A Monte Carlo Framework for Rendering Speckle Statistics in Scattering Media We present a Monte Carlo rendering framework for the physicallyaccurate simulation of speckle patterns arising from volumetric scattering of coherent waves. These noiselike patterns are characterized by strong statistical properties, such as the socalled memory effect, which are at the core of imaging techniques for applications as diverse as tissue imaging, motion tracking, and nonlineofsight imaging. Our framework allows for these properties to be replicated computationally, in a way that is orders of magnitude more efficient than alternatives based on directly solving the wave equations. At the core of our framework is a pathspace formulation for the covariance of speckle patterns arising from a scattering volume, which we derive from first principles. We use this formulation to develop two Monte Carlo rendering algorithms, for computing speckle covariance as well as directly speckle fields. While approaches based on wave equation solvers require knowing the microscopic position of wavelengthsized scatterers, our approach takes as input only bulk parameters describing the statistical distribution of these scatterers inside a volume. We validate the accuracy of our framework by comparing against speckle patterns simulated using wave equation solvers, use it to simulate memory effect observations that were previously only possible through lab measurements, and demonstrate its applicability for computational imaging tasks.

Adaptive Sample Map for Monte Carlo Ray Tracing Monte Carlo ray tracing algorithm is widely used by production quality renderers to generate synthesized images in films and TV programs. Noise artifact exists in synthetic images generated by Monte Carlo ray tracing methods. In this paper, a novel noise artifact detection and noise level representation method is proposed. We first apply discrete wavelet transform (DWT) on a synthetic image; the high frequency subbands of the DWT result encode the noise information. The subbands coefficients are then combined to generate a noise level description of the synthetic image, which is called noise map in the paper. This noise map is then subdivided into blocks for robust noise level metric calculation. Increasing the samples per pixel in Monte Carlo ray tracer can reduce the noise of a synthetic image to visually unnoticeable level. A noisetosample number mapping algorithm is thus performed on each block of the noise map, higher noise value is mapped to larger sample number, and lower noise value is mapped to smaller sample number, the result of mapping is called sample map. Each pixel in a sample map can be used by Monte Carlo ray tracer to reduce the noise level in the corresponding block of pixels in a synthetic image. However, this block based scheme produces blocky artifact as appeared in video and image compression algorithms. We use Gaussian filter to smooth the sample map, the result is adaptive sample map (ASP). ASP serves two purposes in rendering process; its statistics information can be used as noise level metric in synthetic image, and it can also be used by a Monte Carlo ray tracer to refine the synthetic image adaptively in order to reduce the noise to unnoticeable level but with less rendering time than the brute force method.