TY  - GEN
Y1  - 2020///
TI  - Inference and Model Parameter Learning for Image Labeling by Geometric Assignment
CY  - Heidelberg
AV  - public
A1  - Hühnerbein, Ruben
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/28294/
ID  - heidok28294
N2  - Image labeling is a fundamental problem in the area of low-level image analysis. In this work, we present novel approaches to maximum a posteriori (MAP) inference and model
parameter learning for image labeling, respectively. Both approaches are formulated in a smooth geometric setting, whose respective solution space is a simple Riemannian manifold. Optimization
consists of multiplicative updates that geometrically integrate the resulting Riemannian gradient flow.

Our novel approach to MAP inference is based on discrete graphical models. By utilizing local Wasserstein distances for coupling assignment measures across edges of the
underlying graph, we smoothly approximate a given discrete objective function and restrict it to the
assignment manifold. A corresponding update scheme combines geometric integration of the resulting gradient flow, and rounding to integral solutions that represent
valid labelings. This formulation constitutes an inner relaxation of the discrete labeling problem, i.e. throughout this process local marginalization constraints known from the established linear programming relaxation are satisfied.

Furthermore, we study the inverse problem of model parameter learning using the linear assignment flow and training data with ground truth. This is accomplished by a Riemannian gradient flow on the manifold of parameters that determine the regularization properties of the assignment flow. This smooth formulation enables us to tackle the model parameter learning problem from the perspective of parameter estimation of dynamical systems. By using symplectic partitioned Runge--Kutta methods for numerical integration, we show that deriving the sensitivity conditions of the parameter learning problem and its discretization commute. A favorable property of our approach is that learning is based on exact inference.
ER  -