Modern graphics cards are equipped with a vertex cache to reduce the amount of data needing to be transmitted to the graphics pipeline during rendering. To make effective use of the cache and facilitate rendering, it is key to represent a mesh in a manner that maximizes the cache hit rate. In this work, we propose a simple yet effective algorithm for generating a sequence for efficient rendering of 3D polygonal meshes based on greedy optimization. The algorithm outperforms the current state-of-the-art algorithms in terms of rendering efficiency of the resultant sequence. We also adapt it for the rendering of progressive meshes. For any simplified version of the original mesh, the rendering sequence is generated by adaptively updating the reordered sequence at full resolution. The resultant rendering sequence is cheap to compute and has reasonably good rendering performance, which is desirable to many complex rendering environments involving continuous rendering of meshes at various level of details. The experimental results on a collection of 3D meshes are provided.

In electron tomographic reconstructions of biological specimens the information about their structure is not directly, accessible since most of the signal is buried in noise. An interpretation of the images using surface and volume rendering techniques is difficult due to the noise sensitivity of rendering algorithms. We explore the use of various multiscale representations for denoising 2D and 3D images. Orthogonal wavelet transforms applied to multidimensional data exhibit poor results due to the lack of translational and directional invariance. Extending the 1D translation-invariant denoising algorithm of Coifman and Donoho (see Technical Report no.475, Department of Statistics, Stanford University, 1995) to higher dimensions overcomes the poor performance of orthogonal wavelet transforms. We present a method to quantify the loss of information due to denoising artifacts on data with an unknown signal-noise relationship, and propose a scheme for denoising of such data. Experiments show that invariant wavelet denoising perform well in reconstructing signals from noisy 3D data while preserving most of the actual information.

We address the problem of automated detection of biological macromolecules imaged with an electron microscope. These types of images are characterized by a low signal-to-noise ratio (0 dB), a low and varying contrast, in-plane rotated and densely distributed objects in the scene, strong object deformations, and the possible occurrence of false class objects and object agglomerations. We propose a two-step algorithm for rotation invariant and robust multiple 2D-object detection. First, we denoise the image by shrinking the coefficients of a steerable pyramid transform. Second, we employ a correlation-based object detection consisting of a constrained circular harmonic filter. Experiments on our imagery show that this denoising procedure prior to the detection significantly reduces the number of erroneous findings, thus increasing the reliability of object detectors. We elucidate a method to quantify the loss of information due to denoising artifacts on data with an unknown signal-noise relationship. Our experiments prove steerable pyramid denoising to perform well in reconstructing signal out of noisy data.