membrane boundary extraction using circular multiple paths membrane proteins represent over 50 of known drug targets accordingly several widely used assays in the high content analysis area rely on quantitative measures of the translocation of proteins between intracellular organelles and the cell surface in order to increase the sensitivity of these assays one needs to measure the signal specifically along the membrane requiring a precise segmentation of this compartment manual tracing of membrane boundary is very time consuming and confronts us with issues of objectivity and reproducibility in this paper we present an approach based on a circular multiple paths technique on transformed images that enables us to segment the membrane compartment accurately and rapidly we have presented three approaches for image transformation the circular property of the multiple paths ensures that we are obtaining closed contours for the membrane boundary the position of the multiple paths provides the edges of the membrane boundary the effectiveness of our algorithm is illustrated using cells expressing epitope tagged membrane proteins

multiple paths extraction in images using a constrained expanded trellis single shortest path extraction algorithms have been used in a number of areas such as network flow and image analysis in image analysis shortest path techniques can be used for object boundary detection crack detection or stereo disparity estimation sometimes one needs to find multiple paths as opposed to a single path in a network or an image where the paths must satisfy certain constraints in this paper we propose a new algorithm to extract multiple paths simultaneously within an image using a constrained expanded trellis cet for feature extraction and object segmentation we also give a number of application examples for our multiple paths extraction algorithm

symmetric roots and admissible pairing using the discriminant modular form and the noether formula it is possible to write the admissible self intersection of the relative dualising sheaf of a semistable hyperelliptic curve over a number field or function field as a sum over all places of a certain adelic invariant we provide a simple geometric interpretation for this invariant based on the arithmetic of symmetric roots we propose the conjecture that the invariant coincides with the invariant introduced in a recent paper by s w zhang this conjecture is true in the genus 2 case and we obtain a new proof of the bogomolov conjecture for curves of genus 2 over number fields

lower bounds on the arithmetic self intersection number of the relative dualizing sheaf on arithmetic surfaces we give an explicitly computable lower bound for the arithmetic self intersection number of the dualizing sheaf on a large class of arithmetic surfaces if some technical conditions are satisfied then this lower bound is positive in particular these technical conditions are always satisfied for minimal arithmetic surfaces with simple multiplicities and at least one reducible fiber but we have also used our techniques to obtain lower bounds for some arithmetic surfaces with non reduced fibers

interactive segmentation of non star shaped contours by dynamic programming in this paper we present the rack algorithm for the detection of optimal non star shaped contours in images it is based on the combination of a user driven image transformation and dynamic programming the fundamental idea is to interactively specify and edit the general shape of the desired object by using a rack this rack is used to model the image as a directed acyclic weighted graph that contains a path corresponding to the expected contour in this graph the shortest path with respect to an adequate cost function can be calculated efficiently via dynamic programming the experimental results indicate the algorithm s ability of combining an acceptable amount of user interaction with generally good segmentation results

circular shortest paths by branch and bound shortest path algorithms are used for a large variety of optimisation problems in network and transportation analysis they are also used in image analysis for object segmentation disparity estimation path finding and crack detection sometimes the topology of the problem demands that the path be circular such circular path constraints occur in polar object segmentation disparity estimation for panoramic stereo images and in shortest paths around a cylinder in this paper we present a new efficient algorithm for circular shortest path determination on a u by v trellis in o u 1 6 v average time we impose a binary search tree on the set of path endpoints and use a best first branch and bound search technique to efficiently obtain the global minimum circular path the typical running time of our circular shortest path algorithm on a 256 times 256 image is in the order of 0 1 seconds on a 1ghz dell p3 workstation under the linux operating system applications to crack detection and object segmentation are presented

automatic finding of main roads in aerial images by using geometric stochastic models and estimation this paper presents an automated approach to finding main roads in aerial images the approach is to build geometric probabilistic models for road image generation we use gibbs distributions then given an image roads are found by map maximum a posteriori probability estimation the map estimation is handled by partitioning an image into windows realizing the estimation in each window through the use of dynamic programming and then starting with the windows containing high confidence estimates using dynamic programming again to obtain optimal global estimates of the roads present the approach is model based from the outset and is completely different than those appearing in the published literature it produces two boundaries for each road or four boundaries when a mid road barrier is present

analyticity of resonances and eigenvalues and spectral properties of the massless spin boson model abstract we extend the method of pizzo multiscale analysis for resonances introduced in 5 in order to infer analytic properties of resonances and eigenvalues and their eigenprojections as well as estimates for the localization of the spectrum of dilated hamiltonians and norm bounds for the corresponding resolvent operators in neighborhoods of resonances and eigenvalues we apply our method to the massless spin boson model assuming a slight infrared regularization we prove that the resonance and the ground state eigenvalue and their eigenprojections are analytic with respect to the dilation parameter and the coupling constant moreover we prove that the spectrum of the dilated spin boson hamiltonian in the neighborhood of the resonance and the ground state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground state eigenvalue respectively additionally we provide norm estimates for the resolvent of the dilated spin boson hamiltonian near the resonance and the ground state eigenvalue the topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past however to the best of our knowledge this is the first time that it is addressed from the perspective of pizzo multiscale analysis once the multiscale analysis is set up our method gives easy access to analyticity essentially it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic the type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime the latter will be demonstrated in a forthcoming publication the introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent and different from the method we apply to construct resonances

zhang s conjecture and the effective bogomolov conjecture over function fields we prove the effective bogomolov conjecture and so the bogomolov conjecture over a function field of characteristic 0 by proving zhang s conjecture about certain invariants of metrized graphs in the function field case these conjectures were previously known to be true only for curves of good reduction for curves of genus at most 4 and a few other special cases we also either verify or improve the previous results we relate the invariants involved in zhang s conjecture to the tau constant of metrized graphs then we use and extend our previous results on the tau constant by proving another conjecture of zhang we obtain a new proof of the slope inequality for faltings heights on moduli space of curves

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

circular shortest path in images abstract shortest path algorithms have been used in a number of applications such as crack detection road or linear feature extraction in images there are applications where the starting and ending positions of the shortest path need to be constrained in this paper we present several new algorithms for the extraction of a circular shortest path in an image such that the starting and ending positions coincide the new algorithms we developed include multiple search algorithm image patching algorithm multiple backtracking algorithm the combination of image patching and multiple back tracking algorithm and approximate algorithm the typical running time of our circular shortest path extraction algorithm on a 256 256 image is about 0 3 s on a rather slow 85 mhz sun sparc computer a variety of real images for crack detection in borehole data and object boundary extraction have been tested and good results have been obtained

heights and arakelov s intersection theory introduction this paper relates the neron tate height on jacobian varieties to an intersection theory on arithmetic surfaces constructed by s arakelov a1 here i extend and prove a statement of arakelov to the effect that his intersection pairing is a neron pairing a2i i use this to prove an analogue of the hodge index theorem for arithmetic surfaces a result due independently to g faltings the results of this paper have been extracted from my thesis written under the direction of michael artin it differs from the thesis in three ways firstly it employs the language of local height functions as defined by a neron and j tate and expounded by s lang li in the thesis i used neron s language of local intersection pairings n1 the second major difference is in the proof of theorem 1 3 in my thesis i proved this result by using work of raynaud and picard functors r 1 this method was suggested by m artin in this paper i provide a simpler proof observed by s lang and independently by b gross finally the development of arakalov s theory in the context of neron functions in section 2 is due to s lang who has kindly given me leave to publish it this exposition of my results is due in considerable part to s lang it is essentially an edited transcript of a series of conversations between us which he provided it is my great pleasure to thank both him and michael artin for their help and encouragement 1 the neron pairing neron ne has given a pairing between divisors and points on abelian varieties and also on arbitrary varieties under suitable conditions we shall give a complement to the neron theory on curves let c be a curve by which we mean a complete regular curve geometrically irreducible over a field k with an absolute value v let