Expanding images of an object under 3DOF rotation with spherical functions and its applications to image interpolation and pose estimation

SO(3)上の直交関数系である球関数による3自由度回転物体画像系列の展開方法の具体的な実装を提案し、画像補間と姿勢推定への応用について述べる。We propose an implementation for expanding images of an object under 3 DOF rotation with spherical functions, an orthonormal basis on SO(3), and describe its applications to image interpolation and pose estimation

Efficient Shadows from Sampled Environment Maps

This paper addresses the problem of efficiently calculating shadows from environment maps. Since accurate rendering of shadows from environment maps requires hundreds of lights, the expensive computation is determining visibility from each pixel to each light direction, such as by ray-tracing. We show that coherence in both spatial and angular domains can be used to reduce the number of shadow rays that need to be traced. Specifically, we use a coarse-to-fine evaluation of the image, predicting visibility by reusing visibility calculations from four nearby pixels that have already been evaluated. This simple method allows us to explicitly mark regions of uncertainty in the prediction. By only tracing rays in these and neighboring directions, we are able to reduce the number of shadow rays traced by up to a factor of 20 while maintaining error rates below 0.01%. For many scenes, our algorithm can add shadowing from hundreds of lights at twice the cost of rendering without shadows

View-dependent precomputed light transport using non-linear Gaussian function approximations

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.Includes bibliographical references (p. 43-46).We propose a real-time method for rendering rigid objects with complex view-dependent effects under distant all-frequency lighting. Existing precomputed light transport approaches can render rich global illumination effects, but high-frequency view-dependent effects such as sharp highlights remain a challenge. We introduce a new representation of the light transport operator based on sums of Gaussians. The non-linear parameters of the representation allow for 1) arbitrary bandwidth because scale is encoded as a direct parameter; and 2) high-quality interpolation across view and mesh triangles because we interpolate the average direction of the incoming light, thereby preventing linear cross-fading artifacts. However, fitting the precomputed light transport data to this new representation requires solving a non-linear regression problem that is more involved than traditional linear and non-linear (truncation) approximation techniques. We present a new data fitting method based on optimization that includes energy terms aimed at enforcing good interpolation. We demonstrate that our method achieves high visual quality for a small storage cost and fast rendering time.by Paul Elijah Green.S.M

5D Covariance Tracing for Efficient Defocus and Motion Blur

The rendering of effects such as motion blur and depth-of-field requires costly 5D integrals. We dramatically accelerate their computation through adaptive sampling and reconstruction based on the prediction of the anisotropy and bandwidth of the integrand. For this, we develop a new frequency analysis of the 5D temporal light-field, and show that first-order motion can be handled through simple changes of coordinates in 5D. We further introduce a compact representation of the spectrum using the co- variance matrix and Gaussian approximations. We derive update equations for the 5 × 5 covariance matrices for each atomic light transport event, such as transport, occlusion, BRDF, texture, lens, and motion. The focus on atomic operations makes our work general, and removes the need for special-case formulas. We present a new rendering algorithm that computes 5D covariance matrices on the image plane by tracing paths through the scene, focusing on the single-bounce case. This allows us to reduce sampling rates when appropriate and perform reconstruction of images with complex depth-of-field and motion blur effects