An Inverse Method for Policy-Iteration Based Algorithms

We present an extension of two policy-iteration based algorithms on weighted graphs (viz., Markov Decision Problems and Max-Plus Algebras). This extension allows us to solve the following inverse problem: considering the weights of the graph to be unknown constants or parameters, we suppose that a reference instantiation of those weights is given, and we aim at computing a constraint on the parameters under which an optimal policy for the reference instantiation is still optimal. The original algorithm is thus guaranteed to behave well around the reference instantiation, which provides us with some criteria of robustness. We present an application of both methods to simple examples. A prototype implementation has been done

Incrementally Closing Octagons

The octagon abstract domain is a widely used numeric abstract domain expressing relational information between variables whilst being both computationally efficient and simple to implement. Each element of the domain is a system of constraints where each constraint takes the restricted form ±xi±xj≤c. A key family of operations for the octagon domain are closure algorithms, which check satisfiability and provide a normal form for octagonal constraint systems. We present new quadratic incremental algorithms for closure, strong closure and integer closure and proofs of their correctness. We highlight the benefits and measure the performance of these new algorithms

Cardiac motion estimation by joint alignment of tagged MRI sequences

Image registration has been proposed as an automatic method for recovering cardiac displacement fields from Tagged Magnetic Resonance Imaging (tMRI) sequences. Initially performed as a set of pairwise registrations, these techniques have evolved to the use of 3D+t deformation models, requiring metrics of joint image alignment (JA). However, only linear combinations of cost functions defined with respect to the first frame have been used. In this paper, we have applied k-Nearest Neighbors Graphs (kNNG) estimators of the -entropy (H ) to measure the joint similarity between frames, and to combine the information provided by different cardiac views in an unified metric. Experiments performed on six subjects showed a significantly higher accuracy (p < 0.05) with respect to a standard pairwise alignment (PA) approach in terms of mean positional error and variance with respect to manually placed landmarks. The developed method was used to study strains in patients with myocardial infarction, showing a consistency between strain, infarction location, and coronary occlusion. This paper also presents/nan interesting clinical application of graph-based metric estimators, showing their value for solving practical problems found in medical imaging