Abstract-Errors in laser based range measurements can be divided into two categories: intrinsic sensor errors (range drift with temperature, systematic and random errors), and errors due to the interaction of the laser beam with the environment. The former have traditionally received attention and can be modeled. The latter in contrast have long been observed but not well characterized. We propose to do so in this paper. In addition, we present a sensor independent method to remove such artifacts. The objective is to improve the overall quality of 3-D scene reconstruction to perform terrain classification of scenes with vegetation. Our goal is to devise methods for fast and accurate three-dimensional (3-D) representation of natural scenes containing vegetation for autonomous robot operations. We consider both ground and aerial platforms using a LADAR 1 as the primary sensor. Tasks envisioned are obstacle detection, path planning, scene understanding, target detection and tracking in cluttered 3-D environments. We have already reported related work in several publications; see [13] , [14] , [7] In such context, it is important to obtain an accurate 3-D reconstruction of the scene in order to be able to capture thin details such as branches, wires or obstacles hidden inside the grass. However, LADAR tends to produce erroneous range measurements. One source of error is due to the LADAR itself: range drift due to temperature variations, systematic errors and spurious random noise, etc. Large efforts have been devoted to the characterization [8] and the modeling of such errors [6] . Such aspect is out of the scope of this paper. The second source of errors is due to the interaction of the laser beam with the environment, for example when the beam hits simultaneously two targets at different distances. Such errors are known in the literature as mixed pixels. We choose to call them mixed measurements to avoid confusion with 2-D image processing and also to avoid the impression that we are using a sensor that produces a dense range image. If early papers recognized their existence, there has been little effort to characterize them exhaustively. In this paper we do so and present a complete taxonomy of mixed measurements. We refer to measurements which are not mixed as correct measurements to emphasize the fact that these returns correctly represent the scene. This analysis was used to 1 Light Amplification for Detection And Ranging develop a sensor-independent method to filter mixed measurements from data. The several variants of our approach use the specific distribution of mixed measurements in 3-D to detect them. By increasing the overall accuracy of the representation of the scene, this method allowed us to improve classification performance. In the next section we will present the state of the art in sensing in terrain with vegetation and in detection and filtering of mixed measurements. Following that, we introduce the mixed measurement phenomena we have observed and how each was observed. Then we describe our approach to filtering mixed measurements, and finally discuss the performance of these methods. The reader interested in additional details of our work will find a longer version of this paper available as a technical report [12] . II. STATE OF THE ART Depending on the application, several sensing modalities can be used in terrain containing vegetation: 1) color and multispectal cameras, for 2-D scene classification to identify vegetative cover; 2) millimeter wave (MMW) radar or synthetic aperture radar, to see through the vegetation to detect targets or obstacles even at long range but with low resolution. Global properties of the area illuminated can be extracted from the pulse returns but cannot be used for high fidelity reconstruction [10]; 3) echolocation to see through grass at short range and low resolution [11]; 4) stereo vision with specialized pre-processing image filters to reconstruct forest scenes in 3-D at short range [4], [5]; 5) LADAR sensors, which are the most commonly used. The existence of mixed measurements is a long standing problem but very few papers explicitly address it. Continuous Wave (CW) LADAR are particularly prone to such phenomena. In [9] Kweon presents a characterization of the Perceptron laser rangefinder. This work is extended to the Erim laser in [8] . In [16] mixed measurement observations from a SICK laser similar to the one we use are reported but no interpretation or analysis is provided. In this paper, we follow a similar experimental procedure to the one introduced by Matthies in [10] . Mixed measurements for a SICK laser are reported and some partial characterization is provided in terms of range of observability of the phenomenon. We extend this work and in addition propose a method to filter the mixed measurements. In [1], [2] Adams explicitly models the mixed phenomenon for a scan line CW LADAR and proposes a method to detect discontinuities. In [3] , Adams proposes a feature detection scheme based on a smoothness constraint for data from outdoor scenes. An Extended Kalman Filter is used to predict range measurements. Such an approach is difficult to generalize for lower density lasers and even more so when the robot navigates in terrain with noncontinuous surfaces but with higher clutter due to vegetation and thin structures, such as in our case. Our experiments reveal several classes and types of mixed measurement phenomena. Some of these are the result of using LADAR in general, while some are sensor dependent. As such, we will first describe the sensor which recorded these phenomena (III-A), the conditions which generated them (III-B), and finally describe our observations (III-C). The experiments described in this paper used a SICK LMS-291-SO5, a Time of Flight (TOF) pulsed laser mounted on a pushcart. We used several other sensors, such as a Z+F laser, a Riegl LD90-3000, a Riegl LMS-Z210i and also the GDRS mobility LADAR used on the eXperimental Unmanned Vehicle (XUV), but we only report experiments using the SICK laser due to its availability and common usage in robotics sensing research. The SICK laser is a onedimensional scanning LADAR. To obtain a 3-D scene we mount two SICKs together and independently actuate them with Animatics SM3420D Smart Motors. The SICK itself has several scanning modes; we have chosen to scan 100 points at 0.25 o separation. A typical scan consists of 800 steps of the motor. One unit is mounted in an upright position at a height of approximately 127 cm and actuated on its x axis, so that as the laser scans horizontally the mounting sweeps vertically. The second is mounted on its side at approximately 138 cm, sweeping around the z axis, so that the scan line moves horizontally. The laser height was chosen to produce a large Field of View (FOV). All of the data presented here was collected with the sidemounted laser. This configuration has a field of view which is 115 o wide and 100 o high, producing an 800 × 400 range measurements. 2) Beam characteristics: The SICK instrument projects a beam which is rectangular in shape, with two regions of high intensity at either end of the beam, as in Fig. 1 . Such beam shape is consistent with generation by a double stacked laser diode. The image was captured using an infrared camera 2 . The beam is swept by a rotating mirror, set at 45 o to the original beam. This has the effect of rotating the projection of the beam, so that at the edges the high-intensity regions are perpendicular to the scan line. At the center, these regions are parallel to the scan line. Fig. 1 illustrates the projection of the beam at extreme left (top image) and center through right areas (lower two images). In the configuration we use, the projected beam is 0.68 o wide and scans through a 100 o field of view with 1 o angular resolution.  The data returned by the laser is converted to rectangular coordinates with (x, y, z) representing the right, forward and upward offsets (respectively), i.e. the sensor is at the origin. All of our analysis and filtering is performed on this data, which only contains the points in 3-D space. We do not keep the connectivity (row and column identification) of the points. If the data is collected from a moving sensor platform and stored as absolute coordinates, we also keep the location of the sensor with each scan. Thus, our approach may be used with data from other 3-D TOF laser scanners by considering single scans or by accumulating data over time as the scanners move. These points are read into a sparse voxel representation and accessed using a hash key based on the relative position of the points. This structure combines the essential features of several points into one, saving memory and reducing the computational complexity of subsequent use of the points [14] . In order to better understand the observed mixed measurement phenomena, we employ a model of the return signal of the laser beam. By considering the portion of the beam reflected back by the target and that returned by the background (ground plane or vertical wall), it is possible to explain qualitatively the phenomena observed. To model the energy waveform we choose a simple reflectance model: 2 This camera was generously provided by the NAVLAB group 2204 with: ρ, the reflectance; r, the range; θ, the laser incidence angle; A, the normalized area illuminated; δ, the Dirac function. We normalize the area illuminated to conserve the flux of energy. The non-zero length of the pulse and the dynamic of the receiver will smooth the energy waveform. We represent both effects as a Gaussian G(t i , σ i ) . Several techniques can be used to detect pulses [15]: threshold, center of gravity, maximum, zero crossing of second derivative and constant fraction discriminator (CFD). CFD methods are not sensitive to signal amplitude change and are robust to pulse width change; these methods look for the zero crossing of the difference between the attenuated signal waveform and a version of the original waveform delayed by a fraction of the pulse width. We use such an approach. This model improves our understanding of several phenomena, but it is not a perfect solution. One problem is that the beam intensity is not truly homogeneously distributed. Another is the lack of complete manufacturer's technical data on essential characteristics of the laser such as beam duration and trigger condition, which increases the error of the current model. However, the model is still suitable for explaining most phenomena, which will be further discussed in subsection III-C. To simulate vegetation-like structures in controlled conditions, small PVC pipes and dowel rods were used in a variety of scenes, both indoors and outdoors. Figs. 2, 3, 4 , and 5 show sample data from each set of experiments. A similar rod set-up was used in [10] and inspired us. Table I contains a short description of the experiments performed. Additional details can be found in [12] . We used a 26 × 41 cm Plywood board, 6 cm PVC pipes and dowel rods varying in size between 3.2 and 22.2 mm. To simulate vegetation clutter with the PVC pipes or the rods we use a Poisson distribution to determine their locations. Usage of wood targets and clutter ensures that differences in reflectivity are not the source of phenomena we observe. The phenomena observed can be divided into several classes: 1) mixed measurements occurring because of overlap of the laser beam onto two objects at the edge of an object; 2) mixed measurements occurring due to target structures thinner than the beam; 3) mixed measurements occurring due to particular characteristics of the SICK laser; 4) and mixed measurements from ground interaction. Fig. 6 shows the different phenomena observed. The LADAR and two rods (the thinnest and the widest) are static. The background is positioned at three different locations. The bottom part of Fig. 6 shows a side view of the set-up. The top part of the same figure shows different mixed measurement phenomena. Mixed measurements appearing at the edge of objects are the most common. These occur when a beam is projected across the edge of an object, and (with a TOF laser such as the SICK) appear between the two
Tuley et al REF developed a taxonomy of mixed pixel phenomena, with a focus on thin structures.
Analysis and Removal of Artifacts in 3-D LADAR Data
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
Proceedings of the 2005 IEEE International Conference on Robotics and Automation
Engineering Computer Science