An Effective Stratified Sampling Scheme for Environment Maps with Median Cut Method Xing Mei 1 , Marc Jaeger 1,2 , Baogang Hu 1 1 LIAMA/NLPR, Institute of Automation, Chinese Academy of Sciences, Beijing, China 2 Laboratoire AMAP, CIRAD, Montpellier, France xmei@nlpr.ia.ac.cn, jaeger@liama.ia.ac.cn, hubg@nlpr.ia.ac.cn Abstract Environment maps are extensively used as natural light sources in realistic rendering. We propose a stratified sam- pling scheme for environment maps by first stratifying the maps into a set of rectangular regions with Median Cut method, then estimating the contribution of the regions with Monte Carlo integration techniques. In this way, illumi- nation, surface reflectance and spatial distribution are all taken into consideration for the generation of the light sam- ples. Compared with the existing biased lighting tech- niques, the presented scheme produces unbiased rendering results with less noise and better shadow boundaries, par- ticularly at low sampling rates. The proposed spatial dis- tribution of the samples also helps to overcome the sample- clumping problem in traditional illumination-based impor- tance sampling method. Experimental results indicate that the scheme is fast, simple to implement and effective. 1. Introduction Realistic rendering synthetic objects illuminated by envi- ronment maps is a key issue in image synthesis. Following early seminar works in [2] [10], Debevec’s study on cap- turing natural illumination with high dynamic range images [7] has enabled many new image-based lighting techniques for direct light computation, which can be classified into two categories: biased and unbiased. Most of existing methods, falling into biased methods, try to stratify the environment maps into a set of regions and approximate these regions as directional lights. Dif- ferent rules have been proposed for the stratification of the maps, such as k-means clustering[1][5], Lloyd’s Relaxation method[11], and Penrose-based method[13]. With enough directional lights ’mimicking’ the light environment, biased techniques produce nice noise-free images. However, if the number of the lights is relatively low, these techniques may bring visual artifacts. Approximating each region as a di- rectional light fails to consider the variation of the surface reflectance and orientation within the region. If the surface is highly glossy, inaccurate shading and high light will af- fect rendering quality. And unwanted banding near shadow boundaries appears when some directional lights are sud- denly occluded by the scene geometry. This banding ef- fect can be decreased by jittering the direction of the lights, but additional noise and bias are introduced into the render- ing results. Moreover, the stratification process with biased methods is usually expensive. Illumination-based importance sampling is another widely used technique [14]. This method gives unbiased rendering results with Monte Carlo estimators. Although noise is inevitable, it can be combined with Multiple Im- portance Sampling [16] and Bidirectional Importance Sam- pling [3] [15] for further noise reduction. Importance sampling techniques may suffer from the sample-clumping problem at low sampling rates (see section 3). Our concern is to produce better shadow boundaries and more accurate high lights on surfaces than existing biased methods, and to decrease the effect of the sample-clumping problem in traditional importance sampling. We therefore propose an effective stratified sampling scheme for environ- ment maps by combining the two kinds of techniques: first stratify the maps into regions with Median Cut method [8], and then apply sampling techniques on these regions. Basic concepts about Monte Carlo lighting techniques are given in Section 2. We describe the stratified sampling scheme in Section 3, and show the experimental results in Section 4. Conclusions are given in Section 5. 2. Monte Carlo Direct Lighting Monte Carlo integration techniques [9] have been shown to be effective and robust for light computation. The direct radiance, L o , at a surface point p with an outgoing direction Proceedings of the International Conference on Computer Graphics, Imaging and Visualisation (CGIV'06) 0-7695-2606-3/06 $20.00 © 2006