HyBoDT: Hybrid Bounded Distance Transforms of Trimmed NURBS Models

Distance field representation of objects in 3D space has several applications such as shape manipulation, graphics rendering, path planning, etc. Distance transforms (DTs) are discrete representations of distance fields in a regular voxel grid. The two main limitations of using distance transforms are that they are compute-intensive, and there are errors introduced while representing the object using DTs. In this work, we develop an hybrid GPU-accelerated marching wavefront method for computing DTs of models composed of trimmed NURBS surfaces with theoretical bounds. Our hybrid marching approach eliminates the error due to calculating approximate distances by marching. We also calculate the bounds on the error introduced due to the tessellation of the trimmed NURBS surfaces and calculate the propagation of these bounds in computing the DT. Finally, we present computation times for both 2D and 3D GPU DTs of test objects. We show that our GPU-accelerated approach is significantly faster than existing CPU-based methods.

Raymarching Distance Fields with CUDA

Raymarching is a technique for rendering implicit surfaces using signed distance fields. It has been known and used since the 1980s for rendering fractals and CSG (constructive solid geometry) surfaces, but has rarely been used for commercial rendering applications such as film and 3D games. Raymarching was first used for photorealistic rendering in the mid 2000s by demoscene developers and hobbyist graphics programmers, receiving little to no attention from the academic community and professional graphics engineers. In the present work, we explain why the use of Simple and Fast Multimedia Library (SFML) by nearly all existing approaches leads to a number of inefficiencies, and hence set out to develop a CUDA oriented approach instead. We next show that the usual data handling pipeline leads to further unnecessary data flow overheads and therefore propose a novel pipeline structure that eliminates much of redundancy in the manner in which data are processed and passed. We proceed to introduce a series of data structures which were designed with the specific aim of exploiting the pipeline’s strengths in terms of efficiency while achieving a high degree of photorealism, as well as the accompanying models and optimizations that ultimately result in an engine which is capable of photorealistic and real-time rendering on complex scenes and arbitrary objects. Lastly, the effectiveness of our framework is demonstrated in a series of experiments which compare our engine both in terms of visual fidelity and computational efficiency with the leading commercial and open source solutions, namely Unreal Engine and Blender.

Why Use Position Features in Liver Segmentation Performed by Convolutional Neural Network

Liver volumetry is an important tool in clinical practice. The calculation of liver volume is primarily based on Computed Tomography. Unfortunately, automatic segmentation algorithms based on handcrafted features tend to leak segmented objects into surrounding tissues like the heart or the spleen. Currently, convolutional neural networks are widely used in various applications of computer vision including image segmentation, while providing very promising results. In our work, we utilize robustly segmentable structures like the spine, body surface, and sagittal plane. They are used as key points for position estimation inside the body. The signed distance fields derived from these structures are calculated and used as an additional channel on the input of our convolutional neural network, to be more specific U-Net, which is widely used in medical image segmentation tasks. Our work shows that this additional position information improves the results of the segmentation. We test our approach in two experiments on two public datasets of Computed Tomography images. To evaluate the results, we use the Accuracy, the Hausdorff distance, and the Dice coefficient. Code is publicly available at: https://gitlab.com/hachaf/liver-segmentation.git.

Geometric Distance Fields of Plane Curves

This paper introduces a geometric generalization of signed distance fields for plane curves. We propose to store simplified geometric proxies to the curve at every sample. These proxies are constructed based on the differential geometric quantities of the represented curve and are used for queries such as closest point and distance calculations. We investigate the theoretical approximation order of these constructs and provide empirical comparisons between geometric and algebraic distance fields of higher order. We apply our results to font representation and rendering.

Spline Positional Encoding for Learning 3D Implicit Signed Distance Fields

Multilayer perceptrons (MLPs) have been successfully used to represent 3D shapes implicitly and compactly, by mapping 3D coordinates to the corresponding signed distance values or occupancy values. In this paper, we propose a novel positional encoding scheme, called Spline Positional Encoding, to map the input coordinates to a high dimensional space before passing them to MLPs, which help recover 3D signed distance fields with fine-scale geometric details from unorganized 3D point clouds. We verified the superiority of our approach over other positional encoding schemes on tasks of 3D shape reconstruction and 3D shape space learning from input point clouds. The efficacy of our approach extended to image reconstruction is also demonstrated and evaluated.