Boundary Extraction in Images Using Hierarchical Clustering-based Segmentation

Hierarchical organization is one of the main characteristics of human segmentation. A human subject segments a natural image by identifying physical objects and marking their boundaries up to a certain level of detail [1]. Hierarchical clustering based segmentation (HCS) process mimics this capability of the human vision. The HCS process automatically generates a hierarchy of segmented images. The hierarchy represents the continuous merging of similar, spatially adjacent or disjoint, regions as the allowable threshold value of dissimilarity between regions, for merging, is gradually increased. HCS process is unsupervised and is completely data driven. This ensures that the segmentation process can be applied to any image, without any prior information about the image data and without any need for prior training of the segmentation process with the relevant image data. The implementation details of HCS process have been described elsewhere in the author's work [2]. The purpose of the current study is to demonstrate the performance of the HCS process in outlining boundaries in images and its possible application in processing medical images. [1] P. Arbelaez. Boundary Extraction in Natural Images Using Ultrametric Contour Maps. Proceedings 5th IEEE Workshop on Perceptual Organization in Computer Vision (POCV'06). June 2006. New York, USA. [2] A. N. Selvan. Highlighting Dissimilarity in Medical Images Using Hierarchical Clustering Based Segmentation (HCS). M. Phil. dissertation, Faculty of Arts Computing Engineering and Sciences Sheffield Hallam Univ., Sheffield, UK, 2007.</p

Quenching and generation of random states in a kicked Ising model

The kicked Ising model with both a pulsed transverse and a continuous longitudinal field is studied numerically. Starting from a large transverse field and a state that is nearly an eigenstate, the pulsed transverse field is quenched with a simultaneous enhancement of the longitudinal field. The generation of multipartite entanglement is observed along with a phenomenon akin to quantum resonance when the entanglement does not evolve for certain values of the pulse duration. Away from the resonance, the longitudinal field can drive the entanglement to near maximum values that is shown to agree well with those of random states. Further evidence is presented that the time evolved states obtained do have some statistical properties of such random states. For contrast the case when the fields have a steady value is also discussed.Comment: 7 pages, 7 figure

On the ℓ\ell-adic valuation of certain Jacobi sums

Fix distinct primes $\ell$ and $f$, a finite field $\mathbf{F}_{q}$ such that $q \equiv 1 \pmod{\ell f}$, and a character $\chi : \mathbf{F}_{q}^{\times} \to \mathbf{C}^{\times}$ of exact order $\ell f$. We present a new $\ell$-adic congruence for the Jacobi sum $J(\chi^{\ell}, \chi^{f})$. These Jacobi sums are Frobenius eigenvalues of the curve $y^{\ell} = x^{f} + 1$.Comment: 18 pages; improved notation, reorganized sections accordingly, clarified a small subtlety with ell=2 cas