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### 3-D chamfer distances and norms in anisotropic grids

Céline Fouard, Grégoire Malandain
2005 Image and Vision Computing
This allows, first, to derive analytically the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice, and second, to compute optimal chamfer coefficients.  ...  Chamfer distances are widely used in image analysis and many authors have investigated the computation of optimal chamfer mask coefficients.  ...  distance maps on anisotropic grids: (a) Euclidean distance map; (b) chamfer map computed with a 3!  ...

### Systematized Calculation of Optimal Coefficients of 3-D Chamfer Norms [chapter]

Céline Fouard, Grégoire Malandain
2003 Lecture Notes in Computer Science
the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice.  ...  Chamfer distances are widely used in image analysis, and many ways have been investigated to compute optimal chamfer mask coefficients.  ...  Norm constraints A distance is a norm if and only if its ball is convex, symmetric, and homogeneous.  ...

### Lower and Upper Bounds for Scaling Factors Used for Integer Approximation of 3D Anisotropic Chamfer Distance Operator [chapter]

Didier Coquin, Philippe Bolon
2009 Lecture Notes in Computer Science
This allows, first, to derive analytically the maximal normalized error with respect to Euclidean distance, in any 3D anisotropic lattice, and second, to compute optimal chamfer coefficients.  ...  Hence, the sampling grid turns out to be parallelepipedic. In this paper, 3D anisotropic local distance operators are introduced.  ...  Examples of integer chamfer masks are given. 3D Anisotropic Chamfer Distance Operator The objective is to approximate the real Euclidean distance d E .  ...

### 2D Subquadratic Separable Distance Transformation for Path-Based Norms [chapter]

David Coeurjolly
2014 Lecture Notes in Computer Science
More precisely, we describe a O(log 2 m · N 2 ) algorithm for shapes in a N × N domain with chamfer norm of size m.  ...  In this article, we present generic separable algorithms to efficiently compute Voronoi maps and distance transformations for a large class of metrics.  ...  Let d be a metric induced by a norm whose unit ball is symmetric with respect to grid axes and if distance comparison predicate is exact, Algorithm 1 is correct and returns a Voronoi map Π X .  ...

### Weighted distance transforms generalized to modules and their computation on point lattices

Céline Fouard, Robin Strand, Gunilla Borgefors
2007 Pattern Recognition
The first part is dedicated to formalization of definitions and properties (distance, metric, norm) of weighted distances on modules.  ...  Finally, the definitions and computation of weighted distances are applied to the face-centered cubic (FCC) and body-centered cubic (BCC) grids.  ...  The application of these properties and of the chamfer algorithm are numerous for the cubic and parallelepiped grids in the literature.  ...

### Distance Transforms: Academics Versus Industry

Egon L. van den Broek, Theo E. Schouten
2011 Recent Patents on Computer Science
In image and video analysis, distance transformations (DT) are frequently used. They provide a distance image (DI) of background pixels to the nearest object pixel.  ...  A benchmark including eight DT algorithms (i.e., city block, Danielsson's algorithm, chamfer 3-4, hexadecagonal region growing, a recent claimed true Euclidean DT, and three exact Euclidean DT) has been  ...  (2) and (3) present visualizations of chamfer DT with d 1 = 3 and d 2 = 4, as it was introduced in [21, 22] .  ...

### Distance Transforms: Academics Versus Industry

Egon L. van den Broek, Theo E. Schouten
2011 Recent Patents on Computer Science
In image and video analysis, distance transformations (DT) are frequently used. They provide a distance image (DI) of background pixels to the nearest object pixel.  ...  A benchmark including eight DT algorithms (i.e., city block, Danielsson's algorithm, chamfer 3-4, hexadecagonal region growing, a recent claimed true Euclidean DT, and three exact Euclidean DT) has been  ...  (2) and (3) present visualizations of chamfer DT with d 1 = 3 and d 2 = 4, as it was introduced in [21, 22] .  ...

### An Efficient Euclidean Distance Transform [chapter]

Donald G Bailey
2004 Lecture Notes in Computer Science
It works by performing a 1D distance transform on each row of the image, and then combines the results in each column.  ...  For ease of computation, a commonly used approximate algorithm is the chamfer distance transform.  ...  The Euclidean distance metric uses the L 2 norm and is defined as 2 2 2 , y x y x L + = (3) This metric is isotropic in that distances measured are independent of object orientation, subject of course  ...

### Deformation-Aware 3D Model Embedding and Retrieval [article]

Mikaela Angelina Uy and Jingwei Huang and Minhyuk Sung and Tolga Birdal and Leonidas Guibas
2020 arXiv   pre-print
We demonstrate that both of these approaches outperform other baselines in our experiments with both synthetic and real data. Our project page can be found at https://deformscan2cad.github.io/.  ...  fundamental operation for recovering a clean and complete 3D model from a noisy and partial 3D scan.  ...  Corporation and the Dassault Foundation.  ...

### Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction [article]

Rohan Chabra, Jan Eric Lenssen, Eddy Ilg, Tanner Schmidt, Julian Straub, Steven Lovegrove, Richard Newcombe
2020 arXiv   pre-print
DeepLS replaces the dense volumetric signed distance function (SDF) representation used in traditional surface reconstruction systems with a set of locally learned continuous SDFs defined by a neural network  ...  Efficiently reconstructing complex and intricate surfaces at scale is a long-standing goal in machine perception.  ...  In addition to the Chamfer distance we show mesh accuracy, which is defined as the maximum distance d such that 90% of generated points are within d if the ground truth mesh.  ...

### Incremental reconstruction of sharp edges on mesh surfaces

Charlie C.L. Wang
2006 Computer-Aided Design
Either chamfered or blended sharp edges on an input triangular mesh could be successfully reconstructed by the signals inherent in the mesh.  ...  edges and corners are lost on the reconstructed surface.  ...  In detail, the definition of near is d(v, f i ) ≤ αλ (8) where d(v, f ) returns the Euclidean distance from v to the point-set of f i and α is an coefficient for the support size of near.  ...

### From Collective Adaptive Systems to Human Centric Computation and Back: Spatial Model Checking for Medical Imaging

Gina Belmonte, Vincenzo Ciancia, Diego Latella, Mieke Massink
2016 Electronic Proceedings in Theoretical Computer Science
Recent research on formal verification for Collective Adaptive Systems (CAS) pushed advancements in spatial and spatio-temporal model checking, and as a side result provided novel image analysis methodologies  ...  The focus is shifted from pure logics to a mixture of logical, statistical and algorithmic approaches, driven by the logical nature intrinsic to the specification of the properties of interest in the field  ...  Acknowledgements The authors wish to thank Marco Di Benedetto for suggesting the application of distance transforms to improve the complexity of model checking of formulas with distances, and the Medical  ...

### A Survey of Non-Rigid 3D Registration [article]

Bailin Deng and Yuxin Yao and Roberto M. Dyke and Juyong Zhang
2022 arXiv   pre-print
In the past decade, with the advances in 3D sensing technologies that can measure time-varying surfaces, non-rigid registration has been applied for the acquisition of deformable shapes and has a wide  ...  In particular, we review different approaches for representing the deformation field, and the methods for computing the desired deformation.  ...  In [WCMN19], this term is used in conjunction with the Chamfer distance to measure the alignment error.  ...

### Hybrid Distance Field Computation [chapter]

Richard Satherley, Mark W. Jones
2001 Eurographics
This paper concentrates on the latter by presenting a new method for calculating distance fields and comparing it with the current best approximate method and the true Euclidean distance field.  ...  Details are given of the algorithm, and the acceleration methods that are used for calculating the true distance field.  ...  distance field shown in Figure 4 (d) -4(f).  ...

### Multiresolution Tree Networks for 3D Point Cloud Processing [chapter]

Matheus Gadelha, Rui Wang, Subhransu Maji
2018 Lecture Notes in Computer Science
This allows efficient feed-forward processing through 1D convolutions, coarse-to-fine analysis through a multi-grid architecture, and it leads to faster convergence and small memory footprint during training  ...  We present multiresolution tree-structured networks to process point clouds for 3D shape understanding and generation tasks.  ...  We acknowledge support from NSF (IIS-1617917, IIS-1749833, IIS-1423082) and the MassTech Collaborative for funding the UMass GPU cluster.  ...
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