on critical point detection of digital shapes in this paper we present a nonlinear algorithm for critical point detection cpd of 2d digital shapes the algorithm eliminates the problems arising from curvature approximation and gaussian filtering in the existing algorithms based on the definition of critical level we establish a set of criteria for the design of an effective cpd algorithm for the first time by quantifying the critical level to the modified area confined by three consecutive pseudocritical points a simple but very effective algorithm is developed the comparison of our experimental results with those of many other cpd algorithms shows that the proposed algorithm is superior in that it provides a sequence of figures at every detail level and each has a smaller integral error than the others with the same number of critical points the experimental results on shapes with various complexities also show the algorithm is reliable and robust with regard to noise

a shape representation with elastic quadratic polynomials preservation of high curvature points under noisy conditions we present a new shape representation technique for a planar shape using overlapping quadratic splines the technique refines the shape by iteratively updating each spline to reduce the cost associated with c 1 discontinuity it consists of a series of affine commutative linear operators producing a smooth bandpass frequency response the primary purpose of the technique is to remove minute high curvature points while preserving salient ones we compare the performance of the technique against those that are based on either linear splines cubic splines or wavelets we consider three criteria sensitivity of detecting salient high curvature points hausdorff distance between the representation and the original shape and computation time the results show that the proposed technique is highly effective in preserving salient high curvature points with a relatively small hausdorff distance and a computational cost

frequency domain analysis and synthesis of image pyramid generating kernels construction of image pyramids is described as a two di mensional decimation process frequently employed generating kernels are compared to the optimal kernel that assures minimal information loss after the resolution reduction i e the one corresponding to an ideal low pass filter physically realizable optimal generating kernels are presented the amount of computation required for generation of the image pyramid can be reduced significantly by employing half band filters as components of the optimal kernel image pyramids generated by the optimal kernel show a better command of details than the ones generated by a simple 4 4 averaging or a computationally equivalent kernel

scaling theorems for zero crossings we characterize some properties of the zero crossings of the laplacian of signals in particular images filtered with linear filters as a function of the scale of the filter extending recent work by witkin 16 we prove that in any dimension the only filter that does not create generic zero crossings as the scale increases is the gaussian this result can be generalized to apply to level crossings of any linear differential operator it applies in particular to ridges and ravines in the image intensity in the case of the second derivative along the gradient there is no filter that avoids creation of zero crossings unless the filtering is performed after the derivative is applied

on automatic threshold selection for polygonal approximations of digital curves polygonal approximation is a very common representation of digital curves a polygonal approximation depends on a parameter e which is the error value in this paper we present a method for an automatic selection of the error value e let e be a polygonal approximation of the original curve with an error value e we define a set of function ns e s s s such that for a given value of s ns e is the number of edges that contain at least s vertices in e the time complexity for computing the set of functions ns e s ss s is almost linear in n the number of vertices in in this paper we analyse the ns graph and show that for adequate values of s a wide plateau is expected to appear at the top of the graph this plateau corresponds to a stable state in the multi scale representation of e we show that the functions ns s s are a statistical representation of some kind of scale space image

optimized polygonal approximation by dominant point deletion an algorithm for polygonal approximation based on dominant point dp deletion is presented in this paper the algorithm selects an initial set of dps and starts eliminating them one by one depending upon the error associated with each dp the associated error value is based on global measure a local optimization of few neighboring points is performed after each deletion although the algorithm does not guarantee an optimal solution the combination of local and global optimization is expected to produce optimal results the algorithm is extensively tested on various shapes with varying number of dps and error threshold in general optimal results were observed for about 96 of the times a good comparative study is also presented in this paper

boundary simplification using a multiscale dominant point detection algorithm abstract in this paper we intend to characterize boundaries using the scale space theory the aim we try to achieve is the description of a boundary in relation to a subset of points dominant points that are obtained from a new multiscale representation of the boundary dominant points are characterized by a high curvature value in the original or smoothed boundary as a result the boundary is represented using those points as well as an appropriate interpolation method the linear one in the simplest case among them as the basic tool of our work we will introduce a new multiscale dominant point detection algorithm that detects the points at their natural scales through a reliability condition with respect to the original curve because we want to apply the algorithms on complex enough boundaries we use cartographic boundaries in which several structures can be obtained at different scales to evaluate the results

a robust method for scale independent detection of curvature based criticalities and intersections in line drawings a novel two phase iterative method is proposed to identify curvature based criticalities and intersections in line drawings the method is based on evaluating a field obtained from the image via diffusion using adaptively changing ellipse shaped analysis windows the deviation of the average field strength values within the analysis windows from that of an external reference field is used as a metric to evaluate the criticality of a region the external reference field is computed from an image of a straight line the experimental results depict that the method is effective in detecting curvature based criticalities and intersections even for noisy and disconnected drawings as well as drawings drawn with a variety of brush characteristics such as glass ocean ripple scatter stamp strokes effects our method can be employed as a part of a design grammar interpreter highlightsthe method detects curvature based criticalities and intersections efficiently the method is effective for the noisy and disconnected line drawings the method is effective for line drawings with a variety of brush characteristics the method is utilized to represent shapes in a design grammar interpreter features in varying scales can be detected in digital drawings

wavelet based approach to character skeleton character skeleton plays a significant role in character recognition the strokes of a character may consist of two regions i e singular and regular regions the intersections and junctions of the strokes belong to singular region while the straight and smooth parts of the strokes are categorized to regular region therefore a skeletonization method requires two different processes to treat the skeletons in theses two different regions all traditional skeletonization algorithms are based on the symmetry analysis technique the major problems of these methods are as follows 1 the computation of the primary skeleton in the regular region is indirect so that its implementation is sophisticated and costly 2 the extracted skeleton cannot be exactly located on the central line of the stroke 3 the captured skeleton in the singular region may be distorted by artifacts and branches to overcome these problems a novel scheme of extracting the skeleton of character based on wavelet transform is presented in this paper this scheme consists of two main steps namely a extraction of primary skeleton in the regular region and b amendment processing of the primary skeletons and connection of them in the singular region a direct technique is used in the first step where a new wavelet based symmetry analysis is developed for finding the central line of the stroke directly a novel method called smooth interpolation is designed in the second step where a smooth operation is applied to the primary skeleton and thereafter the interpolation compensation technique is proposed to link the primary skeleton so that the skeleton in the singular region can be produced experiments are conducted and positive results are achieved which show that the proposed skeletonization scheme is applicable to not only binary image but also gray level image and the skeleton is robust against noise and affine transform

exact travelling wave solutions for the generalized nonlinear schrodinger gnls equation with a source by extended tanh coth sine cosine and exp function methods the capability of extended tanh coth sine cosine and exp function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed in this study the generalized nonlinear schrodinger gnls equation is solved by three different methods to obtain the single soliton solutions for the equation the extended tanh coth and sine cosine methods are used furthermore for this nonlinear evolution equation the exp function method is applied to derive various travelling wave solution results show that while the first two procedures easily provide a concise solution the exp function method provides a powerful mathematical means for solving nonlinear evolution equations in mathematical physics

nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations we propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the ablowitz kaup newell segur akns and the kaup newell classes based on the simple idea of dimensional analysis and detecting the building blocks of the lax pair along with the well known equations we discover a novel integrable hierarchy of higher order nonholonomic deformations for the akns family e g the korteweg de vries kdv the modified kdv the nonlinear schrodinger and the sine gordon equation showing thus a twofold universality of the recently found deformation for the kdv equation a karsu et al j math phys 49 073516 2008

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

performance comparisons of contour based corner detectors corner detectors have many applications in computer vision and image identification and retrieval contour based corner detectors directly or indirectly estimate a significance measure e g curvature on the points of a planar curve and select the curvature extrema points as corners while an extensive number of contour based corner detectors have been proposed over the last four decades there is no comparative study of recently proposed detectors this paper is an attempt to fill this gap the general framework of contour based corner detection is presented and two major issues curve smoothing and curvature estimation which have major impacts on the corner detection performance are discussed a number of promising detectors are compared using both automatic and manual evaluation systems on two large datasets it is observed that while the detectors using indirect curvature estimation techniques are more robust the detectors using direct curvature estimation techniques are faster

an envelope solitary wave solution for a generalized nonlinear schrodinger equation we derive an envelope solitary wave solution for the following generalized nonlinear schrodinger equation ut ia2uxx a3uxxx ib mod u mod 2u b1 mod u mod 2u x by gauge transformation

corner detection and classification using anisotropic directional derivative representations this paper proposes a corner detector and classifier using anisotropic directional derivative andd representations the andd representation at a pixel is a function of the oriented angle and characterizes the local directional grayscale variation around the pixel the proposed corner detector fuses the ideas of the contour and intensity based detection it consists of three cascaded blocks first the edge map of an image is obtained by the canny detector and from which contours are extracted and patched next the andd representation at each pixel on contours is calculated and normalized by its maximal magnitude the area surrounded by the normalized andd representation forms a new corner measure finally the nonmaximum suppression and thresholding are operated on each contour to find corners in terms of the corner measure moreover a corner classifier based on the peak number of the andd representation is given experiments are made to evaluate the proposed detector and classifier the proposed detector is competitive with the two recent state of the art corner detectors the he yung detector and cpda detector in detection capability and attains higher repeatability under affine transforms the proposed classifier can discriminate effectively simple corners y type corners and higher order corners

envelope exact solutions for the generalized nonlinear schrodinger equation with a source in this letter the generalized nonlinear schrodinger gnls equation phase locked a source ei t is investigated firstly we reduce this equation to a second order non homogeneous nonlinear ordinary differential equation via a plane wave transformation and some constraint conditions then we use some fractional transformations to study exact solutions in obtaining the gnls equation as a consequence many types of exact solutions are deduced such as envelope rational solutions envelope periodic wave solutions envelope solitary wave solutions and envelope doubly periodic solutions similarly the corresponding exact solutions can also be obtained for the hirota type gnls equation with a source and their combined equation

repeatedly smooting discrete scale space evolution and dominant point detection in this paper the fourier analysis is used to derive the properties of an evolving curve an arbitrary kernel repeatedly smoothing akrs evolution of a curve is then introduced it is shown that when the repeated number is large the akrs evolution of a curve is an approximately discrete implementation of the scale based evolution of this curve in the euclidean space as a special case an exponential repeatedly smoothing is proposed to implement the scale based evolution it is shown that in addition to its simple implementation and its desired approximation to a gaussian kernel an exponential function is a function that when it is selected as a repeatedly smoothing kernel the motion both magnitude and direction of a point on a curve from the i 1 th to ith instant is equal to the curvature of the ith smoothed curve at this point finally a perimeter controlled evolution method is proposed to extract dominant points it is shown experimentally that the proposed method is robust to noise object rotation and object changes in sizes

the modified kdv equation with variable coefficients exact uni bi variable travelling wave like solutions in this paper the modified korteweg de vries mkdv equation with variable coefficients vc mkdv equation is investigated via two kinds of approaches and symbolic computation on the one hand we firstly reduce the vc mkdv equation to a second order nonlinear nonhomogeneous ode using travelling wave like similarity transformation and then we obtain its many types of exact fractional solutions with one travelling wave like variable by applying some fractional transformations to the obtained nonlinear ode on the other hand we reduce the vc mkdv equation to two nonlinear pdes with variable coefficients using the anti tangent and anti hypertangent function transformations respectively and then we given its many types of exact solutions with two different travelling wave like variables by studying the obtained nonlinear pde with variable coefficients c 2008 elsevier inc all rights reserved

on exact solitary wave solutions of the nonlinear schrodinger equation with a source we use a fractional transformation to connect the travelling wave solutions of the nonlinear schrodinger equation nlse phase locked with a source to the elliptic equations satisfying f af f3 0 the solutions are necessarily of rational form containing both trigonometric and hyperbolic types as special cases bright and dark solitons as well as singular solitons are obtained in a suitable range of parameter values

singularity theory and phantom edges in scale space the process of detecting edges in a one dimensional signal by finding the zeros of the second derivative of the signal can be interpreted as the process of detecting the critical points of a general class of contrast functions that are applied to the signal it is shown that the second derivative of the contrast function at the critical point is related to the classification of the associated edge as being phantom or authentic the contrast of authentic edges decreases with filter scale while the contrast of phantom edges are shown to increase with scale as the filter scale increases an authentic edge must either turn into a phantom edge or join with a phantom edge and vanish the points in the scale space at which these events occur are seen to be singular points of the contrast function using ideas from singularity or catastrophy theory the scale map contours near these singular points are found to be either vertical or parabolic

fitting digital curve using circular arcs abstract a smoothing procedure is proposed where the gaussian filter is used with an adaptive mechanism to suppress the noise effect and quantization error of a digital curve those points of the smoothed curve where curvature changes abruptly are detected as breakpoints circular arcs are suitably designed between breakpoints to fit the input curve experimental results indicate that our curve fitting method provides good approximations of the input curves

matching of partially occluded planar curves abstract an algorithm for curves partial matching up to a similarity transformation is presented the matching is based on the total curvature graph which is the direction of the first derivative of the curve no higher derivatives are required the algorithm uses dynamic programming it is not dependent on reference or feature points the base step consists of a comparison of the total curvatures of neighborhoods the neighborhoods are dynamically chosen according to local characteristics of the curve in the recursive step ratios of lengths of matched curve segments are compared in order to extend the matches the matching is not sensitive to local deviations of the curves the algorithm is fast and simple its worst case time complexity is o mn where m and n are the number of points in the two digital curves experimental results are presented

bounds on distances between eigenvalues explicit computable lower and upper bounds on the distances between a given real eigenvalue of a real square matrix and the remaining not necessarily real eigenvalues of the matrix are developed

an improved generalized f expansion method and its applications an improved generalized f expansion method is proposed to seek exact solutions of nonlinear evolution equations with the aid of symbolic computation we choose the generalized nonlinear schrodinger equation with a source to illustrate the validity and advantages of the proposed method many new and more general non travelling wave solutions are obtained including single and combined non degenerate jacobi elliptic function solutions solitons like solutions trigonometric function solutions and rational solutions the method is straightforward and concise and it can also be applied to other nonlinear evolution equations in physics

on the detection of dominant points on digital curves a parallel algorithm is presented for detecting dominant points on a digital closed curve the procedure requires no input parameter and remains reliable even when features of multiple sizes are present on the digital curve the procedure first determines the region of support for each point based on its local properties then computes measures of relative significance e g curvature of each point and finally detects dominant points by a process of nonmaximum suppression this procedure leads to the observation that the performance of dominant points detection depends not only on the accuracy of the measure of significance but also on the precise determination of the region of support this solves the fundamental problem of scale factor selection encountered in various dominant point detection algorithms the inherent nature of scale space filtering in the procedure is addressed and the performance of the procedure is compared to those of several other dominant point detection algorithms using a number of examples

a unified curvature definition for regular polygonal and digital planar curves in this paper we propose a new definition of curvature called visual curvature it is based on statistics of the extreme points of the height functions computed over all directions by gradually ignoring relatively small heights a multi scale curvature is obtained the theoretical properties and the experiments presented demonstrate that multi scale visual curvature is stable even in the presence of significant noise to our best knowledge the proposed definition of visual curvature is the first ever that applies to regular curves as defined in differential geometry as well as to turn angles of polygonal curves moreover it yields stable curvature estimates of curves in digital images even under sever distortions we also show a relation between multi scale visual curvature and convexity of simple closed curves

controlling temporal solitary waves in the generalized inhomogeneous coupled nonlinear schrodinger equations with varying source terms in this paper we study the families of solitary wave solutions to the inhomogeneous coupled nonlinear schrodinger equations with space and time modulated coefficients and source terms by means of the similarity reduction method and mobius transformations many types of novel temporal solitary wave solutions of this nonlinear dynamical system are analytically found under some constraint conditions such as the bright bright bright dark dark dark periodic periodic w shaped and rational wave solutions in particular we find that the localized rational type solutions can exhibit both bright bright and bright dark wave profiles by choosing different families of free parameters moreover we analyze the relationships among the group velocity dispersion profiles gain or loss distributions external potentials and inhomogeneous source profiles which provide the necessary constraint conditions to control the emerging wave dynamics finally a series of numerical simulations are performed to show the ro

using simple decomposition for smoothing and feature point detection of noisy digital curves this correspondence presents an algorithm for smoothed polygonal approximation of noisy digital planar curves and feature point detection the resulting smoothed polygonal representation preserves the signs of the curvature function of the curve the algorithm is based on a simple decomposition of noisy digital curves into a minimal number of convex and concave sections the location of each separation point is optimized yielding the minimal possible distance between the smoothed approximation and the original curve curve points within a convex concave section are discarded if their angle signs do not agree with the section sign and if the resulted deviations from the curve are less than a threshold spl epsi which is derived automatically inflection points are curve points between pairs of convex concave sections and cusps are curve points between pairs of convex convex or concave concave sections corners and points of local minimal curvature are detected by applying the algorithm to respective total curvature graphs the detection of the feature points is based on properties of pairs of sections that are determined in an adaptive manner rather than on properties of single points that are based on a fixed size neighborhood the detection is therefore reliable and robust complexity analysis and experimental results are presented

integral invariants for shape matching for shapes represented as closed planar contours we introduce a class of functionals which are invariant with respect to the euclidean group and which are obtained by performing integral operations while such integral invariants enjoy some of the desirable properties of their differential counterparts such as locality of computation which allows matching under occlusions and uniqueness of representation asymptotically they do not exhibit the noise sensitivity associated with differential quantities and therefore do not require presmoothing of the input shape our formulation allows the analysis of shapes at multiple scales based on integral invariants we define a notion of distance between shapes the proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other its computation results in optimal point correspondence as an intermediate step numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts missing parts and noise as a quantitative analysis we report matching scores for shape retrieval from a database

the laplacian pyramid as a compact image code we describe a technique for image encoding in which local operators of many scales but identical shape serve as the basis functions the representation differs from established techniques in that the code elements are localized in spatial frequency as well as in space pixel to pixel correlations are first removed by subtracting a lowpass filtered copy of the image from the image itself the result is a net data compression since the difference or error image has low variance and entropy and the low pass filtered image may represented at reduced sample density further data compression is achieved by quantizing the difference image these steps are then repeated to compress the low pass image iteration of the process at appropriately expanded scales generates a pyramid data structure the encoding process is equivalent to sampling the image with laplacian operators of many scales thus the code tends to enhance salient image features a further advantage of the present code is that it is well suited for many image analysis tasks as well as for image compression fast algorithms are described for coding and decoding

on the convergence of planar curves under smoothing curve smoothing has two important applications in computer vision and image processing 1 the curvature scale space css technique for shape analysis and 2 the gaussian filter for noise suppression in this paper we study how planar curves converge as they are smoothed with increasing scales first two types of convergence behavior are clarified the coined term shrinkage refers to the reduction of arc length of a smoothed planar curve which describes the convergence of the curve latitudinally and another coined term collapse refers to the movement of each point to its limiting position which describes the convergence of the curve longitudinally a systematic study on the shrinkage and collapse of three categories of curve models is then presented the corner models helps to reveal how the local structures of planar curves collapse and what the smoothed curves may converge to the sawtooth models allows us to gain insights regarding how noise is suppressed from noisy planar curves by the gaussian filter our investigation on the closed curves shows that each curve collapses to a point at its center of mass however different curves may yield different limiting shapes at the infinity scale finally based upon the derived results the performance of the css technique in corner detection and shape representation is analyzed and a fast implementation method of the gaussian filter for noise suppression is proposed

on ip1 p2 antinorms of nonnegative matrices let 0 p p1 p2 1 x xi rn a aik rm n i e the vector x is elementwise positive and so is the matrix a the lp antinorm of x is defined by x p ixpi1p the lp1 p2 antinorm of a by a p1 p2 k iap1ikp2p11p2 and the lp1 p2 operator antinorm of a by a minp1 p2 infx rn ax p1 x p2 several properties of the antinorms p p1 p2 and minp1 p2 especially the supermultiplicativity of p1 p2 are studied and generalized to hold for nonnegative matrices the results are analogous with the well known submultiplicativity properties of lq1 q2 norms and lq1 q2 operator norms q1 q2 1 a generalization is outlined

using dominant points and variants for profile extraction from chromosomes abstract the most accurate methods for automatic analysis of chromosomes under a light microscope today extract numerical features from band pattern profiles along their longitudinal axes the construction of a reliable axis is a crucial step in this process we propose a new way based on the dominant points of the contour and cubic splines the dominant points serve as candidates for the tips of the chromosome ambiguities are dissolved by the recently developed method of variants for object identification a voronoi diagram decomposes the chromosome in slices for profile extraction the method improves the currently best classification results significantly yielding a test set error rate of 0 61

the curvature primal sketch in this paper we introduce a novel representation of the significant changes in curvature along the bounding contour of planar shape we call the representation the curvature primal sketch because of the close analogy to the primal sketch representation advocated by marr for describing significant intensity changes we define a set of primitive parameterized curvature discontinuities and derive expressions for their convolutions with the first and second derivatives of a gaussian we describe an implemented algorithm that computes the curvature primal sketch by matching the multiscale convolutions of a shape and illustrate its performance on a set of tool shapes several applications of the representation are sketched

corner detection based on gradient correlation matrices of planar curves an efficient and novel technique is developed for detecting and localizing corners of planar curves this paper discusses the gradient feature distribution of planar curves and constructs gradient correlation matrices gcms over the region of support ros of these planar curves it is shown that the eigen structure and determinant of the gcms encode the geometric features of these curves such as curvature features and the dominant points the determinant of the gcms is shown to have a strong corner response and is used as a cornerness measure of planar curves a comprehensive performance evaluation of the proposed detector is performed using the acu and localization error criteria experimental results demonstrate that the gcm detector has a strong corner position response along with a high detection rate and good localization performance

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

curvature and tangential deflection of discrete arcs a theory based on the commutator of scatter matrix pairs and its application to vertex detection in planar shape data this paper introduces a new theory for the tangential deflection and curvature of plane discrete curves our theory applies to discrete data in either rectangular boundary coordinate or chain coded formats its rationale is drawn from the statistical and geometric properties associated with the eigenvalue eigenvector structure of sample covariance matrices specifically we prove that the nonzero entry of the commutator of a piar of scatter matrices constructed from discrete arcs is related to the angle between their eigenspaces and further we show that this entry is in certain limiting cases also proportional to the analytical curvature of the plane curve from which the discrete data are drawn these results lend a sound theoretical basis to the notions of discrete curvature and tangential deflection and moreover they provide a means for computationally efficient implementation of algorithms which use these ideas in various image processing contexts as a concrete example we develop the commutator vertex detection cvd algorithm which identifies the location of vertices in shape data based on excessive cummulative tangential deflection and we compare its performance to several well established corner detectors that utilize the alternative strategy of finding approximate curvature extrema

partial shape classification using contour matching in distance transformation an algorithm is presented to recognize and locate partially distorted 2d shapes without regard to their orientation location and size the algorithm first calculates the curvature function from the digitized image of an object the points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary matching procedure the boundary matching procedure considers two shapes at a time one shape from the template databank and the other from the object being classified the procedure tries to match the control points in the unknown shape to those of a shape from the template databank and estimates the translation rotation and scaling factors to be used to normalize the boundary of the unknown shape the chamfer 3 4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes the unknown shape is assigned to the class corresponding to the minimum distance the algorithm has been successfully tested on partial shapes using two sets of data one with sharp corners and the other with curve segments this algorithm not only is computationally simple but also works reasonably well in the presence of a moderate amount of noise

motion estimation of two dimensional objects based on the straight line hough transform a new approach abstract in this paper we propose a novel technique for estimating motion of two dimensional objects the technique involves representing objects uniquely by straight line approximations of the boundary p and estimating motion from shifts in the p space the straight line approximation of the boundary is obtained by detecting dominant points during contour tracing and then approximating the pixels between adjacent dominant points along the contour by a straight line using the hough transform we have developed a computationally efficient way of detecting dominant points in a single pass during contour tracing the proposed object representation enables us to determine the translation and rotation with significantly fewer computations compared with existing methods our method can also detect the motion parameters correctly for partially overlapping objects

a new algorithm for dominant points detection and polygonization of digital curves a new algorithm for detecting dominant points and polygonal approximation of digitized closed curves is presented it uses an optimal criterion for determining the region of support of each boundary point and a new mechanism for selecting the dominant points the algorithm does not require an input parameter and can handle shapes that contain features of multiple sizes efficiently in addition the approximating polygon preserves the symmetry of the shape

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