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Minimizing the weighted directed Hausdorff distance between colored point sets under translations and rigid motions

C. Knauer, K. Kriegel, F. Stehn
2011 Theoretical Computer Science  
class T , compute the transformations t ∈ T that minimize the weighted directed Hausdorff distance of t(P ) to Q.  ...  The weighted Hausdorff distance, as introduced in this paper, takes the weights of the point sets into account.  ...  In this paper we discuss the problem of matching two sequences of weighted point sets under the weighted directed Hausdorff distance.  ... 
doi:10.1016/j.tcs.2010.03.020 fatcat:6vvbrbmkw5cndhehzjde7k62vi

Minimizing the Weighted Directed Hausdorff Distance between Colored Point Sets under Translations and Rigid Motions [chapter]

Christian Knauer, Klaus Kriegel, Fabian Stehn
2009 Lecture Notes in Computer Science  
class T , compute the transformations t ∈ T that minimize the weighted directed Hausdorff distance of t(P ) to Q.  ...  The weighted Hausdorff distance, as introduced in this paper, takes the weights of the point sets into account.  ...  In this paper we discuss the problem of matching two sequences of weighted point sets under the weighted directed Hausdorff distance.  ... 
doi:10.1007/978-3-642-02270-8_13 fatcat:jedm2md2ovdalb24vqxrbrf5vy

Partial Shape Recognition for Sea Ice Motion Retrieval in the Marginal Ice Zone from Sentinel-1 and Sentinel-2

Mingfeng Wang, Marcel König, Natascha Oppelt
2021 Remote Sensing  
Hausdorff distance is used to measure the similarity of segmented ice floes.  ...  It is tolerant to perturbations and deficiencies of floe shapes, which enhances the density of retrieved sea ice motion vectors.  ...  Acknowledgments: We kindly acknowledge the provision of Sentinel-1 and Sentinel-2 data by the European Space Agency (ESA). Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/rs13214473 fatcat:g27j5b6nqzguhevljggkt5sfvy

Generalized Gradients: Priors on Minimization Flows

G. Charpiat, P. Maurel, J.-P. Pons, R. Keriven, O. Faugeras
2006 International Journal of Computer Vision  
Here, we investigate the relevance of using (i) other inner products, yielding other gradient descents, and (ii) other minimizing flows not deriving from any inner product.  ...  spatially coherent minimizing flows.  ...  The Hausdorff distance between Γ 1 and Γ 2 is: The Hausdorff distance is a natural distance on the set of shapes and fits well enough our intuition of distances between shapes, in that, if you consider  ... 
doi:10.1007/s11263-006-9966-2 fatcat:4c5vkash6nh6jaktjuhymnbrrm

Hausdorff distance under translation for points and balls

Pankaj K. Agarwal, Sariel Har-Peled, Micha Sharir, Yusu Wang
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in R d .  ...  In the first part of the paper, we consider two sets A, B of balls in R d , d = 2, 3, and wish to find a translation t that minimizes the Hausdorff distance between A + t, the set of all balls in A shifted  ...  The minimum Hausdorff distance between A and B under rigid motion in R 2 can be computed in O((m + n) 6 log mn) time [22] .  ... 
doi:10.1145/777792.777835 dblp:conf/compgeom/AgarwalHSW03 fatcat:4vnmhgmpljbkjgfn3aoe2noljq

Hausdorff distance under translation for points and balls

Pankaj K. Agarwal, Sariel Har-Peled, Micha Sharir, Yusu Wang
2003 Proceedings of the nineteenth conference on Computational geometry - SCG '03  
We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in R d .  ...  In the first part of the paper, we consider two sets A, B of balls in R d , d = 2, 3, and wish to find a translation t that minimizes the Hausdorff distance between A + t, the set of all balls in A shifted  ...  The minimum Hausdorff distance between A and B under rigid motion in R 2 can be computed in O((m + n) 6 log mn) time [22] .  ... 
doi:10.1145/777833.777835 fatcat:zukmxyi26femxcwnimovde2ww4

Hausdorff distance under translation for points and balls

Pankaj K. Agarwal, Sariel Har-Peled, Micha Sharir, Yusu Wang
2010 ACM Transactions on Algorithms  
We propose efficient approximation algorithms for computing the minimum rms and the minimum summed Hausdorff distances under translation, between two point sets in R d .  ...  In the first part of the paper, we consider two sets A, B of balls in R d , d = 2, 3, and wish to find a translation t that minimizes the Hausdorff distance between A + t, the set of all balls in A shifted  ...  The minimum Hausdorff distance between A and B under rigid motion in R 2 can be computed in O((m + n) 6 log mn) time [22] .  ... 
doi:10.1145/1824777.1824791 fatcat:vjezj5gx6fdnpmckw3kh3ih7va

Object tracking

Alper Yilmaz, Omar Javed, Mubarak Shah
2006 ACM Computing Surveys  
, and camera motion.  ...  In this survey, we categorize the tracking methods on the basis of the object and motion representations used, provide detailed descriptions of representative methods in each category, and examine their  ...  -Rigidity assumes that objects in the 3D world are rigid, therefore, the distance between any two points on the actual object will remain unchanged (see Figure 10 (e)).  ... 
doi:10.1145/1177352.1177355 fatcat:ikii77qbundjdadn2mdl4fv4mi

Automatic segmentation of moving objects for video object plane generation

T. Meier, K.N. Ngan
1998 IEEE transactions on circuits and systems for video technology (Print)  
The best match found indicates the translation the object has undergone, and the model is updated every frame to accommodate for rotation and changes in shape.  ...  The core of this algorithm is an object tracker that matches a two-dimensional (2-D) binary model of the object against subsequent frames using the Hausdorff distance.  ...  The best match is found by minimizing the Hausdorff distance between the image and the model for all translations of the model relative to the image.  ... 
doi:10.1109/76.718500 fatcat:6kbkjvo5ozc7rmoqm57sburufi

Dense Semi-rigid Scene Flow Estimation from RGBD Images [chapter]

Julian Quiroga, Thomas Brox, Frédéric Devernay, James Crowley
2014 Lecture Notes in Computer Science  
In order to deal efficiently with a moving camera, we model the motion as a rigid component plus a non-rigid residual and propose an alternating solver.  ...  We give a general formulation to solve for local and global rigid motions by jointly using intensity and depth data.  ...  Under the action of a twist ξ between t and t + 1, the motion of a 3D point induces an image flow (u, v).  ... 
doi:10.1007/978-3-319-10584-0_37 fatcat:cp73xerdavcedomfdd6h53ignm

Robust 3D Human Motion Reconstruction Via Dynamic Template Construction [article]

Zhong Li, Yu Ji, Wei Yang, Jinwei Ye, Jingyi Yu
2018 arXiv   pre-print
Specifically, we combine local rigidity and temporal coherence constraints to maintain geometry and motion consistencies.  ...  Direct estimation of 3D pose, body shape or motion on these low-quality data has been traditionally challenging.In this paper, we present a graph-based non-rigid shape registration framework that can simultaneously  ...  Acknowledgement This research is partially supported by National Science Foundation under the Grant IIS-1422477 and Army Research Office under the grant W911NF14-1-0338.  ... 
arXiv:1801.10434v1 fatcat:s77hht23hvc4bcsvryigu4ymqy

A Robust Linear Feature-Based Procedure for Automated Registration of Point Clouds

Martyna Poreba, François Goulette
2015 Sensors  
The algorithm is valid and ensures valuable results when pre-aligned point clouds with the same scale are used. The studies show that the matching accuracy is at least 99.5%.  ...  The transformation parameters are also estimated correctly. The error in rotation is better than 2.8% full scale, while the translation error is less than 12.7%.  ...  Acknowledgments The work reported in this paper was partly funded by the Cap Digital Business Cluster Terra Mobilita Project.  ... 
doi:10.3390/s150101435 pmid:25594589 pmcid:PMC4327086 fatcat:qokwtn6nbzel5dqravw6c2oene

On Mobility Analysis of Functional Sites from Time Lapse Microscopic Image Sequences of Living Cell Nucleus [chapter]

Lopamudra Mukherjee, Vikas Singh, Jinhui Xu, Kishore S. Malyavantham, Ronald Berezney
2006 Lecture Notes in Computer Science  
Our algorithms are based on interesting ideas from theoretical computer science and database theory and provide for the first time the tools to interpret the seemingly stochastic motion patterns of the  ...  A detailed study and analysis of the motion dynamics of these sites can reveal an interesting insight into their role in DNA replication and function.  ...  L 2 distance between p j i and p j+1 k .  ... 
doi:10.1007/11866763_71 fatcat:fxgj6vpj5bgb3hymuxmivsuxve

Automatic Registration for Articulated Shapes

Will Chang, Matthias Zwicker
2008 Computer graphics forum (Print)  
We explicitly sample the motion, which gives a priori the set of possible rigid transformations between parts of the shapes.  ...  We present an unsupervised algorithm for aligning a pair of shapes in the presence of significant articulated motion and missing data, while assuming no knowledge of a template, user-placed markers, segmentation  ...  We wish to thank Bob Sumner for the galloping horse animation, Brett Allen for the body scans, and Thibaut Weise for the hand scan dataset.  ... 
doi:10.1111/j.1467-8659.2008.01286.x fatcat:asnili7usjatrbl7lrfhwq753i

A Gromov-Hausdorff Framework with Diffusion Geometry for Topologically-Robust Non-rigid Shape Matching

Alexander M. Bronstein, Michael M. Bronstein, Ron Kimmel, Mona Mahmoudi, Guillermo Sapiro
2009 International Journal of Computer Vision  
While the traditionally used geodesic distance exploits the shortest path between points on the surface, the diffusion distance averages all paths connecting the points.  ...  compare to the classical geodesic distances in the presence of topological changes between the non-rigid shapes.  ...  Facundo Memoli, Stanford University, with whom the travel into the Gromov-Hausdorff and metric shape comparison world started.  ... 
doi:10.1007/s11263-009-0301-6 fatcat:2q455zniu5f6pimklgyt6edysa
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