A Geometric Method for Accelerated Sphere Tracing of Implicit Surfaces

Sphere tracing is a common raytracing technique used for rendering implicit surfaces defined by a signed distance function (SDF). However, these distance functions are often expensive to compute, prohibiting several real-time applications despite recent efforts to accelerate it. This paper presents a method to precompute a slightly augmented distance field that hugely accelerates rendering. This novel method called quadric tracing supports two configurations: (i) accelerating raytracing without losing precision, so the original SDF is still needed; (ii) entirely replacing the SDF and tracing an interpolated surface. Quadric tracing can offer 20% to 100% speedup in rendering static scenes and thereby amortizing the slowdown caused by the complexity of the geometry.

Mask-R$$^{2}$$CNN: a distance-field regression version of Mask-RCNN for fetal-head delineation in ultrasound images

Background and objectives Fetal head-circumference (HC) measurement from ultrasound (US) images provides useful hints for assessing fetal growth. Such measurement is performed manually during the actual clinical practice, posing issues relevant to intra- and inter-clinician variability. This work presents a fully automatic, deep-learning-based approach to HC delineation, which we named Mask-R$$^{2}$$ 2 CNN. It advances our previous work in the field and performs HC distance-field regression in an end-to-end fashion, without requiring a priori HC localization nor any postprocessing for outlier removal. Methods Mask-R$$^{2}$$ 2 CNN follows the Mask-RCNN architecture, with a backbone inspired by feature-pyramid networks, a region-proposal network and the ROI align. The Mask-RCNN segmentation head is here modified to regress the HC distance field. Results Mask-R$$^{2}$$ 2 CNN was tested on the HC18 Challenge dataset, which consists of 999 training and 335 testing images. With a comprehensive ablation study, we showed that Mask-R$$^{2}$$ 2 CNN achieved a mean absolute difference of 1.95 mm (standard deviation $$=\pm 1.92$$ = ± 1.92 mm), outperforming other approaches in the literature. Conclusions With this work, we proposed an end-to-end model for HC distance-field regression. With our experimental results, we showed that Mask-R$$^{2}$$ 2 CNN may be an effective support for clinicians for assessing fetal growth.

Geodesic Distance Field-based Process Planning for Five-Axis Machining of Complicated Parts

A critical task in multi-pass process planning for five-axis machining of complicated parts is to determine the intermediate surfaces for rough machining. Traditionally, the intermediate surfaces are simply parallel Z-level planes, and the machining is of the simplest three-axis type. However, for complicated parts, this so-called Z-level method lacks flexibility and causes isolated islands on layers, which require extraneous air movements by the tool. Moreover, the in-process workpiece machined according to the Z-level method suffers from the staircase effect, which often induces unstable dynamic problems on the tool-spindle system. In this paper, we propose a new method of planning a five-axis machining process for a complicated freeform solid part. In our method, the intermediate surfaces are no longer planar but curved, and they are intrinsically influenced by the convex hull of the part. The powerful algebraic tool of geodesic distance field is utilized to generate the desired intermediate surfaces, for which collision-free five-axis machining tool paths are then planned. In addition, we propose a novel idea of alternating between the roughing and finishing machining operations, which helps improve the stiffness of the in-process workpiece. Ample physical cutting experiments are performed, and the experimental results convincingly confirm the advantages of our method.