Evaluating the performance of optical flow algorithms has been difficult because of the lack of ground-truth data sets for complex scenes. We describe a simple modification to a ray tracer that allows us to generate ground-truth motion fields for scenes of arbitrary complexity. The resulting flow maps are used to assist in the comparison of eight optical flow algorithms using three complex, synthetic scenes. Our study found that a modified version of Lucas and Kanade's algorithm has superior performance but produces sparse flow maps. Proesmans et al.'s algorithm performs slightly worse, on average, but produces a very dense depth map.

Evaluating the performance of optical flow algorithms has been difficult because of the lack of ground truth data sets for complex scenes. We present a new method for generating motion fields from real sequences containing polyhedral objects and present a test suite for benchmarking optical flow algorithms consisting of complex synthetic sequences and real scenes with ground truth. We provide a preliminary quantitative evaluation of seven optical flow algorithms using these synthetic and real sequences. Ultimately, we feel that researchers should benchmark their own algorithms using a standard suite. To that end, we offer our Web site as a repository for standard sequences and results. c 2001 Elsevier Science (USA)

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Traditional methods for evaluating the low-albedo volume rendering integral do not include bounds on the magnitude of approximation error. In this paper, we examine three techniques for solving this integral with error bounds: trapezoid rule, Simpson's rule, and a power series method. In each case, the expression for the error bound provides a mechanism for computing the integral to any specified precision. The formulations presented are appropriate for polynomial reconstruction from point samples; however, the approach is considerably mom general. The three techniques we present differ in relative efficiency for computing results to a given precision. The trapezoid rule and Simpson's rule are most efficient for low-to medium-precision solutions. The power series method converges rapidly to a machine precision solution, providing both an efficient means for high-accuracy volume rendering, and a reference standard by which other approximations may be measured.

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