Image synthesis algorithms are commonly compared on the basis of running times and/or perceived quality of the generated images. In the case of Monte Carlo techniques, assessment often entails a qualitative impression of convergence toward a reference standard and severity of visible noise; these amount to subjective assessments of the mean and variance of the estimators, respectively. In this paper we argue that such assessments should be augmented by well-known statistical hypothesis testing methods. In particular, we show how to perform a number of such tests to assess random variables that commonly arise in image synthesis such as those estimating irradiance, radiance, pixel color, etc. We explore five broad categories of tests: 1) determining whether the mean is equal to a reference standard, such as an analytical value, 2) determining that the variance is bounded by a given constant, 3) comparing the means of two different random variables, 4) comparing the variances of two different random variables, and 5) verifying that two random variables stem from the same parent distribution. The level of significance of these tests can be controlled by a parameter. We demonstrate that these tests can be used for objective evaluation of Monte Carlo estimators to support claims of zero or small bias and to provide quantitative assessments of variance reduction techniques. We also show how these tests can be used to detect errors in sampling or in computing the density of an importance function in MC integrations.
For point cloud data obtained from 3D scanning devices, excessively large storage and long postprocessing time are required. Due to this, it is very important to simplify the point cloud to reduce calculation cost. In this paper, we propose a new point cloud simplification method that can maintain the characteristics of surface shape for unstructured point clouds. In our method, a segmentation range based on mean curvature of point cloud can be controlled. The simplification process is completed by maintaining the position of the representative point and removing the represented points using the range. Our method can simplify results with highly simplified rate with preserving the form feature. Applying the proposed method to 3D stone tool models, the method is evaluated precisely and effectively.
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