A Liver Atlas Using the Special Euclidean Group

Hefny, Mohamed S.; Okada, Toshiyuki; Hori, Masatoshi; Sato, Yoshinobu; Ellis, Randy E.

doi:10.1007/978-3-319-24571-3_29

Cited by 4 publications

(2 citation statements)

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“…Examples of group theoretical techniques, closely related to G-CNNs, are orientation score [Duits et al, 2007, Janssen et al, 2018 methods such as crossing preserving vessel enhancement based on gauge theory on Lie groups [Franken and Duits, 2009, Hannink et al, 2014, Duits et al, 2016, vessel and nerve fiber enhancement (in diffusion imaging) via group convolutions with Gaussian (derivative) kernels [Duits and Franken, 2011, Zhang et al, 2015, Portegies et al, 2015, and anatomical landmark recognition via group convolutions [Bekkers, 2019]. In other, non-convolutional methods in medical image analysis, group theory provides a powerful tool to deal with symmetries and geometric structure, such as in statistical shape atlases [Hefny et al, 2015], shape matching [Hou et al, 2018], registration [Arsigny et al, 2006, Ashburner, 2007 and in general in statistics on non-Euclidean data structures [Pennec et al, 2019]. Following this successful line of geometry driven methods in medical image analysis, we propose in this paper to rely on G-CNNs to solve tasks in histopathology in an end-to-end learning setting.…”

Section: Group Theory In Medical Image Analysismentioning

confidence: 99%

Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis

Lafarge¹,

Bekkers²,

Pluim³

et al. 2020

Preprint

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Rotation-invariance is a desired property of machine-learning models for medical image analysis and in particular for computational pathology applications. We propose a framework to encode the geometric structure of the special Euclidean motion group SE(2) in convolutional networks to yield translation and rotation equivariance via the introduction of SE(2)group convolution layers. This structure enables models to learn feature representations with a discretized orientation dimension that guarantees that their outputs are invariant under a discrete set of rotations.Conventional approaches for rotation invariance rely mostly on data augmentation, but this does not guarantee the robustness of the output when the input is rotated. At that, trained conventional CNNs may require test-time rotation augmentation to reach their full capability.This study is focused on histopathology image analysis applications for which it is desirable that the arbitrary global orientation information of the imaged tissues is not captured by the machine learning models. The proposed framework is evaluated on three different histopathology image analysis tasks (mitosis detection, nuclei segmentation and tumor classification). We present a comparative analysis for each problem and show that consistent increase of performances can be achieved when using the proposed framework.

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Section: Group Theory In Medical Image Analysismentioning

confidence: 99%

Roto-Translation Equivariant Convolutional Networks: Application to Histopathology Image Analysis

Lafarge¹,

Bekkers²,

Pluim³

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…However, in the presence of large shape variations, the non linearity of the shape space demands more sophisticated analyses (e.g. kernel PCA [23], and PCA in the tangent space of Euclidean special group [24]). …”

Section: • Authors Are With the Center Of Computational Imaging And Simmentioning

confidence: 99%