Adaptive polynomial rendering

#Monte Carlo (MC) ray tracing is a rendering algorithm for synthesizing photo-realistic images from 3D models. MC rendering algorithm can typically be used to simulate a variety of rendering effects through a unified framework, i.e., ray tracing. The rendering time of MC ray tracing, however in many cases, is unacceptable since it typically requires integrating a huge number of ray samples, e.g., more than 10K ray samples per pixel, to generate a converged rendered image.

#In attempting to tackle the aforementioned ray performance problem of MC ray tracing, various adaptive rendering techniques have been developed. Those techniques typically involve locally controlled sampling rate to adaptively adjust the image reconstruction. For example, some of those techniques involve adaptive sampling the heterogeneous noise property of rendered images to guide irregular sampling density rather than a uniform sampling, and locally controlling smoothing by considering MC noise so that high-frequency edges are properly preserved.

#Adaptive image rendering has a long history. For example, Kajiya, J. T, in the paper entitled “the rendering equation” [ACM SIGGRAPH '86, 143-150], presented a general idea that high-dimensional MC samples can be allocated adaptively in a hierarchical structure by using the variances of the samples and these samples can be integrated to generate rendered images. Approaches using those techniques typically show high-quality rendering results for a moderate dimension (e.g., 2 to 5), but they typically suffer from the curse-of-dimensionality as the dimension of MC samples can be high (e.g., more than 10) when global illumination is simulated.

#FIG. 1 illustrates generally a computer system that can be used to adaptively filter an image in accordance with the disclosure.

#FIG. 2 is a flowchart of a method for adaptively filtering an image in accordance with the disclosure.

#FIGS. 3A-B illustrate results of using function of different polynomial orders to reconstruct an image having a non-linear edge in accordance with the disclosure.

#As used herein, a part of an image may be referred to as a pixel or a block of pixels of the image. For example, an image of 10000 pixels may be broken into 100×100 blocks, with each block having 100 pixels, such that there are 100 blocks on each pixel row and 100 blocks on each pixel column in the image. An image value for a part of the image as used herein can thus be referred to as an image value (e.g., color and opacity) for a pixel or a block of the image. For example, a block of pixels in the image can have an overall image value representing a color and opacity of the image block as a whole.

#As used herein, filtering or reconstructing an image may be referred to as filtering or reconstructing a specific part of the image using an approximation function selected for that part of the image. The filtered or reconstructed image typically has an improved image quality compared to the original image.

#As used herein, reconstructing a part of an image may be used interchangeably with filtering an part of an image. Either involves using an approximation function, such as a polynomial function, to enhance one or more image values of the part of the image.