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Parzer F, Kirisits C, Scherzer O. Uncertainty Quantification for Scale-Space Blob Detection. JOURNAL OF MATHEMATICAL IMAGING AND VISION 2024; 66:697-717. [PMID: 39156696 PMCID: PMC11329558 DOI: 10.1007/s10851-024-01194-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 04/24/2024] [Indexed: 08/20/2024]
Abstract
We consider the problem of blob detection for uncertain images, such as images that have to be inferred from noisy measurements. Extending recent work motivated by astronomical applications, we propose an approach that represents the uncertainty in the position and size of a blob by a region in a three-dimensional scale space. Motivated by classic tube methods such as the taut-string algorithm, these regions are obtained from level sets of the minimizer of a total variation functional within a high-dimensional tube. The resulting non-smooth optimization problem is challenging to solve, and we compare various numerical approaches for its solution and relate them to the literature on constrained total variation denoising. Finally, the proposed methodology is illustrated on numerical experiments for deconvolution and models related to astrophysics, where it is demonstrated that it allows to represent the uncertainty in the detected blobs in a precise and physically interpretable way.
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Affiliation(s)
- Fabian Parzer
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
| | - Clemens Kirisits
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
| | - Otmar Scherzer
- Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
- Johann Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstrasse 69, 4040 Linz, Austria
- Christian Doppler Laboratory for Mathematical Modeling and Simulation of Next Generations of Ultrasound Devices (MaMSi), Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
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2
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Choi G, Oh HS. Elastic-Band Transform for Visualization and Detection. Pattern Recognit Lett 2023. [DOI: 10.1016/j.patrec.2023.01.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
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Huh J, Dyal D, Park C. Nonparametric estimation of single-index models in scale-space. J STAT COMPUT SIM 2021. [DOI: 10.1080/00949655.2021.1898610] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Jib Huh
- Department of Statistics, Duksung Women's University, Seoul, South Korea
| | - Derek Dyal
- Department of Statistics, University of Georgia, Athens, GA, USA
| | - Cheolwoo Park
- Department of Statistics, University of Georgia, Athens, GA, USA
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Hindberg K, Hannig J, Godtliebsen F. A novel scale-space approach for multinormality testing and the k-sample problem in the high dimension low sample size scenario. PLoS One 2019; 14:e0211044. [PMID: 30668596 PMCID: PMC6342313 DOI: 10.1371/journal.pone.0211044] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2018] [Accepted: 01/07/2019] [Indexed: 11/17/2022] Open
Abstract
Two classical multivariate statistical problems, testing of multivariate normality and the k-sample problem, are explored by a novel analysis on several resolutions simultaneously. The presented methods do not invert any estimated covariance matrix. Thereby, the methods work in the High Dimension Low Sample Size situation, i.e. when n ≤ p. The output, a significance map, is produced by doing a one-dimensional test for all possible resolution/position pairs. The significance map shows for which resolution/position pairs the null hypothesis is rejected. For the testing of multinormality, the Anderson-Darling test is utilized to detect potential departures from multinormality at different combinations of resolutions and positions. In the k-sample case, it is tested whether k data sets can be said to originate from the same unspecified discrete or continuous multivariate distribution. This is done by testing the k vectors corresponding to the same resolution/position pair of the k different data sets through the k-sample Anderson-Darling test. Successful demonstrations of the new methodology on artificial and real data sets are presented, and a feature selection scheme is demonstrated.
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Affiliation(s)
- Kristian Hindberg
- Department of Mathematics and Statistics, University of Tromsø - The Arctic University of Norway, Tromsø, Norway
| | - Jan Hannig
- Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC, United States of America
| | - Fred Godtliebsen
- Department of Mathematics and Statistics, University of Tromsø - The Arctic University of Norway, Tromsø, Norway
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Li D, Mei C. SiZer inference for generalized varying coefficient models. J STAT COMPUT SIM 2018. [DOI: 10.1080/00949655.2018.1525383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Dengkui Li
- Department of Statistics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, PR China
| | - Changlin Mei
- Department of Statistics, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, PR China
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Pasanen L, Aakala T, Holmström L. A scale space approach for estimating the characteristic feature sizes in hierarchical signals. Stat (Int Stat Inst) 2018. [DOI: 10.1002/sta4.195] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Leena Pasanen
- Research Unit of Mathematical Sciences; University of Oulu; Oulu 90014 Finland
| | - Tuomas Aakala
- Department of Forest Sciences; University of Helsinki; Helsinki 00014 Finland
| | - Lasse Holmström
- Research Unit of Mathematical Sciences; University of Oulu; Oulu 90014 Finland
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Vuollo V, Holmström L, Aarnivala H, Harila V, Heikkinen T, Pirttiniemi P, Valkama AM. Analyzing infant head flatness and asymmetry using kernel density estimation of directional surface data from a craniofacial 3D model. Stat Med 2016; 35:4891-4904. [PMID: 27383684 DOI: 10.1002/sim.7032] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Revised: 05/11/2016] [Accepted: 06/13/2016] [Indexed: 11/12/2022]
Abstract
Infant skull deformation is analyzed using the distribution of head normal vector directions computed from a 3D image. Severity of flatness and asymmetry are quantified by functionals of the kernel estimate of the normal vector direction density. Using image data from 99 infants and clinical deformation ratings made by experts, our approach is compared with some recently suggested methods. The results show that the proposed method performs competitively. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Ville Vuollo
- Department of Orthodontics, Oral Health Sciences, Faculty of Medicine, University of Oulu, Oulu, Finland. .,Medical Research Center Oulu, Oulu University Hospital, Oulu, Finland. .,Department of Mathematical Sciences, University of Oulu, Oulu, Finland.
| | - Lasse Holmström
- Department of Mathematical Sciences, University of Oulu, Oulu, Finland
| | - Henri Aarnivala
- Medical Research Center Oulu, Oulu University Hospital, Oulu, Finland.,Department of Children and Adolescence, Oulu University Hospital, Oulu, Finland.,PEDEGO Research Group, University of Oulu, Oulu, Finland
| | - Virpi Harila
- Department of Orthodontics, Oral Health Sciences, Faculty of Medicine, University of Oulu, Oulu, Finland.,Medical Research Center Oulu, Oulu University Hospital, Oulu, Finland
| | - Tuomo Heikkinen
- Department of Orthodontics, Oral Health Sciences, Faculty of Medicine, University of Oulu, Oulu, Finland.,Medical Research Center Oulu, Oulu University Hospital, Oulu, Finland
| | - Pertti Pirttiniemi
- Department of Orthodontics, Oral Health Sciences, Faculty of Medicine, University of Oulu, Oulu, Finland.,Medical Research Center Oulu, Oulu University Hospital, Oulu, Finland
| | - Arja Marita Valkama
- Medical Research Center Oulu, Oulu University Hospital, Oulu, Finland.,Department of Children and Adolescence, Oulu University Hospital, Oulu, Finland.,PEDEGO Research Group, University of Oulu, Oulu, Finland
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Pasanen L, Laukkanen-Nevala P, Launonen I, Prusov S, Holmström L, Niemelä E, Erkinaro J. Extraction of sea temperature in the Barents Sea by a scale space multiresolution method – prospects for Atlantic salmon. J Appl Stat 2016. [DOI: 10.1080/02664763.2016.1252731] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Leena Pasanen
- Department of Mathematical Sciences, University of Oulu, Oulu, Finland
| | | | - Ilkka Launonen
- Department of Mathematical Sciences, University of Oulu, Oulu, Finland
| | - Sergey Prusov
- Knipovich Polar Research Institute of Marine Fisheries and Oceanography, Murmansk, Russia
| | - Lasse Holmström
- Department of Mathematical Sciences, University of Oulu, Oulu, Finland
| | - Eero Niemelä
- Natural Resources Institute Finland, Oulu, Finland
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Jang D, Oh HS, Naveau P. Identifying local smoothness for spatially inhomogeneous functions. Comput Stat 2016. [DOI: 10.1007/s00180-016-0694-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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