Truncated Signed Distance Fields (TSDFs) have become a popular tool in 3D reconstruction, as they allow building very high-resolution models of the environment in realtime on GPU. However, they have rarely been used for planning on robotic platforms, mostly due to high computational and memory requirements. We propose to reduce these requirements by using large voxel sizes, and extend the stand...

The computation speed for distance transforms becomes important in a wide variety of image processing applications. Current ITK library filters do not see any benefit from a multithreading environment. We introduce a three-dimensional signed parallel implementation of the exact Euclidean distance transform algorithm developed by Maurer et al.[1] with a theoretical complexity of O(n/p) for n vox...

In many areas, the ability to create accurate 3D models is of great interest, for example, in computer vision, robotics, architecture, and augmented reality. In this paper we show how a textured indoor environment can be reconstructed in 3D using an RGB-D camera. Real-time performance can be achieved using a GPU. We show how the camera pose can be estimated directly using the geometry that we r...

The computation speed for distance transforms becomes important in a wide variety of image processing applications. Current ITK library filters do not see any benefit from a multithreading environment. We introduce an N-dimensional signed parallel implementation of the exact Euclidean distance transform algorithm developed by Maurer et al.[1] with a theoretical complexity of O(n/p) for n voxels...

In this paper we present an hp-adaptive algorithm to generate discrete higher-order polynomial Signed Distance Fields (SDFs) on axis-aligned hexahedral grids from manifold polygonal input meshes. Using an orthonormal polynomial basis, we efficiently fit the polynomials to the underlying signed distance function on each cell. The proposed error-driven construction algorithm is globally adaptive ...

We propose a novel 3D object reconstruction framework that is able to fully capture the accurate coloured geometry of an object using an RGB-D sensor. Building on visual odometry for trajectory estimation, we perform pose graph optimisation on collected keyframes and reconstruct the scan variationally via coloured signed distance fields. To capture the full geometry, we conduct multiple scans w...

We propose a new signed or unsigned Euclidean distance transformation algorithm, based on the local corrections of the well-known 4SED algorithm of Danielsson. Those corrections are only applied to a small neighborhood of a small subset of pixels from the image, which keeps the cost of the operation low. In contrast with all fast algorithms previously published, our algorithm produces perfect E...

From a geometric perspective most nonlinear binary classification algorithms, including state of the art versions of Support Vector Machine (SVM) and Radial Basis Function Network (RBFN) classifiers, and are based on the idea of reconstructing indicator functions. We propose instead to use reconstruction of the signed distance function (SDF) as a basis for binary classification. We discuss prop...

In this paper, we consider fuzzy inventory with backorder. First, we fuzzify the storing cost a, backorder cost b, cost of placing an order c, total demand r, order quantity q, and shortage quantity s as the triangular fuzzy numbers in the total cost. From these, we can obtain the fuzzy total cost. Using the signed distance method to defuzzify, we get the estimate of the total cost in the fuzzy...

Distribution of material density and other properties of heterogeneous objects can be parametrized by the Euclidean distance function from the object boundary or from special material features. For objects constructed using geometric primitives and set-theoretic operations, an approximation of the distance function can be obtained in a constructive manner by applying special compositing operati...