Assessing knee OA severity with CNN attention-based end-to-end architectures

This work proposes a novel end-to-end convolutional neural network (CNN) architecture to automatically quantify the severity of knee osteoarthritis (OA) using X-Ray images, which incorporates trainable attention modules acting as unsupervised fine-grained detectors of the region of interest (ROI). The proposed attention modules can be applied at different levels and scales across any CNN pipeline helping the network to learn relevant attention patterns over the most informative parts of the image at different resolutions. We test the proposed attention mechanism on existing state-of-the-art CNN architectures as our base models, achieving promising results on the benchmark knee OA datasets from the osteoarthritis initiative (OAI) and multicenter osteoarthritis study (MOST).Postprint (published version

Assessing knee OA severity with CNN attention-based end-to-end architectures

This work proposes a novel end-to-end convolutional neural network (CNN) architecture to automatically quantify the severity of knee osteoarthritis (OA) using X-Ray images, which incorporates trainable attention modules acting as unsupervised fine-grained detectors of the region of interest (ROI). The proposed attention modules can be applied at different levels and scales across any CNN pipeline helping the network to learn relevant attention patterns over the most informative parts of the image at different resolutions. We test the proposed attention mechanism on existing state-of-the-art CNN architectures as our base models, achieving promising results on the benchmark knee OA datasets from the osteoarthritis initiative (OAI) and multicenter osteoarthritis study (MOST). All code from our experiments will be publicly available on the github repository: https://github.com/marc-gorriz/KneeOA-CNNAttentio

A recombination algorithm for the decomposition of multivariate rational functions

International audienceIn this paper we show how we can compute in a deterministic way the decomposition of a multivariate rational function with a recombination strategy. The key point of our recombination strategy is the used of Darboux polynomials. We study the complexity of this strategy and we show that this method improves the previous ones. In appendix, we explain how the strategy proposed recently by J. Berthomieu and G. Lecerf for the sparse factorization can be used in the decomposition setting. Then we deduce a decomposition algorithm in the sparse bivariate case and we give its complexit

Factorization theory: From commutative to noncommutative settings

We study the non-uniqueness of factorizations of non zero-divisors into atoms (irreducibles) in noncommutative rings. To do so, we extend concepts from the commutative theory of non-unique factorizations to a noncommutative setting. Several notions of factorizations as well as distances between them are introduced. In addition, arithmetical invariants characterizing the non-uniqueness of factorizations such as the catenary degree, the $\omega$-invariant, and the tame degree, are extended from commutative to noncommutative settings. We introduce the concept of a cancellative semigroup being permutably factorial, and characterize this property by means of corresponding catenary and tame degrees. Also, we give necessary and sufficient conditions for there to be a weak transfer homomorphism from a cancellative semigroup to its reduced abelianization. Applying the abstract machinery we develop, we determine various catenary degrees for classical maximal orders in central simple algebras over global fields by using a natural transfer homomorphism to a monoid of zero-sum sequences over a ray class group. We also determine catenary degrees and the permutable tame degree for the semigroup of non zero-divisors of the ring of $n \times n$ upper triangular matrices over a commutative domain using a weak transfer homomorphism to a commutative semigroup.Comment: 45 page

Using monodromy to recover symmetries of polynomial systems

Galois/monodromy groups attached to parametric systems of polynomial equations provide a method for detecting the existence of symmetries in solution sets. Beyond the question of existence, one would like to compute formulas for these symmetries, towards the eventual goal of solving the systems more efficiently. We describe and implement one possible approach to this task using numerical homotopy continuation and multivariate rational function interpolation. We describe additional methods that detect and exploit a priori unknown quasi-homogeneous structure in symmetries. These methods extend the range of interpolation to larger examples, including applications with nonlinear symmetries drawn from vision and robotics.Comment: Extended journal version of conference paper published at ISSAC 202