56 citations · 99 across the 19 of their papers we have counts for
21 papers
Generative Modeling of Discrete Data Using Geometric Latent Subspaces
Daniel Gonzalez-Alvarado, Jonas Cassel, Stefania Petra +1
We propose a geometric latent-subspace framework for generative modeling of discrete data. Specifically, we introduce latent subspaces in the exponential parameter space of product…
Riemannian Patch Assignment Gradient Flows
Daniel Gonzalez-Alvarado, Fabio Schlindwein, Jonas Cassel +3
This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of…
Sigma Flows for Image and Data Labeling and Learning Structured Prediction
Jonas Cassel, Bastian Boll, Stefania Petra +2
This paper introduces the sigma flow model for the prediction of structured labelings of data observed on Riemannian manifolds, including Euclidean image domains as special case. T…
Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data
Bastian Boll, Daniel Gonzalez-Alvarado, Stefania Petra +1
We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure t…
A Geometric Embedding Approach to Multiple Games and Multiple Populations
Bastian Boll, Jonas Cassel, Peter Albers +2
This paper studies a meta-simplex concept and geometric embedding framework for multi-population replicator dynamics. Central results are two embedding theorems which constitute a…
Multilevel Geometric Optimization for Regularised Constrained Linear Inverse Problems
Sebastian Müller, Stefania Petra, Matthias Zisler
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models…
Self-Certifying Classification by Linearized Deep Assignment
Bastian Boll, Alexander Zeilmann, Stefania Petra +1
We propose a novel class of deep stochastic predictors for classifying metric data on graphs within the PAC-Bayes risk certification paradigm. Classifiers are realized as linearly…
Learning Linearized Assignment Flows for Image Labeling
Alexander Zeilmann, Stefania Petra, Christoph Schnörr
We introduce a novel algorithm for estimating optimal parameters of linearized assignment flows for image labeling. An exact formula is derived for the parameter gradient of any lo…
Multi-Channel Potts-Based Reconstruction for Multi-Spectral Computed Tomography
Lukas Kiefer, Stefania Petra, Martin Storath +1
We consider reconstructing multi-channel images from measurements performed by photon-counting and energy-discriminating detectors in the setting of multi-spectral X-ray computed t…
Superiorization vs. Accelerated Convex Optimization: The Superiorized/Regularized Least-Squares Case
Yair Censor, Stefania Petra, Christoph Schnörr
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermin…
Self-Assignment Flows for Unsupervised Data Labeling on Graphs
Matthias Zisler, Artjom Zern, Stefania Petra +1
This paper extends the recently introduced assignment flow approach for supervised image labeling to unsupervised scenarios where no labels are given. The resulting self-assignment…
Learning Adaptive Regularization for Image Labeling Using Geometric Assignment
Ruben Hühnerbein, Fabrizio Savarino, Stefania Petra +1
We study the inverse problem of model parameter learning for pixelwise image labeling, using the linear assignment flow and training data with ground truth. This is accomplished by…
Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment
Artjom Zern, Matthias Zisler, Stefania Petra +1
This paper introduces the unsupervised assignment flow that couples the assignment flow for supervised image labeling with Riemannian gradient flows for label evolution on feature…
Performance Bounds For Co-/Sparse Box Constrained Signal Recovery
Jan Kuske, Stefania Petra
The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is describe…
Geometric Numerical Integration of the Assignment Flow
Alexander Zeilmann, Fabrizio Savarino, Stefania Petra +1
The assignment flow is a smooth dynamical system that evolves on an elementary statistical manifold and performs contextual data labeling on a graph. We derive and introduce the li…
A Novel Convex Relaxation for Non-Binary Discrete Tomography
Jan Kuske, Paul Swoboda, Stefania Petra
We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few…
Image Labeling by Assignment
Freddie Åström, Stefania Petra, Bernhard Schmitzer +1
We introduce a novel geometric approach to the image labeling problem. Abstracting from specific labeling applications, a general objective function is defined on a manifold of sto…
Single Projection Kaczmarz Extended Algorithms
Stefania Petra, Constantin Popa
To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the erro…
Phase Transitions and Cosparse Tomographic Recovery of Compound Solid Bodies from Few Projections
Andreea Deniţiu, Stefania Petra, Claudius Schnörr +1
We study unique recovery of cosparse signals from limited-angle tomographic measurements of two- and three-dimensional domains. Admissible signals belong to the union of subspaces…
Critical Parameter Values and Reconstruction Properties of Discrete Tomography: Application to Experimental Fluid Dynamics
Stefania Petra, Christoph Schnörr, Andreas Schröder
We analyze representative ill-posed scenarios of tomographic PIV with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interes…
Average Case Recovery Analysis of Tomographic Compressive Sensing
Stefania Petra, Christoph Schnörr
The reconstruction of three-dimensional sparse volume functions from few tomographic projections constitutes a challenging problem in image reconstruction and turns out to be a par…