Probabilistic Surface Reconstruction with Unknown Correspondence

Madsen, Dennis and Vetter, Thomas and Lüthi, Marcel. (2019) Probabilistic Surface Reconstruction with Unknown Correspondence. In: Uncertainty for Safe Utilization of Machine Learning in Medical Imaging and Clinical Image-Based Procedures, 11840. Cham, pp. 3-11.

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Official URL: https://edoc.unibas.ch/74967/

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We frequently encounter the need to reconstruct the full 3D surface from a given part of a bone in areas such as orthopaedics and surgical planning. Once we establish correspondence between the partial surface and a Statistical Shape Model (SSM), the problem has an appeal- ing solution. The most likely reconstruction, as well as the full posterior distribution of all possible surface completions, can be obtained in closed form with an SSM. In this paper, we argue that assuming known corre- spondence is unjustified for long bones. We show that this can lead to re- constructions, which greatly underestimate the uncertainty. Even worse, the ground truth solution is often deemed very unlikely under the poste- rior. Our main contribution is a method which allows us to estimate the posterior distribution of surfaces given partial surface information with- out making any assumptions about the correspondence. To this end, we use the Metropolis-Hastings algorithm to sample reconstructions with unknown pose and correspondence from the posterior distribution. We introduce a projection-proposal to propose shape and pose updates to the Markov-Chain, which lets us explore the posterior distribution much more efficiently than a standard random-walk proposal. We use less than 1 % of the samples needed by a random-walk to explore the posterior. We compare our method with the analytically computed posterior distribution, which assumes fixed correspondence. The comparison shows that our method leads to much more realistic posterior estimates when only small fragments of the bones are available.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Computergraphik Bilderkennung (Vetter)
UniBasel Contributors:Vetter, Thomas and Lüthi, Marcel and Madsen, Dennis
Item Type:Conference or Workshop Item, refereed
Conference or workshop item Subtype:Conference Paper
Series Name:Lecture notes in Computer Science
Note:Publication type according to Uni Basel Research Database: Conference paper
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Last Modified:20 Jun 2023 13:51
Deposited On:31 Jan 2020 15:07

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