Adaptive Sampling with Renyi Entropy in Monte Carlo Path Tracing Qing Xu, Ruijuan Hu, Lianping Xing, Yuan Xu School of Information, Tianjin University, Tianjin City, 300072,China qingxu@tju.edu.cn Abstract-Adaptive sampling is an interesting tool to lower noise, which is one of the main problems of Monte Carlo global illumination algorithms such as the famous and baseline Monte Carlo path tracing. The classic information measure, namely, Shannon entropy has been applied successfully for adaptive sampling in Monte Carlo path tracing. In this paper we investigate the generalized Renyi entropy to establish the refinement criteria to guide both pixel super sampling and pixel subdivision adaptively. Implementation results show that the adaptive sampling based on Renyi entropy outperforms the counterpart based on Shannon entropy consistently. Keywords-Adaptive sampling, Monte Carlo path tracing, Reny entropy 1. INTRODUCTION Monte Carlo based methods are quite suitable for the calculation of global illumination problem when highly complicated scenes with very general and difficult reflection models are rendered [1]. However, the synthesized image generated by using Monte Carlo based global illumination algorithms is very noisy. Usually, we can reduce the noise through taking more samples within each pixel to get a visually acceptable image, but a lot of rendering time must be spent because of the slow convergence of the Monte Carlo technique. The general Monte Carlo global illumination methods always employ the baseline Monte Carlo path tracing (MCPT) to produce the synthetic images pixel by pixel. MCPT uses sample paths through a pixel to calculate the pixel value by averaging the sample values, namely the light transport contribution of sample values. Adaptive image sampling tries to use more samples in the difficult region of the synthesized image where the sample values vary obviously. In this way, each pixel is firstly sampled at a low density, and then more samples are taken for complex part based on the initial sample values. Hence, adaptive sampling avoids the problem of using a fixed and high number of samples per pixel [2]. Adaptive sampling can be done in way of super sampling within a pixel in which more samples are used for each or by image region subdivision. The research on adaptive sampling started from the anti- aliasing in ray tracing [3]. Painter and Sloan presented adaptive progressive refinement to place more samples along image edges [4]. Based on the root mean square signal to noise ratio (RMS SNR), Dippe and Wold proposed an error estimate of the mean to derive the stopping condition of adaptive sampling [5]. Mitchell utilized the concept of contrast, which represents an important feature of human vision, to carry out adaptive sampling scheme [6]. Lee et al. sampled pixel on the basis of variance of pixel values [7]. Purgathofer proposed the use of confidence interval for instructing adaptive sampling [8]. In order to consider the device display and the human observation of the synthesized image, Tamstorf and Jensen refined the idea of Purgathofer and derived confidence interval including tone mapping operator to relieve using absolutely stochastic estimate [2]. Kirk and Arvo demonstrated a correction scheme to avoid the bias of variance based adaptive sampling approaches [9]. Bolin and Meyer developed a perceptually based method using human vision models [10]. Rigau, Feixas and Sbert introduced the Shannon entropy and f-divergences as the measure of uniformity of the rays through a pixel or subpixel to conduct adaptive sampling [11, 12, 13, 14]. Considering the power of Renyi entropy that is one of the most popular generalized entropies [15], we explore Renyi entropy to perform both pixel super sampling and pixel subdivision adaptively in Monte Carlo path tracing in this paper. Experimental results indicate that Renyi entropy based adaptive sampling can accomplish better than classic Shannon entropy based adaptive sampling. This paper is the organized as follows. Section 2 is the description of Renyi entropy. Details of the Renyi entropy based adaptive sampling are depicted in section 3. The fourth portion discusses the implementation and the experimental results. Finally, conclusion and future works are presented. 2. RENYI ENTROPY Let P={p 1, ....,p n } be a probability distribution, the Shannon entropy is defined as [16] : 2 1 ( ) log n k k k H X p p = =− ∑ . Renyi entropy [15] is a generalization of Shannon entropy: R q 2 1 1 H (X)= log ( ) (1 ) n q k k p q = − ∑ (1) 784 0-7803-9314-7/05/$20.00©2005 IEEE 2005 IEEE International Symposium on Signal Processing and Information Technology