Fast Depth of Field Rendering with Surface Splatting Jaroslav Kˇ riv´ anek 1,2 e-mail: xkrivanj@fel.cvut.cz Jiˇ r´ ı ˇ Z´ ara 1 e-mail: zara@fel.cvut.cz Kadi Bouatouch 2 e-mail: kadi@irisa.fr 1 Department of Computer Science and Engineering, Czech Technical University in Prague, Karlovo n´ amˇ est´ ı 13, 121 35 Praha 2, Czech Republic 2 IRISA - INRIA Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France Abstract We present a new fast algorithm for rendering the depth- of-field effect for point-based surfaces. The algorithm han- dles partial occlusion correctly, it does not suffer from in- tensity leakage and it renders depth-of-field in presence of transparent surfaces. The algorithm is new in that it exploits the level-of-detail to select the surface detail according to the amount of depth-blur applied. This makes the speed of the algorithm practically independent of the amount of depth-blur. The proposed algorithm is an extension of the Elliptical Weighted Average (EWA) surface splatting. We present a mathematical analysis that extends the screen space EWA surface splatting to handle depth-of-field ren- dering with level-of-detail, and we demonstrate the algo- rithm on example renderings. Keywords point-based rendering, EWA surface splat- ting, depth-of-field, lens effect, level-of-detail, LOD. 1. Introduction The ability to render the depth-of-field (DOF) effect is an important feature of any image synthesis algorithm. DOF makes the image look more natural and it is also an im- portant depth cue that helps humans to perceive the spatial configuration of a scene [17]. The effect of DOF is that out- of-focus points in 3D space form circular patterns (circle of confusion, CoC) in the image plane. Algorithms for DOF rendering can be divided into two groups: post-filtering and multi-pass algorithms. The post-filtering algorithms work as follows. First the image is computed using a pinhole camera model, then the image is sent to the focus processor which turns every pixel into a CoC according to its depth. Potmesil and Chakravarty [13] have given formulas for ra- dius of the CoC and described the light intensity distribution within the CoC by Lommel functions. Chen [2] simplify the distribution to uniform. The post-filtering algorithms suffer from intensity leakage (blurred background leaks into a fo- cused object in the foreground) and they do not take into account the partial occlusion (visibility of objects change for different points on the lens). Some approaches to par- tially solve those problems are given in [9, 19]. Other post- filtering algorithms are presented in [16, 4, 17, 5, 10]. Multi- pass algorithms [11, 3] are more general, can handle the partial occlusion, but are slower. We present a new fast algorithm which renders DOF for point-based surfaces. Our algorithm is similar to post- filtering algorithms, but unlike them it does not involve a separate focus processor. Instead, the individual points are blurred before they form the final image. This allows to handle the partial occlusion and avoids intensity leakage. The algorithm can also render DOF in presence of transpar- ent surfaces (Figure 1). The presented algorithm builds on top of the Elliptical Weighted Average (EWA) surface splat- ting proposed by Zwicker et al. [20, 21]. The related work on splatting include [8, 15, 14]. Namely R¨ as¨ anen [14] pro- pose a point rendering pipeline that handles DOF rendering. His method is based on stochastic sampling, it requires high number of samples to produce noise-free images and thus it is somewhat slow. The basic idea of our algorithm is to blur the individual splats by convolving them with a Gaussian low-pass filter instead of blurring the image itself. It essentially means that each splat is enlarged proportionally to the amount of depth- blur appertaining to its depth. To accelerate DOF rendering, we use coarser level-of-detail (LOD) for blurred surfaces. This makes the speed of the algorithm independent of the amount of depth-blur. The contributions of this paper are consist in a mathe- matical analysis extending the EWA surface splatting with DOF rendering, an analysis allowing the use of the LOD as a means for DOF rendering, an implementation of the algo- rithm, and a discussion of practical implementation issues. The paper is organized as follows: Section 2 reviews the screen-space EWA surface splatting algorithm, Section 3 contains the mathematical analysis of our DOF rendering algorithm, Section 4 presents its implementation, Section 5 gives the results, and Section 6 concludes the work. From Proceedings of Computer Graphics International 2003