A Framework for Symmetric Part Detection in Cluttered Scenes

The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critical for their recognition. The medial axis community has long exploited the ubiquitous regularity of symmetry as a basis for the decomposition of a closed contour into medial parts. However, today's recognition systems are faced with cluttered scenes, and the assumption that a closed contour exists, i.e. that figure-ground segmentation has been solved, renders much of the medial axis community's work inapplicable. In this article, we review a computational framework, previously reported in Lee et al. (2013), Levinshtein et al. (2009, 2013), that bridges the representation power of the medial axis and the need to recover and group an object's parts in a cluttered scene. Our framework is rooted in the idea that a maximally inscribed disc, the building block of a medial axis, can be modeled as a compact superpixel in the image. We evaluate the method on images of cluttered scenes.Comment: 10 pages, 8 figure

Color structure for soft gluon resummation - a general recipe

A strategy for calculating the color structure needed for soft gluon resummation for processes with any number of colored partons is introduced using a N_c --> infinity inspired basis. In this basis a general formalism can be found at the same time as the calculations are simplified. The advantages are illustrated by recalculating the soft anomalous dimension matrix for the processes gg --> gg, q\qbar --> q \qbar g and q\qbar --> ggg.Comment: 16 page

Renormalization group flows of Hamiltonians using tensor networks

A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)], [S. Yang, Z.-C. Gu, and X.-G Wen, Phys. Rev. Lett. 118, 110504 (2017)]) we obtain approximate fixed point tensor networks at criticality. Our formalism however preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.Comment: accepted version for Phys. Rev. Lett, main text: 5 pages, 3 figures, appendices: 9 pages, 1 figur

Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography

This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement Hamiltonians from Projected Entangled Pair States (PEPS), and the relation between the Multi-scale Entanglement Renormalization Ansatz (MERA) and the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement in the emergence of several physical properties and objects through the TN language. Some recent results along these lines are also discussed.Comment: Invited Colloquium for EPJB, 31 pages, 13 figures; revised version, accepted for publicatio

Distributed graph-based state space generation

LTSMIN provides a framework in which state space generation can be distributed easily over many cores on a single compute node, as well as over multiple compute nodes. The tool works on the basis of a vector representation of the states; the individual cores are assigned the task of computing all successors of states that are sent to them. In this paper we show how this framework can be applied in the case where states are essentially graphs interpreted up to isomorphism, such as the ones we have been studying for GROOVE. This involves developing a suitable vector representation for a canonical form of those graphs. The canonical forms are computed using a third tool called BLISS. We combined the three tools to form a system for distributed state space generation based on graph grammars. We show that the time performance of the resulting system scales well (i.e., close to linear) with the number of cores. We also report surprising statistics on the memory\ud consumption, which imply that the vector representation used to store graphs in LTSMIN is more compact than the representation used in GROOVE