Image-based rendering of range data with estimated depth uncertainty

Hardware-Assisted Visibility Ordering for Point-Based and Volume Rendering

“…Unless otherwise noted, all images are rendered using the basic algorithm. Figure 1 shows the result of our technique applied to classic splatting (Figure 1(a) and (b)) and to the ellipsoid projection method of [16] (Figure 1(c) and (d)) using range data with estimated depth uncertainty [13]. Notice how we cannot see the discontinuity of the axes region borders in (a) and (c).…”

“…This model has 362880 points. In (c) and (d), instead of only using the depth information per pixel, we compute a depth uncertainty region around it [13]. Next, we render the depth with uncertainty by splatting 3D ellipsoidal Gaussian kernels (based on the EWA Volume Splatting work in [16]).…”

“…(2) In a perspective view, the decision can be made per pixel ray, using clipping. This was first introduced in [13] and is generalized here for any point-based and volume rendering data. (It is the basic algorithm presented in section 5.)…”

“…Furthermore, for the purpose of using the framework presented in this paper for volume rendering, we have to select a filter that fits our 2D technique. In fact, it can be shown that in an orthogonal projection, the integral of a 3D Gaussian is a 2D Gaussian [15] (see Figure 2a). This is based on the Volume Splatting work of Zwicker in [16], and can be proved by integration along the projection direction.…”

“…We know that the perspective projection of an ellipsoid is an ellipse. Figure 2b illustrates that the projection of an ellipsoid is a conic section [15].…”