Section: New Results

Reconstruction

Participants : Panagiotis Koutsourakis, Helene Langet, Loic Simon, Olivier Teboul, Gilles Fleury, Elisabeth Lahalle, Yves Trousset, Cyril Riddell, Nikos Paragios.

• Image-based Procedural Modeling of Urban environments: In [20] we develop a multiple hypotheses testing algorithm for image-based/grammar-driven building modeling. Shape grammars are used to express the variation of the observed architecture. Such a model is coupled with the observations through a maximum likelihood principle where the aim is to maximize the posterior segmentation probability in the image plane given the partition being determined from the grammar derivation. The unknown parameters of the process involve the grammar derivation tree and the associated parameters. Such a mixed continuous/discrete problem is solved through a hill climbing approach that involves joint perturbations in the derivation and parameter space. Promising results demonstrated the potentials of such a formulation for complex Parisian architectures. This idea was further extended in [40] where reinforcement learning was used as optimization principle. 2D Image-based grammar parsing was expressed as a Markov decision process where an agent ought to take actions in an environment so as to maximize some notion of cumulative reward. Performance in particular computational gain over [20] demonstrated the extreme potentials of such a formulation. In order to cope with multi-view geometry, the grammar was further derived to include 3D components and the optimization process was amended to deal with multiple views. An evolutionary computation process (based on consistent mutation and recombination of partial grammar trees) was proposed to fuse image and depth-based information. The use of the Pareto frontier between the two concurrent components of the objective function provides a principle way to determine the optimal solution of the designed objective function.

• Compressed Sensing Digital Subtraction Rotational Angiography: in [39] we develop an extension of iterative filtered backprojection method for reconstruction of three-dimensional vascular structures from two spins. Our contribution refers to an approach that improves the reconstruction quality of non-sparse volumes when there exists a sparse combination of these volumes. This is achieved through a joint reconstruction of the mask and contrast volumes via ${}^{\text{'}}{𝓁}^{\text{'}}-1$-minimization of sparse priors. These ideas were further explored to address three-dimensional reconstruction in interventional radiology in [30] through a regularized extension of the iterative filtered backprojection algorithm. To this end the conventional TV-norm was replaced from a new sparsity constraint that relies on the ${}^{\text{'}}{𝓁}^{\text{'}}-1$-minimization-norm and the positivity constraint. The use of such a constraint allows for removing most of the subsampling artifacts while preserving background structures.