The detection and analysis of features in fluid flow are important tasks in fluid mechanics and flow visu alization. One recent class of methods to approach this problem is to first compute objective optimal reference frames, relative to which the input vector field becomes as steady as possible. However, existing methods either optimize locally over a fixed neighborhood, which might not match the extent of interesting features well, or perform global optimization, which is costly. We propose a novel objective method for the computation of optimal reference frames that automatically adapts to the flow field locally, without having to choose neighborhoods a priori. We enable adaptivity by formulating this problem as a moving least squares approximation, through which we determine a continuous field of reference frames. To incorporate fluid features into the computation of the reference frame field, we introduce the use of a scalar guidance field into the moving least squares approximation. The guidance field determines a curved manifold on which a regularly sampled input vector field becomes a set of irregularly spaced samples, which then forms the input to the moving least squares approximation. Although the guidance field can be any scalar field, by using a field that corresponds to flow features the resulting reference frame field will adapt accordingly. We show that using an FTLE field as the guidance field results in a reference frame field that adapts better to local features in the flow than prior wo rk. However, our moving least squares framework is formulated in a very general way, and therefore other types of guidance fields could be used in the future to adapt to local fluid features.

We present a novel framework for 3D tomographic reconstruction and visualization of tomograms from noisy electron microscopy tilt-series. Our technique takes as an input aligned tilt-series from cryogenic electron microscopy and creates denoised 3D tomograms using a proximal jointly-optimized approach that iteratively performs reconstruction and denoising, relieving the users of the need to select appropriate denoising algorithms in the pre-reconstruction or post-reconstruction steps. The whole process is accelerated by exploiting parallelism on modern GPUs, and the results can be visualized immediately after the reconstruction using volume rendering tools incorporated in the framework. We show that our technique can be used with multiple combinations of reconstruction algorithms and regularizers, thanks to the flexibility provided by proximal algorithms. Additionally, the reconstruction framework is open-source and can be easily extended with additional reconstruction and denoising methods. Furthermore, our approach enables visualization of reconstruction error throughout the iterative process within the reconstructed tomogram and on projection planes of the input tilt-series. We evaluate our approach in comparison with state-of-the-art approaches and additionally show how our error visualization can be used for reconstruction evaluation.