extracting natural scales using fourier descriptors since contours often contain many different sized structures they need to be described at multiple scales rather than describe a contour at all scales it is more efficient to identify the most significant scales that best represent the structures present these natural scales are determined by examining the fourier descriptors of the contour and searching for significant bands these correspond to bandwidths required to extract features at qualitatively significant resolution examples are given of using the determined scales in both low pass and high pass filters to eliminate fine and coarse detail

on the power of logic resynthesis a linear arrangement problem called the minmax mincut problem emerging from circuit design is investigated its input is a series parallel directed hypergraph spdh and the output is a linear arrangement and a layout the primary objective is to minimize the longest path and the secondary objective is to minimize the cutwidth it is shown that cutwidth d subject to longest path minimization is affected by two terms pattern number k and balancing number m also k and m are both lower bounds on the cutwidth an algorithm running in linear time produces layouts with cutwidths d leq 2 k m there exist examples with k omega n where n is the number of vertices however m is always o log n we show that every spdh after local logic resynthesis specifically after reordering the serial paths can be linearly placed with cutwidth d o log n simultaneously its dual spdh can be linearly placed with the same vertex order and with cutwidth d o log n therefore after local resynthesis the area can be reduced by a factor of n log n application to gate matrix layout style is demonstrated

a syntactic approach to scale space based corner description planar curves are described by information about corners integrated over various levels of resolution the detection of corners takes place on a digital representation to compensate for ambiguities arising from sampling problems due to the discreteness results about the local behavior of curvature extrema in continuous scale space are employed

nonlinear discrete sturm liouville problems at resonance abstract in this paper we study nonlinear bounded value problems of the form p t 1 y t 1 q t y t k y t f t y t h t a 11 y a a 12 y a 0 a 21 y b 1 a 22 y b 1 0 where k is an eigenvalue of the associated linear problem f is subject to the sublinear growth condition f t s a s b t a 1 b 1 s r for some 0 1 and a b 0 we prove the existence and multiplicity of solutions by using the connectivity properties of solution sets of parameterized families of compact vector fields

existence and multiplicity results for a class of nonlinear elliptic boundary value problems at resonance are positive and form an increasing sequence i 0 in sz which by the maximum principle satisfies an 0 on 30 where

existence and uniqueness results for a third order implicit differential equation the purpose of this paper is to give sufficient conditions for the existence and uniqueness of solutions to the boundary value problem of a third order implicit differential equation as follows f t u t u t u t 0 email protected email protected 1u 0 u 0 u 1 0 the lower and upper solutions method maximum principle together with an iterative technique are employed an example illustrates the application of results obtained

solvability of multipoint boundary value problems at resonance for higher order ordinary differential equations let f 0 1 x r n r be a continuous function and e l 1 0 1 let b j 1 j m 2 r 0 h 1 h 2 h m 2 1 be given this paper is concerned with the existence of solutions for the following n t h order multipoint boundary value problems at resonance case x n t f t x t x t x n 1 t e t email protected 0 1 x 0 x 0 x n 2 0 0 x 1 email protected email protected jx h j and x n t f t x t x t x n 1 t e t email protected 0 1 x 0 x 0 x n 2 0 0 x 1 email protected email protected jx h j some existence results are obtained by using the coincidence degree theory of mawhin

acord an adaptive corner detector for planar curves abstract in contrast to the conventional method of smoothing a curve at multiple scales and integrating the information at various scales a technique for smoothing a curve adaptively based on the roughness present in the curve is suggested the procedure does not require smoothing at all levels of detail and it does not require construction of complete scale space map and representation of the map by tree the procedure has been applied on a number of digital curves and the results have been compared with those of the recent work

scale based detection of corners of planar curves a technique for detecting and localizing corners of planar curves is proposed the technique is based on gaussian scale space which consists of the maxima of absolute curvature of the boundary function presented at all scales the scale space of isolated simple and double corners is first analyzed to investigate the behavior of scale space due to smoothing and interactions between two adjacent corners the analysis shows that the resulting scale space contains line patterns that either persist terminate or merge with a neighboring line next the scale space is transformed into a tree that provides simple but concise representation of corners at multiple scales finally a multiple scale corner detection scheme is developed using a coarse to fine tree parsing technique the parsing scheme is based on a stability criterion that states that the presence of a corner must concur with a curvature maximum observable at a majority of scales experiments were performed to show that the scale space corner detector is reliable for objects with multiple size features and noisy boundaries and compares favorably with other corner detectors tested

existence of solutions to functional boundary value problem of second order nonlinear differential equation abstract in this paper a functional boundary value problem is studied based on mawhin s coincidence degree theory some existence theorems are obtained in the case of non resonance and the cases of dim ker l 1 and dim ker l 2 at resonance the results not only generalize and improve some known results of multi point and integral boundary value problems but also give some existence theorems for boundary value problems that all their boundary value conditions are relied on both x and x

representing curves at their natural scales abstract the shapes of curves generally contain several structures at different scales an expressive curve representation should explicitly describe each structure at its appropriate scale this greatly simplifies any reasoning processes e g matching applied to the curve rather than exhaustively represent the curve over a full range of scales just the most significant ones should be retained for a compact and useful representation a technique is presented that identifies the significant or natural scales in a curve

multiscale corner detection by using wavelet transform a multiscale corner detection algorithm based on the wavelet transform of contour orientation is proposed it can utilize both the information of the local extrema and modulus of transform results to detect corners and arcs effectively the ramp width of contour orientation profile which can be computed using the transformed modulus of two scales reveals the difference between corner and arc and is utilized in the determination of corner points the experimental results have shown that the detector is more effective than both the single and multiple scale detectors they also demonstrate that the detector is insensitive to boundary noise in addition the proposed method is more efficient than the other multiscale corner detector because it operates on fewer number of scales which can be implemented by a fast transform algorithm

scale preserving smoothing of polygons a smoother version of a polygon is defined as a polygon which approximates according to a given criterion and which simultaneously has no more edges than itself in this paper a scale preserving smoothing algorithm is presented the input to the algorithm is a polygon and the output is its smoothed version which contains all the scale information that contains is called the linear minimum perimeter polygon lmpp of within a tolerance of using the quantity the degree of with approximates can be controlled from the lmpp a representation for a polygon approximating can be procured which is invariant to scale and translation changes examples of smoothing maps and characters have been presented

on the structure of the solution set of nonlinear equations 1 let e f be banach spaces uc e be open and bounded and f ir f be a continuous map such that f x f 0 for every x e au we say that f is 0 epi zero epi if for every continuous and compact map h ir f such that h x 0 for every x e au the nonlinear operator equation f x h x 1 1 has a solution x e u the notion of 0 epi maps was introduced in 6 where the main properties of 0 epi maps were also established and they were used to obtain existence results for nonlinear operator equations of the form

a polynomial algorithm for the min cut linear arrangement of trees an algorithm is presented that finds a min cut linear arrangement of a tree in o n log n time an extension of the algorithm determines the number of pebbles needed to play the black and white pebble game on a tree

corner detection and interpretation on planar curves using fuzzy reasoning the problem of corner detection on planar curves is examined based on human perception of local graphic features first a set of fuzzy patterns of contour points are established then corner detection is characterized as a fuzzy classification problem that contains three stages evaluation classification and location compared with existing methods the proposed approach is superior in that it explains the curve instead of simple labeling and it performs based on human perception experimental results on shapes of various complexities are presented the performance with respect to noise is also addressed

extraction of trend lines and extrema from multiscale curves abstract multiscale planar curves are curves conveying information at several levels of detail to extract polygonal approximations of such curves at different resolutions we propose a parallel method based on connecting locally computed centroids the implementation makes use of a new pyramidal data structure the chain pyramid coarser and coarser approximations are obtained through a hierarchy of increasingly coarse tessellations significant extrema of the curves are localized at the highest resolution by segmenting at a natural scale and employing the structure of the chain pyramid for down projection

techniques for segmenting image curves into meaningful descriptions abstract this paper describes an approach to the detection of straight lines and circular arcs in images the algorithm uses a measure based on significance proposed by d g lowe three dimensional object recognition from single two dimensional images artificial intelligence 31 355 395 1987 edge points are processed to produce a description combining lines and arcs no thresholds are required for either 1 fitting the best lines and arcs to the data or 2 choosing between the best line and arc fits as the most appropriate description results are presented demonstrating the performance on complex images

positive solutions for semipositone k n k conjugate boundary value problems for 1 k n 1 positive solutions are obtained for the boundary value problem 1 n k y n fx y x 0 1y i 0 0 0 i k 1 y j 1 0 0 j n k 1 where f x y m and m is a positive constant we show the existence of positive solutions by using a fixed point theorem in cones

solvability of a second order multi point boundary value problem at resonance abstract based on the coincidence degree theory of mawhin we get a general existence result for the following second order multi point boundary value problem at resonance x t f t x t x t e t t 0 1 x 0 i 1 m i x i x 1 j 1 n j x j where f 0 1 r 2 r is a caratheodory function e l 1 0 1 0 1 2 m 1 i r i 1 2 m m 2 and 0 1 n 1 j r j 1 n n 1 in this paper both of the boundary value conditions are responsible for resonance

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area