For ray-casting of non-rigid deformations, the direct approach (as opposed to the traditional indirect approach) does not require the computation of an intermediate volume to be used for the rendering step. The aim of this study was to compare the two approaches in terms of performance (speed) and accuracy (image quality). The direct and the indirect approach were carefully implemented to benefit of the massive GPU parallel power, using CUDA. They were then tested with Computed Tomography (CT) datasets of varying sizes and with a synthetic image, the Marschner-Lobb function. The results show that the direct approach is dependent on the ray sampling steps, number of landmarks and image resolution. The indirect approach is mainly affected by the number of landmarks, if the volume is large enough. These results exclude extreme cases, i.e. if the sampling steps are much smaller than the voxel size and if the image resolution is much higher than the ones used here. For a volume of size 512×512×512, using 100 landmarks and image resolution of 1280×960, the direct method performs better if the ray sampling steps are approximately above 1 voxel. Regarding accuracy, the direct method provides better results for multiple frequencies using the Marschner-Lobb function. The conclusion is that the indirect method is superior in terms of performance, if the sampling along the rays is high, in comparison to the voxel grid, while the direct is superior otherwise. The accuracy analysis seems to point out that the direct method is superior, in particular when the implicit function is used.
[Boo89] BOOKSTEIN F.: Principal warps: Thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 11 (1989), 567–585. 3
[CBC*01] CARR J. C., BEATSON R. K., CHERRIE J. B., MITCHELL T. J., FRIGHT W. R., MCCALLUM B. C., EVANS T. R.: Reconstruction and representation of 3d objects with radial basis functions. In Proceedings of the 28th annual conference on Computer graphics and interactive techniques (New York, NY, USA, 2001), SIGGRAPH ’01, ACM, pp. 67–76. 3
[CHM03] CHEN H., HESSER J., MANNER R.: Raycasting freeform deformed-volume objects. The Journal of Visualization and Computer Animation 14 (2003), 61–72. 2, 6
[CSC10] CORREA C. D., SILVER D., CHEN M.: Constrained illustrative volume deformation. Computer & Graphics 34 (2010), 370–377. 2
[CSW03] CHEN M., SILVER D., WINTER A. S., SINGH V., CORNEA N.: Spatial transfer functions - a unified approach to
specifying deformation in volume modeling and animation. Proceedings of volumegraphics’03, pp. 35–44. 2
[Cud10] Nvidia cuda c programming guide, version 3.1, 2010. 1,
2
[FRS01] FORNEFETT M., ROHR K., STIEHL H.: Radial basis functions with compact support for elastic registration of medical images. Image and Vision Computing 19 (2001), 87–96. 6
[FSRR00] FANG S., SRINIVASAN R., RAGHAVAN R., RICHTSMEIER J. T.: Volume morphing and rendering - an integrated approach. Comput. Aided Geom. Des. 17 (January
2000), 59–81. 2, 6
[Gib97] GIBSON S. F.: 3d chainmail:a fast algorithm for deforming volumetric objects. Proceedings of the 1997 symposium on
interactive 3D graphics. 2
[HLSR09] HADWIGER M., LJUNG P., SALAMA C. R., ROPINSKI
T.: Eurographics 2009 course notes: Gpu-based volume raycasting
with advanced illumination. In Eurographics 2009 course
(2009), Eurographics 2009. 2
[KW03] KRÜGER J., WESTERMANN R.: Acceleration Techniques
for GPU-based Volume Rendering. In Proceedings IEEE
Visualization 2003 (2003). 2
[KY97] KURZION Y., YAGEL R.: Interactive space deformation
with hardware-assisted rendering. IEEE Computer Graphics and
Applications 17, 5 (1997), 66–77. 2
[LDS04] LEVIN D., DEY D., SLOMKA P. J.: Acceleration of 3d,
nonlinear warping using standard video graphics hardware: implementation
and initial validation. Computerized Medical Imaging and Graphics 28, 8 (2004), 471–83. 2
[LMK03] LI W., MUELLER K., KAUFMAN A.: Empty space
skipping and occlusion clipping for texture-based volume rendering.
In Proc. IEEE Visualization 2003 (2003), pp. 317–324.
2
[LP00] LAPEER R., PRAGER R.: 3d shape recovery of a newborn
skull using thin-plate splines. Computerized Medical Imaging
and Graphics 24 (2000), 193–204. 3
[LSR10] LAPEER R., SHAH S., R.S. R.: An optimised radial basis function algorithm for fast non-rigid registration of medical
images. Computers in Biology and Medicine 40, 1 (2010), 1–7.
2, 6
[ML94] MARSCHNER S. R., LOBB R. J.: An evaluation of reconstruction
filters for volume rendering. IEEE Visualization’94.
5
[MRH10] MENSMANN J., ROPINSKI T., HINRICHS K. H.: An
advanced volume raycasting technique using gpu stream processing.
In GRAPP: International Conference on Computer Graphics Theory and Applications (Angers, 2010), INSTICC Press,
pp. 190–198. 2
[NMK*05] NEALEN A., MÜLLER M., KEISER R., BOXERMAN
E., CARLSON M.: Physically based deformable models in computer
graphics, 2005. 2
[RGW*03] RÖTTGER S., GUTHE S., WEISKOPF D., ERTL T.,
STRASSER W.: Smart hardware-accelerated volume rendering.
In VisSym (2003). 2
[Row07] ROWLAND R. S.: Fast Registration of Medical Imaging Data Using Optimised Radial Basis Functions :PhD Dissertation. PhD thesis, University of East Anglia, 2007. 2, 6
[San10] SANDERSON C.: Armadillo: An open source c++ linear
algebra library for fast prototyping and computationally intensive
experiments, 2010. 3
[Sig06] SIGG C.: Representation and rendering of implicit surfaces,
2006. 1
[WBSS04] WANG Z., BOVIK A. C., SHEIKH H. R., SIMONCELLI
E. P.: Image quality assessment: From error visibility to
structural similarity. IEEE Transactions on Image Processing 13
(2004), 600–612. 6
[WRS01] WESTERMANN R., REZK-SALAMA C.: Real-time volume
deformations. Computer Graphics Forum 20, 3 (2001). 2,
6
