2.3 Structured-light Range Imaging
2.3.1 Source Illumination Categories
Although we have mentioned several approaches to range imaging in a previous section, the most promising for CARE are the structured-light approaches. Re- call that these are triangulation methods, in which the geometry of the laser, camera, and object are exploited to recover the distance from the camera to the object. This distance, or range value, is a function of three parameters: the base- line distance between the light source and the camera, the viewing angle of the camera, and the illumination angle of the light source. Recall the geometry in Figure 2.6. We have the following equation for the range value, r:
(
, , , ,)
r=F α B i jK , (2.1)
where F is a function, possibly nonlinear, α is the illumination angle, and B is the baseline distance between the camera and the light source. The variables i and j represent the horizontal and vertical positions, respectively, of a pixel in the camera image. (A pixel is the fundamental picture element from a digital camera.
We commonly represent images as a matrix where a pixel is an element of the matrix. We classify the quality of a digital camera in terms of the number of pix- els. For example, a 1-megapixel camera usually has 960 rows × 1280 columns for its pixel matrix.) This pixel is the brightest spot where the light source falls on the imaging plane of the camera. The point on the image directly correlates with the range, i.e., distance, of the object from the laser. The sequence in Figure 2.7 dem- onstrates how the pixel location changes with increasing range. Due to the view disparity between the light source, as the object moves further away from the light source, in this case a point laser, the projection of the laser onto the image plane from where it strikes the object moves as well. When the object is closest to the laser, Figure 2.7a, the projection is near the left edge of the image plane, but when the object is farthest, Figure 2.7c, the projection is near the right edge.
In Figure 2.7, we have used a point laser for illumination, but other types of light sources are possible. The three most common sources of illumination are single-point lasers, sheet-of-light lasers, and coded-light patterns. As already discussed, Figure 2.7 shows the point laser. If we do not move the object, we can scan the laser in a raster fashion across the scene to obtain a range measurement for every pixel. If the image has M × N pixels (i.e., 0 i < M – 1, 0 j < N – 1), then we require M × N measurements. The second type of illumination is the sheet-of- light laser shown in Figure 2.8. It projects a plane of light onto the object so that this plane intersects the object and forms a line. That line becomes a projection onto the image plane of the camera. This method is a direct extension of the point laser approach, except that the line represents a collection of simultaneous point sources. Thus, one can readily see that a sheet-of-light system allows one to increase scanning speed over a point laser with almost no increase in effort. The sheet-of-light method requires only M measurements for an M × N image. The third method is the coded-light source. This method illustrated in Figure 2.9 is
Figure 2.7. Demonstration of how a structured-light system determines distance. (a) The object is close to the laser source. (b) The object has been moved a slight distance further away. (c) The object is at an even greater distance. Note the change where the laser projects onto the image plane of the camera as the object moves.
24 2 Methodologies and Techniques for Reverse Engineering
much different from either of the prior two methods. Usually, this method does not use a laser source but rather uses a slide projector with patterns placed in the slide carousel. The system projects these patterns as coded light onto the object, as the figure illustrates. The patterns take different forms but one tech- nique uses a checkerboard. The range resolution of this method is a function of the number of patterns used. Thus, an M × N image would require R measure- ments where R = log(M) if we seek a resolution similar to a sheet-of-light scan- ner (Integrated Vision Products 2000).
The primary difference between these three illumination methods is the speed with which one can collect data. Accuracy varies little among them. Initially, one might think that the coded-light method offers the fastest scanning speeds, but in practice, the mechanisms necessary to exchange and display patterns onto an object are a bottleneck. The sheet-of-light method lends itself to the fastest im- plementation. Commercial sheet-of-light scanners are available that can gener- ate 10,000 data points per second, and this number is growing as technology advances. Such speeds are beyond the capabilities of a mechanical CMM probe Figure 2.8. Sheet-of-light range scanner. The laser source fans out to create a plane that intersects the object of interest. The resulting line of light on the object projects as a line onto the imaging plane of the camera.
Figure 2.9. Coded-light range scanner. The light source is usually a projector with a screen pattern placed over the lens. The pattern projects onto the object and subsequently projects onto the image plane of the camera.
that would need to bounce around the object at a very high rate. These data rates are the unique advantage that computer vision laser scanners–specifically sheet- of-light scanners–bring to CARE. In the next section, we take a more in-depth look at these scanners.