Assignment Flows

Schnörr, Christoph

doi:10.1007/978-3-030-31351-7_8

Cited by 17 publications

(18 citation statements)

References 44 publications

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“…Compared to methods [ 9 , 16 ] and [ 19 ] that have proven to be particularly effective on tissue classification with a priory known retina shape orientation, our ansatz merely relies on local features and yields ordered labelings which are directly enforced through the underlying geometry of statistical manifold. Consequently, by building on the feasible concept of spatially regularized assignment [ 22 ], the ordered flow (Definition 2 ) possesses the potential to be extended towards the detection of pathological retina changes and vascular vessel structure, which is the objective of our current research.…”

Section: Discussionmentioning

confidence: 99%

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Assignment Flow for Order-Constrained OCT Segmentation

Sitenko

Boll

Schnörr

2021

Lecture Notes in Computer Science

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At the present time Optical Coherence Tomography (OCT) is among the most commonly used non-invasive imaging methods for the acquisition of large volumetric scans of human retinal tissues and vasculature. Due to tissue-dependent speckle noise, the elaboration of automated segmentation models has become an important task in the field of medical image processing. We propose a novel, purely data driven geometric approach to order-constrained 3D OCT retinal cell layer segmentation which takes as input data in any metric space. This makes it unbiased and therefore amenable for the detection of local anatomical changes of retinal tissue structure. To demonstrate robustness of the proposed approach we compare four different choices of features on a data set of manually annotated 3D OCT volumes of healthy human retina. The quality of computed segmentations is compared to the state of the art in terms of mean absolute error and Dice similarity coefficient.

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Section: Discussionmentioning

confidence: 99%

“…We summarize the assignment flow approach introduced by [ 4 ] and refer to the recent survey [ 22 ] for more background and a review of recent related work.…”

Section: Assignment Flowmentioning

confidence: 99%

Assignment Flow for Order-Constrained OCT Segmentation

Sitenko

Boll

Schnörr

2021

Lecture Notes in Computer Science

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“…To deal with highly variable layer boundaries another possible extension of our method is to predict weights for geometric averaging (23) in an optimal control theoretic way, to cope with the linearized dynamics of the assignment flow (Zeilmann et al 2020) as in detail elaborated in Hühnerbein et al (2021). Consequently, by building on the feasible concept of spatially regularized assignments (Schnörr 2020), the ordered flow (2) possesses the potential to be extended towards the detection of pathological retina changes and vascular vessel structure. We expect that the joint interaction of retina tissues and blood vessels during the segmentation with the assignment flow will lead to more effective layer detection, which is the objective of our current research.…”

Section: Discussionmentioning

confidence: 99%

“…We summarize the assignment flow approach introduced by Åström et al (2017) and refer to the recent survey (Schnörr 2020) for more background and a review of recent related work.…”

Section: Assignment Flowmentioning

confidence: 99%

Assignment Flow for Order-Constrained OCT Segmentation

2021

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At the present time optical coherence tomography (OCT) is among the most commonly used non-invasive imaging methods for the acquisition of large volumetric scans of human retinal tissues and vasculature. The substantial increase of accessible highly resolved 3D samples at the optic nerve head and the macula is directly linked to medical advancements in early detection of eye diseases. To resolve decisive information from extracted OCT volumes and to make it applicable for further diagnostic analysis, the exact measurement of retinal layer thicknesses serves as an essential task be done for each patient separately. However, manual examination of OCT scans is a demanding and time consuming task, which is typically made difficult by the presence of tissue-dependent speckle noise. Therefore, the elaboration of automated segmentation models has become an important task in the field of medical image processing. We propose a novel, purely data driven geometric approach to order-constrained 3D OCT retinal cell layer segmentation which takes as input data in any metric space and can be implemented using only simple, highly parallelizable operations. As opposed to many established retinal layer segmentation methods, we use only locally extracted features as input and do not employ any global shape prior. The physiological order of retinal cell layers and membranes is achieved through the introduction of a smoothed energy term. This is combined with additional regularization of local smoothness to yield highly accurate 3D segmentations. The approach thereby systematically avoid bias pertaining to global shape and is hence suited for the detection of anatomical changes of retinal tissue structure. To demonstrate its robustness, we compare two different choices of features on a data set of manually annotated 3D OCT volumes of healthy human retina. The quality of computed segmentations is compared to the state of the art in automatic retinal layer segmention as well as to manually annotated ground truth data in terms of mean absolute error and Dice similarity coefficient. Visualizations of segmented volumes are also provided.

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“…Adopting this viewpoint, we introduced a dynamical system -called assignent flow -for contextual data classification and image labelling on graphs [6]. We refer to [27] for a review of recent work including parameter estimation (learning) [18], adaption of data prototypes during assignment [34] and learning prototypes from low-rank data representations and self-assignment [37]. Convergence and stability of the assignment flow have been studied by [33].…”

Section: Introductionmentioning

confidence: 99%

Continuous-domain assignment flows

Savarino¹,

Schnörr²

2020

Eur. J. Appl. Math

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Assignment flows denote a class of dynamical models for contextual data labelling (classification) on graphs. We derive a novel parametrisation of assignment flows that reveals how the underlying information geometry induces two processes for assignment regularisation and for gradually enforcing unambiguous decisions, respectively, that seamlessly interact when solving for the flow. Our result enables to characterise the dominant part of the assignment flow as a Riemannian gradient flow with respect to the underlying information geometry. We consider a continuous-domain formulation of the corresponding potential and develop a novel algorithm in terms of solving a sequence of linear elliptic partial differential equations (PDEs) subject to a simple convex constraint. Our result provides a basis for addressing learning problems by controlling such PDEs in future work.

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Assignment Flows

Cited by 17 publications

References 44 publications

Assignment Flow for Order-Constrained OCT Segmentation

Assignment Flow for Order-Constrained OCT Segmentation

Assignment Flow for Order-Constrained OCT Segmentation

Continuous-domain assignment flows

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