Surface critical behavior of random systems at the ordinary transition

We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation, as well as in $d=4-\epsilon$ dimensions. At $d=4-\epsilon$ we extend, up to the next-to-leading order, the previous first-order results of the $\sqrt{\epsilon}$ expansion by Ohno and Okabe [Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface exponents are computed using Pade approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.Comment: 11 pages, 11 figure

Hierarchical Discriminative Framework for Detecting Tubular Structures in 3D Images

Abstract. Detecting tubular structures such as airways or vessels in medical images is important for diagnosis and surgical planning. Many state-of-the-art approaches address this problem by starting from the root and progressing towards thinnest tubular structures usually guided by image filtering techniques. These approaches need to be tailored for each application and can fail in noisy or lowcontrast regions. In this work, we address these challenges by a two-layer model which consists of a low-level likelihood measure and a high-level measure verifying tubular branches. The algorithm starts by computing a robust measure of tubular presence using a discriminative classifier at multiple image scales. The measure is then used in an efficient multi-scale shortest path algorithm to generate candidate centerline branches and corresponding radii measurements. Finally, the branches are verified by a learning-based indicator function that discards false candidate branches. The experiments on detecting airways in rotational X-ray volumes show that the technique is robust to noise and correctly finds airways even in the presence of imaging artifacts.