Range Scanner and Range Images

This work assumes that the range sensor is monostatic. Monostatic refers to the fact that the transmitter and receiver of light (or other forms of energy) are located at the same location. This excludes the class of range sensors based on triangulation, where the transmitters and receivers need to be at different locations. Many range sensors based on the time-delay (time-of-flight) principle are monostatic. The consequence of this requirement is that the visibility of a surface point depends only on a single line of sight from the sensor location.

The next assumption is that all the range samples in a range image are measured from the same sensor location, as if there is a single center of projection or viewpoint for the entire range image. This requires the sensor to be swept in a rotational manner about the sensor location, as opposed to a translational sweep which produces a range image that has multiple centers of projection.

The monostatic and single-center-of-projection assumptions should simplify the visibility evaluations during the view planning computation, but more importantly, the “visibility coherence” around the single viewpoint can be better exploited for more efficient visibility evaluations using the hierarchical approach described in Chapter 4.

It is also assumed that the range scanner has a 360° horizontal field of view, and it is always oriented such that its vertical axis is parallel to the vertical of the environment. Together, the two assumptions simplify each scanner view to just a 3D location, instead of a 6D pose. To allow acquisition of the floors and ceilings of indoor environments, it is required that the vertical field of view of the scanner should span from below the horizon to above it. Many mid-range and long-range scanners on the market today have 360° horizontal field of views and limited vertical field of views, for example, the DeltaSphere-3000 3D Scene Digitizer [DeltaSphere], the MENSI GS200 3D Laser Scanner [MENSI], and several models by RIEGL [RIEGL].

The DeltaSphere-3000 3D Scene Digitizer [DeltaSphere] is one of the range scanners that fulfill the above scanner requirements. It is used in the view planning experiments described in this dissertation. Figure 3.3 shows a DeltaSphere-3000 mounted on a tripod. The scanner scans the environment by rotating itself step-by-step about the tripod, and in each step, a

rotating mirror sweeps a laser beam in a vertical plane. The range sensor is monostatic, and the center of projection of the range image is located at the center of the rotating mirror. The field of view of the scanner is adjustable. When placed in the normal upright pose, as shown in Figure 3.3, the scanner can have a maximum horizontal field of view of 360°, and a maximum vertical field of view spanning from 55° below the horizon to 90° above the horizon. The depth of field is also adjustable, but the maximum range extends from about 1 foot to 50 feet from the sensor. At this maximum depth of field, the range measurement precision is about 0.3 inch standard deviation. The scanner can scan with a maximum scanning resolution of 20 samples per degree in both the vertical and horizontal directions. The scanning time is dependent only on the horizontal field of view and the scanning resolution. A scan with 360° horizontal field of view and 10 samples per degree resolution takes about 8 minutes to complete.

Figure 3.3: A DeltaSphere-3000 3D Scene Digitizer mounted on a tripod. Photograph courtesy of DeltaSphere, Inc.

The local 3D coordinate frame of the range image has its origin located at the center of the rotating mirror, and all range measurements are expressed as distances from the origin. Each sample 3D point in the range image is expressed in polar coordinates (r, θ, φ ) in the scanner’s local coordinate frame, where r is the distance from the origin to the 3D point, θ is

rotating mirror

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the azimuth angle, and φ is the elevation angle (see Figure 3.4). The polar coordinates can be easily converted to Cartesian coordinates.

Figure 3.4: The local 3D coordinate frame of the DeltaSphere-3000 range scanner. The origin is located at the viewpoint and its y-axis is pointing up. Each sample 3D point in the range image is expressed in polar coordinates ( r, θ, φ ), where r is the distance from the origin to the 3D point, θ is the azimuth angle, and φ is the elevation angle.

An example range image produced by the DeltaSphere-3000 is shown in Figure 3.5. The horizontal field of view of the scan is 360° (θ =−180°_K180°), and the vertical field of view is 125° (φ =−55°_K70°). The scanning resolution is 10 samples per degree in both the vertical and horizontal directions. In the figure, the intensity at each pixel is proportional to the range value at the corresponding sample. The brown-colored pixels correspond to drop- outs, which are samples that cannot be measured successfully by the sensor. The DeltaSphere-3000 also records the reflected laser intensity detected at each sample point, and Figure 3.6 shows the image of the reflected laser intensities corresponding to the range image in Figure 3.5. The sample points in the range image are converted into Cartesian coordinates, and the 3D points are used to create a triangle-mesh model shown in Figure 3.7.

y z x p θ φ r O

Figure 3.5: A panoramic range image produced by the DeltaSphere-3000 scanner. The intensity at each pixel is proportional to the range value at the corresponding sample. The brown-colored pixels correspond to drop-outs, which are samples that cannot be measured by the sensor.

Figure 3.6: The image of the reflected laser intensities corresponding to the range image in Figure 3.5. φ θ (180°, 70°) (−180°, −55°) φ θ (180°, 70°) (−180°, −55°)

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Figure 3.7: A 3D triangle-mesh model created from the range image in Figure 3.5.