. MATERIALS AND METHODS The instruments used in this experiment are one reference plane and four range cameras present in the Reverse Modeling Lab at Politecnico di Milano. In particular we used: - 2 range cameras Minolta Vivid 910 provided with tripod that permits a rotational movement of the head scanner along three axes; - 1 range camera ShapeGrabber SG100 provided with a mechanical linear rail system; this permits a 60 cm horizontal translation of the sensor side by side the supporting plane; - 1 range camera ShapeGrabber SG1000 provided with mechanic rotational head that permit a 330 rotation along vertical axes. 3.1 Reference plane The dimensions of the plane used as reference are 700 x 528 x 11 mm. In order to guarantee the small deviation from planarity and a low cost, it was chosen to use a thick piece of glass. The particular manufacture process of this material allows to obtain a plate characterized by peak deviation inside a range of few microns, so proper to be used as target test. The problem with glass is its transparency, therefore one side of the plane was painted with matt white flat varnish obtained with a particular method that includes a furnace treatment, as for car painting. This permits to avoid the clearness problem of the glass, obtaining a perfectly smooth and optically cooperative surface. 3.2 Laser line triangulation scanner The SG100 (produced by Shape Grabber Inc., Ontario, Canada) is mounted on a high precision linear rail. It represents an example of precise and expensive scanning platform compared to other range camera on the market place. The minimum distance (standoff) is 130 mm and the Depth of Field (DOF) is 160 mm. The maximum working distance is 290 mm while the overall scan volume is 590x160x165 mm.

4 Fig. 2. Three different typology of range cameras: a Minolta Vivid 910 mounted on a tripod, a ShapeGrabber SG100 mounted on a high precision rail, a ShapeGrabber SG1000 mounted on a tripod provided with rotating mechanism. The range camera is provided with a linear sensor capable to acquire n=1280 points for each profile. The angle covered by the laser line is ϕ=21.49, hence the resolution along this axis (x) is directly related to the camera-to-surface distance d, according to the following equation: x d x d ϕ π n 180 and, substituting the actual numerical values: π d ( ) For example on a planar object orthogonal to the laser light plane, located at d=250 mm, we obtain x=73µm. The resolution along the rail (y axis) depends only on the mechanical movement step controllable by an operator, whose value can be set as low as 100 µm. The SG 1000 is produced by the same manufacturer is mounted on a rotating head. A scan head with longer baseline permits to reach minimum measuring distance of 250 mm, and a DOF of 900mm, giving a maximum working distance of 1150mm. The laser line aperture angle is ϕ=26.61 and the points acquired by the sensor for each profile are the same of SG100. Therefore the resolution along the laser line changes according with the relationship seen before, replacing the numerical value for the angle becomes: x d π d ( ) The aforementioned planar object oriented as mentioned above (d=250 mm), gives a x resolution of x=91 µm. Similarly, on the y axis, the resolution is defined by the range d and rotation step of the head θ, according to the following formula: y d θ π 180 Choosing a proper value of θ, a range maps characterized by a homogeneous resolution in the two horizontal directions x and y, can be obtained.

5 Fig. 3. 3D scanning of the glass plane used as planar reference for characterizing the four range cameras used in this experiment, such as the SG100 (left) or the Minolta Vivid 910 (right). The last range camera used is Minolta Vivid 910, a range camera equipped with three exchangeable lenses characterized by three different focal distance (25, 14, 8 mm). With a baseline of 250 mm, the minimum measuring distance is 600 mm and the DOF reported on the datasheet is 1900 mm, giving a maximum working distance of 2500 mm. The points acquired by the sensor are 640 x 480 for each scan. The range camera is provided with a bi-dimensional CCD, so the dimensional relationship between resolution in x and y axis is fixed, depending only on the CCD geometry. 3.3 Methodology The principal methodological problem consists in obtaining a quality evaluation starting only from a set of measured data, without a corresponding set of reference data measured with an alternative (and far more precise) method, as rigorous metrology would require. As a simplified solution we choose to carry out test measurements on a planar test object, generating the theoretical data set as the plane minimizing the least square deviation from the acquired data. Therefore we made the simplifying assumption that the summation of accuracy and precision errors was a zero mean random process. By comparing the acquired range map with the theoretical (best fit) plane equation, it was possible to perform a statistical analysis of residual deviations that gives a first approximation of the range camera measurement uncertainty. Once the amount of random error is estimated, the cloud of points is processed in order to cancel (or at least strongly attenuate) the small random variation in the measured coordinates, leaving the underlying behavior, presumably characterized by a lower spatial frequency, due to equipment systematic errors. On the processed cloud of point another theoretical vs. real coordinates comparison can be done, creating color maps of error distribution and calculating average and peak deviations of the residual error. The latter step gives an estimate of the system accuracy. 3.4 Software employed Four different pieces of software were used during the experiments. The first is a procedure ( pe ) specifically developed in Matlab for performing a statistical analysis of data coming from range camera. The outputs of this program are resolution, evaluated as the average point-to-point difference along x and y, standard deviation of error (RMS) and peak deviations. The extraction of such parameters involves both the range map and a plane created from best fitting with a plane equation the range map points. At the end of the process the program gives also a color map provided with color scale, which describes range map deviations from the reference plane. A small piece of software ( PIFavg ) developed in C++ for averaging range maps and saving them in PIF (Innovmetric) format. Polyworks (InnovMetric Inc., Quebec, Canada) was used for data format conversion of the range map, and for comparing sections extracted from different range maps.

6 Finally 3DOutlook, a research product developed by National Research Council Canada (NRCC), was used for smoothing the cloud of points with a Gaussian filter. 3.5 Experiment setting The experiments were performed at the Reverse Modeling Lab at Politecnico di Milano. It is located underground in order to minimize measurement errors due to external or environment factors (building vibrations). For these reasons this lab is considered a proper setting to carry on the described experiment, assuring a good reliability level during the scan phases. In this lab it is possible to use different light sources like halogen lamp or incandescent lamp. This condition permits to control the ambient lighting intensity, defining the optimal operating conditions. 4. EXPERIMENTS 4.1 Resolution and Precision vs. distance The first step is the definition of survey set. The Glass plane is positioned at the same distance from the laser source presented in the manufacturing datasheet, so at the beginning of the experiment a rough degree of homogeneity between scanned to given parameters can be verified. At the end of this first task we choose the better lighting condition for the scanning process in order to avoid low contrast areas, and we adjust the glass orientation respect to the range camera for eliminating (or at least minimizing) possible laser light reflections that generate unreliable data. The second stage is the acquisition of the test plane; during this phase the sampling step along x and y axis is carefully controlled in order to obtain a set of homogeneous measurements. This check is necessary only for the SG100 and SG1000 range cameras, which permit to modify the input resolution along axis controlled by mechanical system, while Minolta Vivid 910 has a bidimensional CCD that guarantee a regular acquisition grid. The range map obtained is given to the Matlab procedure, capable to open Innovmetric PIF format. If the raw data are in a different format (i.e. Minolta Vivid CDM files), these are converted in PIF format through a Polyworks module. Once the data are accepted by our custom Matlab tool, it allows to select a portion of range map from which calculating the best fitting plane through the principal components analysis (the plane whose normal corresponds to the smaller autovector of the scatter matrix is chosen, and is assumed as z direction). At the end of this phase, uncertainly measures and resolution parameters are extracted from the range map. The first one is defined as the standard deviation of the scanned points in comparison with the best fitting plane, while the second one is obtained from an algorithm that evaluates the average sampling step along x and y directions. Fig. 4. This sequence of images summarize the different phases of parameters extraction through the comparison between range map and best fitting plane. The first one on the left show a range map, the second one the same data with a plane (in pink colour) defined by best fitting method of selected points; on the right is presented a colour map of the deviations between range map and primitive geometry defined as reference.

7 4.2 Accuracy vs. distance In order to define the measurement accuracy starting only from the acquired data set, with no absolute references, it was necessary to establish a process capable to separate random errors from systematic errors, trying to extract a suitable index from the cloud of points, once the random component was cut off. A first step towards this goal was obtained by averaging the spatial positions of points belonging to range maps generated from the same scenario. Indicating with N the number of averaged range maps the measurement uncertainty due to truly random errors can be reduced of a factor proportional to the root square of N [5]. In this reduction it is not taken into account the speckle related component, which behaves apparently as a random error, but which gives the same pseudo-random pattern if the scenario (i.e. the senor-to-target distances) remains exactly unchanged. This operation was therefore carried out maintaining unchanged the scanner position and acquiring apparently equal data sets. In this way the random error changes distribution in every range map, while the systematic one remains unchanged. On the averaged data the same process described above was applied, evaluating its standard deviation. In this way, for the same scanner-to-target distance, several range maps were created, corresponding to an increasing number of averages N. The results in figure 5 shows the value of standard deviation vs. N for Minolta Vivid 910 range scanner equipped with 14 mm focal lens, set at 600 mm from the planar reference. This result demonstrates the progressive standard deviation reduction corresponding to a larger number of averaged sets. Although such reduction continues as the number N grows, a stronger effect can be noticed at the first steps of the graph. A reasonable tradeoff between the time for acquiring the range maps and the degree of random error reduction was chosen setting N=4. Once the first noise reduction step is completed, a residual random variation remains. For this reason a second noise reduction step was added, consisting in a Gauss filtering of the range map with a cutoff frequency high enough for leaving unchanged the systematic components and strongly attenuating the random ones. It is possible that a non correct application of the filter produces an alteration of systematic errors. For this reason at the end of such filtering the range map was qualitatively compared with other ones through by comparing sections coming from different level of filtering, starting from unfiltered data. The averaging and filtering process was then applied at the various analyzed distances, and the accuracy parameter was defined as the peak fit-plane to filtered data distance. Fig. 5. Behavior of the RMS measurement error vs. the number of averaged range maps N. It is clear that the strongest RMS reduction is obtained at the first steps of the graph. Averaging more than four range maps the improvement becomes negligible.

8 5. RESULTS Precision and resolution parameters are extracted from every range map, while accuracy is defined only for three selected distances (near, middle, far) due to the long procedure. But results obtained are at least sufficient to define a trend value. Fig. 6. Colour map obtained at the end of the analyzing process on a single range map. Such representation makes evident the presence of a periodic fluctuation of range data due to systematic errors, that can be evaluated by detecting the peak deviation. The experiment has lead to results similar to those reported in table 1, where the specific data obtained from a Minolta Vivid 910 with middle lens are presented. In grey columns the list of parameters extracted from every range map acquired for a particular distance are shown. In red the difference between data extracted from experiment and data given by manufacturer are reported. As can be seen the variation of resolution and standard deviation between new and original parameters is very small while the accuracy divergence is evident. This can derive from the articulate process that lead to this parameter, but it is hard to judge because in unknown the method applied by manufacturer to determine accuracy parameters Table 1. List of resolution, measurement uncertainty and measurement accuracy obtained with the proposed method for a Minolta Vivid 910 with middle lens. These have been compared with the data contained into the datasheets given by manufacturer. Distance Resolution Res / / / / -0,116 / Std. Dev Std Dev. -0,008-0,017-0,033-0,016-0,019-0,002 0,063 0,096 0,099 0,157 Accuracy Acc. 0, , ,103

9 6. CONCLUSION This procedure demonstrates that is possible to obtain 3D scanners operating parameters by a low cost and easy-to-apply method realized in lab. This characterization system permits to verify data contained in datasheet supplied by manufacturer and, during recurrent check of instrument, to compare the real performance of range camera with its nominal one. Moreover, homogeneity between experimental results and data contained in datasheet confirms the effectiveness of this proposed method, which enables to define range camera characteristics with a good approximation level. This kind of inspection should be executed at the beginning of every survey project or, at least, with a timely frequency (e.g. once a month). This routine, unlike the customary way to uncritically accept the instrumental data, should lead to a more correct 3D survey, combining every range map with the certification of the scanner performance, which can change in time. Finally this method gives an objective rule in range camera control in order to decide if it is necessary a manufacturer maintenance. REFERENCES 1. El-Hakim, S.F., Beraldin, J-A., Blais, F., 1995, A comparative evaluation of the performance of Passive and Active 3-D Vision Systems, in: Proc. St. Petersburg Conference on Digital Photogrammetry, St. Petersburg, Russia. 2. Guidi, G., Beraldin, J-A., Ciofi, S., Atzeni, C., 2003, Fusion of range camera and photogrammetry: a systematic procedure for improving 3D models metric accuracy, in: IEEE Transactions on Systems Man and Cybernetics Part B- Cybernetics, Vol 33-4, pp Guidi, G., Beraldin, J-A., 2004, Acquisizione 3D e modellazione poligonale. Dall oggetto fisico al suo calco digitale, ed Poli.Design, Milano. 4. Beraldin, J-A., Gaiani, M., 2005, Evaluating the performance of close range 3D active vision systems for industrial design applications, In: Proceedings of the Videometrics VIII, part of the IS&T/SPIE Symposium Electronic Imaging 2005, San Josè Convention Center, California, USA. 5. P.D. Welch, The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms, IEEE Transactions on Audio Electroacoustics, Volume AU-15 (June 1967), pages Rioux, M., 1997, Colour 3-D Electronic Imaging of the Surface of the Human Body, in: Optics Lasers in Engineering, 28, pp Beraldin, J-A., El-Hakim, S.F., Cournoyer, L., 1993, Pratical Range Camera Calibration, in: Proc. Videometrics II, SPIE, pp