Assessment of visual quality and spatial accuracy of fast anisotropic diffusion and scan conversion algorithms for real-time three-dimensional spherical ultrasound

Three-dimensional ultrasound machines based on matrix phased-array transducers are gaining predominance for real-time dynamic screening in cardiac and obstetric practice. These transducers array acquire three-dimensional data in spherical coordinates along lines tiled in azimuth and elevation angles at incremental depth. This study aims at evaluating fast filtering and scan conversion algorithms applied in the spherical domain prior to visualization into Cartesian coordinates for visual quality and spatial measurement accuracy. Fast 3d scan conversion algorithms were implemented and with different order interpolation kernels. Downsizing and smoothing of sampling artifacts were integrated in the scan conversion process. In addition, a denoising scheme for spherical coordinate data with 3d anisotropic diffusion was implemented and applied prior to scan conversion to improve image quality. Reconstruction results under different parameter settings, such as different interpolation kernels, scaling factor, smoothing options, and denoising, are reported. Image quality was evaluated on several data sets via visual inspections and measurements of cylinder objects dimensions. Error measurements of the cylinder's radius, reported in this paper, show that the proposed fast scan conversion algorithm can correctly reconstruct three-dimensional ultrasound in Cartesian coordinates under tuned parameter settings. Denoising via three-dimensional anisotropic diffusion was able to greatly improve the quality of resampled data without affecting the accuracy of spatial information after the modification of the introduction of a variable gradient threshold parameter

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field