Signed distance function implicit geologic modeling

Prior to every geostatistical estimation or simulation study there is a need for delimiting the geologic domains of the deposit, which is traditionally done manually by a geomodeler in a laborious, time consuming and subjective process. For this reason, novel techniques referred to as implicit modelling have appeared. These techniques provide algorithms that replace the manual digitization process of the traditional methods by some form of automatic procedure. This paper covers a few well established implicit methods currently available with special attention to the signed distance function methodology. A case study based on a real dataset was performed and its applicability discussed. Although it did not replace an experienced geomodeler, the method proved to be capable in creating semi-automatic geological models from the sampling data, especially in the early stages of exploratio

Motion Segmentation of Truncated Signed Distance Function based Volumetric Surfaces

© 2015 IEEE.Truncated signed distance function (TSDF) based volumetric surface reconstructions of static environments can be readily acquired using recent RGB-D camera based mapping systems. If objects in the environment move then a previously obtained TSDF reconstruction is no longer current. Handling this problem requires segmenting moving objects from the reconstruction. To this end, we present a novel solution to the motion segmentation of TSDF volumes. The segmentation problem is cast as CRF-based MAP inference in the voxel space. We propose: a novel data term by solving sparse multi-body motion segmentation and computing likelihoods for each motion label in the RGB-D image space, and, a novel pair wise term based on gradients of the TSDF volume. Experimental evaluation shows that the proposed approach achieves successful segmentations on reconstructions acquired with Kinect Fusion. Unlike the existing solutions which only work if the objects move completely from their initially occupied spaces, the proposed method permits segmentation of objects when they start to move

Sets of constant distance from a Jordan curve

We study the $\epsilon$-level sets of the signed distance function to a planar Jordan curve $\Gamma$, and ask what properties of $\Gamma$ ensure that the $\epsilon$-level sets are Jordan curves, or uniform quasicircles, or uniform chord-arc curves for all sufficiently small $\epsilon$. Sufficient conditions are given in term of a scaled invariant parameter for measuring the local deviation of subarcs from their chords. The chordal conditions given are sharp

Orthogonal signed-distance coordinates and vector calculus near evolving curves and surfaces

We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and collate useful vector calculus identities for these coordinates. These results and provided code enable consistent accounting of geometric effects in the derivation of boundary layer asymptotics for a wide range of physical systems.Comment: 24 pages, 3 figures, Mathematica code available at https://github.com/ericwhester/signed-distance-cod