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s are shown in Figure 3c. We note that it is desirable to combine the lens distortion correction and projective transform into a single nonlinear transformation on the image, thus requiring only one resampling of the image. Furthermore it is straightforward to perform this entire calculation on a graphics processing unit (GPU), where the transformation is specified as a mesh.

Image Fusion:

After rectification the same point ) , ( y x in both left I and right I refer to the same point on the display surface. Thus, if some image feature f is computed on left I and right I , and), ( ), ( y x f y x f right left a‰ , we may conclude that there is no object present at the point), ( y x on the display surface. The touch image mask is computed by performing such pixel-wise comparisons of the left and right images. This is essentially the disparity is constrained to zero, and the rectification process serves to align image rasters.

In the case where a strong IR illuminant is available, and the goal is to identify hands and other IR reflective materials on the display surface, it may suffice to simply pixel-wise multiply the two rectified images. Regions which are bright in both images at the same location will survive multiplication. Sample resulting fused images are shown in Figure 3d. We note that it is possible to implement this image comparison as a pixel shader program running on the GPU. As with traditional stereo computer vision techniques, it is possible to confuse the image comparison process by presenting a large uniformly textured object at some height above the display. Indeed, the height above the surface at which any bright regions are matched is related to the size of the object and to the baseline, the distance between the cameras. For the same size object, larger baselines result in fusion at a smaller height above the surface, consequently allowing a finer distinction as to whether an object is on the display, or just above the display. Similarly, it is possible to arrange two distinct bright objects above the display surface such that they are erroneously fused as a single object on the surface. More sophisticated feature matching techniques may be used to make different tradeoffs on robustness and sensitivity. For example, one possibility is to first compute the edge map of the rectified image before multiplying the two images. Figure 4 illustrates the result of applying a Sobel edge filter on the rectified images. Only edges which are present in the same location in both images will survive the multiplication. Thus, large uniform bright objects are less likely to be matched above the surface, since the edges from both views will not overlay one another. In the case of using edges, it is possible and perhaps desirable to reduce the baseline, resulting in better overall resolution in the rectified images due to a less extreme projective transform. The use of edge images takes advantage of the typical distribution of edges in the scene, in which the accidental alignment of two edges is unlikely. Similarly, motion magnitude, image differences and other features and combinations of such features may be used, depending on the nature of the objects placed on the surface, the desired robustness, and the nature of subsequent image processing steps. It should be noted that the touch plane is arbitrarily defined to coincide with the display. It is possible to configure the plane such t