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4D Minimal Non-simple Sets [chapter]

C. J. Gau, T. Yung Kong
2002 Lecture Notes in Computer Science  
Loosely speaking, a set of 1's in a binary image is said to be simple if parallel deletion of those 1's "preserves topology". A non-simple set of 1's must contain a minimal non-simple (MNS) set.  ...  One method of verifying that a given parallel thinning algorithm "preserves topology" is to show that no iteration ever deletes a minimal non-simple ("MNS") set of 1's.  ...  Concluding Remarks We have identified all types of sets of 4-xels that can be minimal non-simple (MNS) in a 4D binary image, and all types that can be MNS without being an 80-component of the image, when  ... 
doi:10.1007/3-540-45986-3_7 fatcat:vyn5y54girft3ilsp42ouki63i

Minimal non-deletable sets and minimal non-codeletable sets in binary images

T. Yung Kong
2008 Theoretical Computer Science  
In the 1990s and early 2000s analogous results were obtained by Hall, Ma, Gau, and the author for binary images on the 2D hexagonal grid, the 3D Cartesian and face-centered cubic grids, and the 4D Cartesian  ...  The concepts of strongly 8-deletable and strongly 4-deletable sets of 1s in binary images on the 2D Cartesian grid were introduced by Ronse in the mid-1980s to formalize the connectivity preservation conditions  ...  Characterizations of minimal non-deletable and minimal non-codeletable sets We say that a set D of 1s of a binary image I is minimal non-simple (minimal non-cosimple) if D is a non-simple (non-cosimple  ... 
doi:10.1016/j.tcs.2008.02.001 fatcat:lipjtf4us5bqvbbz3zqwnxepmu

Minimal Non-simple and Minimal Non-cosimple Sets in Binary Images on Cell Complexes [chapter]

T. Yung Kong
2006 Lecture Notes in Computer Science  
Background: Ronse's Theorems In the 1960's Rosenfeld introduced the concepts of 8-simple and 4-simple 1's in binary images on a 2D Cartesian grid.  ...  . a, b, ..., j are some 8-simple 1's of a 2D binary image (whose 1's are the gray squares). w, x, y, z are some non-8-simple 1's. 4-deletable sets are analogous--just switch "4" and "8".  ...  ( ( Cor. 1: For any finite collection S of polyhedra in 3-space, the following are equivalent: (a) Proof of Claim 4 (part 2): We have just shown is contractible, and so, by (*), Lemma 1 now tells us  ... 
doi:10.1007/11907350_15 fatcat:psvpzzsffvamdlpe4gt2przdlu

Image processing tools for better incorporation of 4D seismic data into reservoir models

Ratiba Derfoul, Sebastien Da Veiga, Christian Gout, Carole Le Guyader, Elodie Tillier
2013 Journal of Computational and Applied Mathematics  
In this paper, we focus on the integration of dynamic data related to 4D inverted seismic data.  ...  This simplification involves filtering and segmentation techniques, as well as image comparison methods rooted in image analysis, such as the local modified Haussdorff distance.  ...  This set consists of binary images obtained with all possible thresholds applied to image I.  ... 
doi:10.1016/j.cam.2012.08.022 fatcat:tp4qcmr2f5getieu4bin3gqvie

Automatic heart localization from a 4D MRI data set

Wolfgang Sorgel, Vincent Vaerman, Kenneth M. Hanson
1997 Medical Imaging 1997: Image Processing  
The purpose of the presented work is the automatic localization of the heart from 4D multi-slice magnetic resonance images MRI.  ...  This mask allows us to extract one binary image of the heart for each spatial slice location, regardless of temporal location.  ...  Luc Bidaut head of the Digital Imaging Unit of the University Hospital of Geneva, Switzerland for providing the MR images and guiding them through this captivating research.  ... 
doi:10.1117/12.274120 fatcat:bndrpxr5lrhmdiopiuk3aj6yyu

Scalable Full Flow with Learned Binary Descriptors [article]

Gottfried Munda, Alexander Shekhovtsov, Patrick Knöbelreiter, Thomas Pock
2017 arXiv   pre-print
In contrast to current state of the art approaches for learning binary CNNs we can compute the exact non-zero gradient within our model.  ...  This enables evaluation of the cost on the fly and allows to perform learning and CRF inference on high resolution images without ever storing the 4D cost volume.  ...  This hybrid model is interesting because minimization in v i can be computed efficiently on the binarized cost with Hamming distance, and the minimization in u i has a non-zero gradient in c u .  ... 
arXiv:1707.06427v1 fatcat:6s7tq2kmfzdndm5cqxzczq5opm

Reconstruction of heterogeneous materials via stochastic optimization of limited-angle X-ray tomographic projections

Hechao Li, Nikhilesh Chawla, Yang Jiao
2014 Scripta Materialia  
X-ray tomography has provided a non-destructive means for microstructure characterization in 3D and 4D.  ...  X-ray tomography is an extremely attractive, non-destructive technique for characterizing microstructure in 3D and 4D [4] [5] [6] .  ...  smaller minimal set without losing the accuracy in reconstruction compared to those obtained from the larger data sets.  ... 
doi:10.1016/j.scriptamat.2014.05.002 fatcat:fpfroxwjbjapznmzgwpwkmiytu

The JPEG Pleno Light Field Coding Standard 4D-Transform Mode: How to Design an Efficient 4D-Native Codec

Gustavo De Oliveira Alves, Murilo Bresciani De Carvalho, Carla L. Pagliari, Pedro Garcia Freitas, Ismael Seidel, Marcio Pinto Pereira, Carla Florentino Schueler Vieira, Vanessa Testoni, Fernando Pereira, Eduardo A. B. Da Silva
2020 IEEE Access  
Although static light fields are inherently 4D structures, the coding solutions in the literature mostly employ traditional 2D coding tools associated with techniques such as depth-based image rendering  ...  In this context, this paper describes and analyzes in detail the conceptual and algorithmic design process which has led to the creation of the JPEG Pleno Light Field Coding standard 4D-Transform coding  ...  BINARY-TREE-ORIENTED BIT-PLANE CLUSTERING The binary-tree-oriented bit-plane clustering aims at locating, in the 4D-DCT coefficients scanned array, those coefficients which are quantized as non-zero.  ... 
doi:10.1109/access.2020.3024844 fatcat:zxdcz4m4l5dqjmdiofdem6duj4

Some Weighted Distance Transforms in Four Dimensions [chapter]

Gunilla Borgefor
2000 Lecture Notes in Computer Science  
In 4D, using 3×3×3×3 neighbourhoods, there are four different weights. In this paper, optimal real and integer weights are computed for one type of 4D weighted distance transforms.  ...  In a digital distance transform, each picture element in the shape (background) has a value measuring the distance to the background (shape).  ...  Acknowledgement Thanks to Stina Svensson for computing and visualising the two balls in Figs 2 and 3.  ... 
doi:10.1007/3-540-44438-6_27 fatcat:qlcccmapcvahhh6dnzndtgfb7u

Phase reconstruction using fast binary 4D STEM data

C. M. O'Leary, C. S. Allen, C. Huang, J. S. Kim, E. Liberti, P. D. Nellist, A. I. Kirkland
2020 Applied Physics Letters  
We thank the Diamond Light Source for access and support in the use of the electron Physical Science Imaging Centre (Instrument E02, Proposal Nos.  ...  To minimize the beam current at the sample, the probe semi-convergence angle was set to 7.6 mrad.  ...  In conclusion, we have demonstrated the application of binary 4D STEM data to post-processing phase reconstruction techniques.  ... 
doi:10.1063/1.5143213 fatcat:op6spyhd55b3lnhvvvcbr5quju

Surface Volume Estimation of Digitized Hyperplanes Using Weighted Local Configurations [chapter]

Joakim Lindblad
2005 Lecture Notes in Computer Science  
We present a method for estimating the surface volume of four-dimensional objects in discrete binary images. A surface volume weight is assigned to each 2 × 2 × 2 × 2 configuration of image elements.  ...  The algorithm is appealingly simple; the use of only a local neighbourhood enables efficient implementations in hardware and/or in parallel architectures.  ...  In this paper we present a method to perform accurate surface volume estimations of 4D objects in binary digital images using a technique based on local cell tiling.  ... 
doi:10.1007/978-3-540-31965-8_24 fatcat:ryt7utjsurbb3lmbnscfb4syde

Morphological Operations on 3D and 4D Images: From Shape Primitive Detection to Skeletonization [chapter]

Pieter P. Jonker
2000 Lecture Notes in Computer Science  
The formalism is expanded to four-dimensional images and elaborates on the extension of 3D skeletonization to 4D skeletonization.  ...  The first chapters treat a formalism that has the potential of implementing morphological operations on binary images of arbitrary dimensions.  ...  Figures 3 and 4 show some structuring elements in the form of mask-sets for simple operations in 2 X and 3 X .  ... 
doi:10.1007/3-540-44438-6_31 fatcat:5l25miqs3fa6vdm2ork44ajxvq

Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation

Chunming Li, John C. Gore, Christos Davatzikos
2014 Magnetic Resonance Imaging  
More importantly, the energy in our formulation is convex in each of its variables, which leads to the robustness of the proposed energy minimization algorithm.  ...  This paper proposes a new energy minimization method called multiplicative intrinsic component optimization (MICO) for joint bias field estimation and segmentation of magnetic resonance (MR) images.  ...  in this paper.  ... 
doi:10.1016/j.mri.2014.03.010 pmid:24928302 pmcid:PMC4401088 fatcat:iy2j3wcq5bea7haredyr5tgaee

Order Independence in Binary 2D Homotopic Thinning [chapter]

Marcin Iwanowski, Pierre Soille
2006 Lecture Notes in Computer Science  
This paper investigates binary homotopic 2D thinning in view of its independence of the order of processing image pixels.  ...  Two kinds of pixels to be removed are considered: simple and b-simple. Use of each of those pixels yields to different types of order independent thinnings: homotopic marking and local-SKIZ.  ...  According to the results presented in [7] such a set cannot contain a minimal non deletable set.  ... 
doi:10.1007/11907350_50 fatcat:3dphvoz54zb2jnweenjankeaxe

Page 9536 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
Yung Kong, 4D minimal non-simple sets (81-91); Luc Brun and Walter G.  ...  Reeves, Non-parametric estimation of properties of combinatorial landscapes (31—40); Jano I. van Hemert, Com- paring classical methods for solving binary constraint satisfaction problems with state of  ... 
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