Neophytos Neophytou - Post Convolved Splatting

Post-Convolved Splatting

Neophytos Neophytou and Klaus Mueller

Abstract:

One of the most expensive operations in volume rendering is the interpolation of samples in volume space. The number of samples, in turn, depends on the resolution of the final image. Hence, viewing the volume at high magnification will incur heavy computation. In this paper, we explore an approach that limits the number of samples to the resolution of the volume, independent of the magnification factor, using a cheap post-convolution process on the interpolated samples to generate the missing samples. For X-ray, this post-convolution is needed only once, after the volume is fully projected, while in full volume rendering, the post-convolution must be applied before each shading and compositing step. Using this technique, we are able to achieve speedups of two and more, without compromising rendering quality. We demonstrate our approach using an image-aligned sheet-buffered splatting algorithm, but our conclusions readily generalize to any volume rendering algorithm that advances across the volume in a slice-based fashion.

Publication:

N. Neophytou and K. Mueller, Post-convolved splatting Joint Eurographics - IEEE TCVG Symposium on Visualization 2003, Grenoble, France, May, 2003

Presentation file:

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Various Notes (Relevant if already familiar with the above material):

The method described in the paper was implemented in software. It describes a two stage process, where in the first stage one splats the volume using a low resolution splat kernel onto a low resolution equivalent of the grid, and then convolves the corresponding high resolution grid with the appropriate convolution kernel.

Since the convolution operator is becoming available on latest GPU hardware, one would assume that it is straight forward to implement the same two-stage post-convolved splatting approach, using the simple glPoint primitive for the splatting stage, and then apply convolution using the newly provided OpenGL functionality. For high magnification images, the software implementation uses a straight forward way of "simulating" a low-resolution grid in the same memory as the high resolution grid. When rendering in the low resolution grid, we just skpip pixels, depending on the magnification scale. This could be achieved in hardware by using a little bit of hacking, and adjusting the size of the glPoints, along with applying a stipple_pattern for the rasterization of these points, or even a simple stencil mask.

This, however, would be exactly equivalent to splatting at the first stage using a radially-symmetric bilinear filter, and then convolving at the second stage using a gaussian kernel. In the paper above, we explain why this approach is not accurate and it is prone to aliasing artifacts, both in X-Ray as well as Post-Convolved Splatting. The aliasing artifacts are not visible for non-magnified viewing, but they become more pronounced as the scale is increased. The following figures illustrate these findings for magnified X-Ray viewing. Please refer to the paper for a rigorous explanation using signal processing theory.

The first four images were rendered using a bilinear kernel for splatting the first stage (equivalent to glPoints), and the last image used the recommended gaussian kernel for the first stage splatting.


The following comparison shows how much uglier things can become if we would use the glPoint approach for Post-Shaded splatting.

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