an optimum solution for scale invariant object recognition based on the multiresolution approximation this paper presents a multiresolution approximation approach to obtaining boundary representations for object recognition our technique combines a multiresolution approximation and the curvature scale space representation for obtaining representations our research consists of two main parts in the first part of our research we introduce the continuous multiresolution approximation cma in terms of the continuous wavelet transform cwt then we implement a fast algorithm to compute the cma we apply the cma to a boundary to obtain approximations of the boundary at various resolutions the cma provides a consistent interpretation of objects with scale variations moreover we can quickly compute our representations by using the fast algorithm for the cma in the second part we propose three representations for object recognition which cover most boundary based object recognition problems all three representations use the approximations obtained by the cma each representation has different features and covers different types of matching problems but all representations are constructed by using curvature zero crossings of the approximations our representations provide a general but reliable solution to most boundary based object matching problems finally we investigate the properties of our representations such as validity efficiency and reliability we verified our results experimentally to demonstrate the feasibility of using our representations for object recognition

fourier inversion theorem in mesoscopic transport abstract the fourier inversion theorem on the graded hyperbolic plane a supermanifold closely analogous to the quotient spaces of efetov s nonlinear models is described an application to the calculation of the average conductance of quasi one dimensional disordered samples is given

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 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 curve bend function based method to characterize contour shapes in this paper a new curve bend function cbf based method is presented to extract main features of a contour it utilizes two quantities one called a curve bend angle cba and the other known as a type coefficient of curve segment defined on a contour the cba measures the bending degree at each point on the contour while the type coefficient characterizes the properties convexity and concavity of simple curve segments the cbf combines the advantages of the two quantities and provides an overall description of a contour a local maximum or minimum of the cbf corresponds to a critical point of the contour and the peak value is the cosine of the cba hence the problem of locating critical points of a contour is reduced to the problem of finding peak points of the cbf the sign of a peak value indicates the related cba being an inner or outer angle our experimental results and comparisons between the cbf method and rosenfeld johnston s method show that our method is effective and accurate in generating the description of a contour

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

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

direct estimation of the fiber orientation density function from diffusion weighted mri data using spherical deconvolution diffusion weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers the diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel however this model has been shown to fail in regions containing several fiber populations with distinct orientations a number of alternative models have been suggested such as multiple tensor fitting q space and q ball imaging however each of these has inherent limitations in this study we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion weighted mr data without the need for prior assumptions regarding the number of fiber populations present we assume that all white matter fiber bundles in the brain share identical diffusion characteristics thus implicitly assigning any differences in diffusion anisotropy to partial volume effects the diffusion weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function the diffusion weighted attenuation profile for a typical fiber bundle with the fiber orientation density function odf the fiber odf the distribution of fiber orientations within the voxel can therefore be obtained using spherical deconvolution the properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1 5 t clinical scanner the technique can recover the fiber odf in regions of multiple fiber crossing and holds promise for applications such as tractography

on representations of super coalgebras the general structure of the representation theory of a z2 graded coalgebra is discussed the result contains the structure of fourier analysis on compact supergroups and quantizations thereof as a special case the general linear supergroups serve as an explicit illustration and the simplest example is carried out in detail

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

direct curvature scale space theory and corner detection the curvature scale space css technique is considered to be a modern tool in image processing and computer vision direct curvature scale space dcss is defined as the css that results from convolving the curvature of a planar curve with a gaussian kernel directly in this paper we present a theoretical analysis of dcss in detecting corners on planar curves the scale space behavior of isolated single and double corner models is investigated and a number of model properties are specified which enable us to transform a dcss image into a tree organization and so that corners can be detected in a multiscale sense to overcome the sensitivity of dcss to noise a hybrid strategy to apply css and dcss is suggested

multiscale signal enhancement beyond the normality and independence assumption current approaches to denoising or signal enhancement in a wavelet based framework have generally relied on the assumption of normally distributed perturbations in practice this assumption is often violated and sometimes prior information of the probability distribution of a noise process is not even available to relax this assumption we propose a novel nonlinear filtering technique in this paper the key idea is to project a noisy signal onto a wavelet domain and to suppress wavelet coefficients by a mask derived from curvature extrema in its scale space representation for a piecewise smooth signal it can be shown that filtering by this curvature mask is equivalent to preserving the signal pointwise holder exponents at the singular points and lifting its smoothness elsewhere

fourier analysis on a hyperbolic supermanifold with constant curvature the fourier inversion theorem is proved for a rank one noncompact homogeneous space the hyperbolic superplane the proof makes use of some novel features of perfectly graded superspaces which are not encountered in classical geometric analysis an application to quasi one dimensional disordered one electron systems is given

optimal polygonal approximation of digital curves abstract an algorithm for optimal polygonal approximation is presented given a value for the maximal allowed distance between the approximation and the curve the algorithm finds an approximation with the minimal number of vertices the city block metric is used to measure the distance between the approximation and the curve the algorithm worst case complexity is o n 2 where n is the number of points in the curve an efficient and optimal solution for the case of closed curves where no initial point is given is also presented

a parallel algorithm for detecting dominant points on multiple digital curves abstract a new parallel algorithm is proposed for detecting corners of multiple planar curves or shapes this algorithm is based on an analysis of morphological residues and corner characteristics the method is different from traditional chain code based corner detection algorithms which associate with a chain coding and floating point computation for multiple objects in an image the proposed algorithm treats them uniformly and applies simultaneously on curves and shapes of multiple objects the experiments demonstrate that the algorithm can be effectively executed on an simd parallel computer a boundary constrained morphological method is presented for filling closed curves into shapes which are subsequently used for corner detection

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

range data based object surface segmentation via edges and critical points a novel method for range image segmentation is presented in this paper it is based on an integration of edge and region information the algorithm consists of three steps edge and critical point detection triangulation and region growing experimental results show that the method is efficient for segmentation of the range images that contain polyhedral objects a three dimensional 3 d surface structure graph ssg obtained from the segmentation is a description of the surface structure about an object therefore a segmentation result also presents a data set that can be used to establish a surface model for computer aided design based cad based vision and object recognition

nonparametric segmentation of curves into various representations this paper describes and demonstrates the operation and performance of an algorithm for segmenting connected points into a combination of representations such as lines circular elliptical and superelliptical arcs and polynomials the algorithm has a number of interesting properties including being scale invariant nonparametric general purpose and efficient

an improved curvature scale space corner detector and a robust corner matching approach for transformed image identification there are many applications such as image copyright protection where transformed images of a given test image need to be identified the solution to this identification problem consists of two main stages in stage one certain representative features such as corners are detected in all images in stage two the representative features of the test image and the stored images are compared to identify the transformed images for the test image curvature scale space css corner detectors look for curvature maxima or inflection points on planar curves however the arc length used to parameterize the planar curves by the existing css detectors is not invariant to geometric transformations such as scaling as a solution to stage one this paper presents an improved css corner detector using the affine length parameterization which is relatively invariant to affine transformations we then present an improved corner matching technique as a solution to the stage two finally we apply the proposed corner detection and matching techniques to identify the transformed images for a given image and report the promising results

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

scale space derived from b splines this paper proposes a scale space theory based on b spline kernels our aim is twofold 1 present a general framework and show how b splines provide a flexible tool to design various scale space representations in particular we focus on the design of continuous scale space and dyadic scale space frame representations a general algorithm is presented for fast implementation of continuous scale space at rational scales in the dyadic case efficient frame algorithms are derived using b spline techniques to analyze the geometry of an image the relationship between several scale space approaches is explored the behavior of edge models the properties of completeness causality and other properties in such a scale space representation are examined in the framework of b splines it is shown that besides the good properties inherited from the gaussian kernel the b spline derived scale space exhibits many advantages for modeling visual mechanism including the efficiency compactness orientation feature and parallel structure

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

reduced resolution and scale space for dominant feature detection in contours abstract analysis of contours or curves at various scales or levels of smoothing scale space is an important tool in curve segmentation and feature detection in this paper we propose the application of the hierarchical discrete correlation algorithm for efficiently calculating and creating a scale space of curves in conjunction with this procedure we also investigate the use of the reduced resolution or gaussian pyramid representation of the set of smoothed curves as the basis for initially localizing and detecting features we also create an approximation to the above algorithms that is computationally less expensive finally we propose a new inter scale method for curve segmentation and feature detection based on the motion of a curve through scale space

accurate junction detection and characterization in natural images accurate junction detection and characterization are of primary importance for several aspects of scene analysis including depth recovery and motion analysis in this work we introduce a generic junction analysis scheme the first asset of the proposed procedure is an automatic criterion for the detection of junctions permitting to deal with textured parts in which no detection is expected second the method yields a characterization of l y and x junctions including a precise computation of their type localization and scale contrary to classical approaches scale characterization does not rely on the linear scale space first an a contrario approach is used to compute the meaningfulness of a junction this approach relies on a statistical modeling of suitably normalized gray level gradients then exclusion principles between junctions permit their precise characterization we give implementation details for this procedure and evaluate its efficiency through various experiments

laplacian scale space behavior of planar curve corners scale space behavior of corners is important for developing an efficient corner detection algorithm in this paper we analyze the scale space behavior with the laplacian of gaussian log operator on a planar curve which constructs laplacian scale space lss the analytical expression of a laplacian scale space map lss map is obtained demonstrating the laplacian scale space behavior of the planar curve corners based on a newly defined unified corner model with this formula some laplacian scale space behavior is summarized although lss demonstrates some similarities to curvature scale space css there are still some differences first no new extreme points are generated in the lss second the behavior of different cases of a corner model is consistent and simple this makes it easy to trace the corner in a scale space at last the behavior of lss is verified in an experiment on a digital curve

probabilistic diffusion tractography with multiple fibre orientations what can we gain we present a direct extension of probabilistic diffusion tractography to the case of multiple fibre orientations using automatic relevance determination we are able to perform online selection of the number of fibre orientations supported by the data at each voxel simplifying the problem of tracking in a multi orientation field we then apply the identical probabilistic algorithm to tractography in the multi and single fibre cases in a number of example systems which have previously been tracked successfully or unsuccessfully with single fibre tractography we show that multi fibre tractography offers significant advantages in sensitivity when tracking non dominant fibre populations but does not dramatically change tractography results for the dominant pathways

finding contour based abstractions of planar patterns abstract an algorithm is described to detect a number of points on the contour of a planar shape which constitute the vertices of a schematic polygonal representation of the shape itself a set of points initially extracted from the chain coded representation of the contour is iteratively examined while removing some points and inserting new ones the number of selected points decreases in size from iteration to iteration and the selection process converges towards an expected perceptually significant set of points the polygon obtained by linking successive points approximates the contour in an intuitive way it is not constrained within a given tolerance and is likely to locally change from a coarse to a more faithful approximating shape in correspondence with contour regions increasing in details

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

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

wavelet transformation for gray level corner detection abstract corners are very attractive features for many applications in computer vision in this paper a new gray level corner detection algorithm based on the wavelet transform is presented the wavelet transform is used because the evolution across scales of its magnitudes and orientations can be used to characterize localized signals like edges and corners most conventional corner detectors detect corners based on the edge detection information however these edge detectors perform poorly at corners adversely affecting their overall performance to overcome this drawback we first propose a new edge detector based on the ratio of the inter scale wavelet transform modulus this edge detector can correctly detect edges at the corner positions making accurate corner detection possible to reduce the number of points required to be processed we apply the non minima suppression scheme to the edge image and extract the minima image based on the orientation variance these non corner edge points are eliminated in order to locate the corner points we propose a new corner indicator based on the scale invariant property of the corner orientations by examining the corner indicator the corner points can be located accurately as shown by experiments with our algorithm in addition since wavelet transform possesses the smoothing effect inherently our algorithm is insensitive to noise contamination as well

boundary based corner detection using neural networks abstract in this paper we present a novel boundary based corner detection approach using artificial neural networks anns two neural networks are proposed one for detecting corner points with high curvature and the other for detecting tangent points and inflection points that generally have low curvature for a given boundary point p i the first ann uses the normalized coordinates of points on the forward arm neighboring points succeeding p i or on the backward arm neighboring points preceding p i of the point p i as the input vector the output feature of the network is the angle of the forward arm or backward arm with respect to the x axis the boundary point with sufficiently small angle between the forward and backward arms is identified as a corner since the feature points of tangency and inflection have relatively low curvature the signs of curvature rather than the magnitude of curvature for points in the neighborhood of p i are used as the input vector to the second ann the curvature sign at each boundary point is derived from the outputs of the first ann the outputs of the second ann only respond to the sign patterns of tangent points and inflection points by using both anns all features of corners tangent points and inflection points can be extracted from the boundary of any arbitrary shape experimental results have shown that the proposed anns have good detection and localization for objects in random orientations and with moderate scale changes

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

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

unified bundling and registration of brain white matter fibers magnetic resonance diffusion tensor imaging is being widely used to reconstruct brain white matter fiber tracts to characterize structural properties of the tracts reconstructed fibers are often grouped into bundles that correspond to coherent anatomic structures for further group analysis of fiber bundles it is desirable that corresponding bundles from different studies are coregistered to address these needs simultaneously a unified fiber bundling and registration ufibre framework is proposed in this work the framework is based on maximizing a posteriori bayesian probabilities using an expectation maximization algorithm given a set of segmented template bundles and a whole brain target fiber set the ufibre algorithm optimally bundles the target fibers and registers them with the template the bundling component in the ufibre algorithm simplifies fiber based registration into bundle to bundle registration and the registration component in turn guides the bundling process to find bundles consistent with the template experiments with in vivo data demonstrate that the estimated bundles have an 80 consistency with ground truth and the root mean square error between their bundle medial axes is less than one voxel the proposed algorithm is highly efficient offering potential routine use for group analysis of white matter fibers

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

invariant representation matching and pose estimation of 3d space curves under similarity transformations this paper presents a system for matching and pose estimation of 3d space curves under the similarity transformation composed of rotation translation and uniform scaling the system makes use of constraints not only on the feature points but also on curve segments a representation called the similarity invariant coordinate system sics is presented for deriving semi local invariants of 3d curves the sics also enables an efficient exploration of constraints on the shape of the entire curve model based curve matching is performed in the principle of maximum a posteriori map probability in which markov random fields mrfs are used to model the prior probability results are given to demonstrate the matching with missing and extra feature points the extensive exploration of the curve shape constraints in both the matching and the pose estimation stages are shown to significantly improve the quality of the recognition and pose estimation

tract based morphometry for white matter group analysis we introduce an automatic method that we call tract based morphometry or tbm for measurement and analysis of diffusion mri data along white matter fiber tracts using subject specific tractography bundle segmentations we generate an arc length parameterization of the bundle with point correspondences across all fibers and all subjects allowing tract based measurement and analysis in this paper we present a quantitative comparison of fiber coordinate systems from the literature and we introduce an improved optimal match method that reduces spatial distortion and improves intra and inter subject variability of fa measurements we propose a method for generating arc length correspondences across hemispheres enabling a tbm study of interhemispheric diffusion asymmetries in the arcuate fasciculus af and cingulum bundle cb the results of this study demonstrate that tbm can detect differences that may not be found by measuring means of scalar invariants in entire tracts such as the mean diffusivity md differences found in af we report tbm results of higher fractional anisotropy fa in the left hemisphere in af caused primarily by lower 3 the smallest eigenvalue of the diffusion tensor in the left af and higher left hemisphere fa in cb related to higher 1 the largest eigenvalue of the diffusion tensor in the left cb by mapping the significance levels onto the tractography trajectories for each structure we demonstrate the anatomical locations of the interhemispheric differences the tbm approach brings analysis of dti data into the clinically and neuroanatomically relevant framework of the tract anatomy

efficient synthesis of gaussian filters by cascaded uniform filters gaussian filtering is an important tool in image processing and computer vision in this paper we discuss the background of gaussian filtering and look at some methods for implementing it consideration of the central limit theorem suggests using a cascade of simple filters as a means of computing gaussian filters among simple filters uniform coefficient finite impulse response digital filters are especially economical to implement the idea of cascaded uniform filters has been around for a while 13 16 we show that this method is economical to implement has good filtering characteristics and is appropriate for hardware implementation we point out an equivalence to one of burt s methods 1 3 under certain circumstances as an extension we describe an approach to implementing a gaussian pyramid which requires approximately two addition operations per pixel per level per dimension we examine tradeoffs in choosing an algorithm for gaussian filtering and finally discuss an implementation

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

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

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

optimal generating kernels for image pyramids by piecewise fitting a novel class of generating kernels for image pyramids is introduced when these kernels are convolved with intensity functions of images continuous piecewise surfaces composed of polynomial tensor products are fitted to the intensity functions the fittings are optimal in the sense that the mean square error between them and the original intensity functions is minimized two members of the class are introduced and symmetry normalization unimodality and equal contribution properties are proved these kernels possess attractive properties such as small window size fast inverse transformation and minimum error experiments show that they compare favorably with existing ones in terms of mean square error

corner point detection using nest moving average abstract corners are rich in high frequency components a low pass filter suppresses corners and results in a smooth curve therefore corner points have a larger amount of shift than other points and can easily be detected by a low pass filter experiments suggest that a moving average can do this job suitably with a low computational load and good locality in spatial domain a moving average with a smaller size window is used to perprocess the digital boundary with quantization error or noise

techniques for assessing polygonal approximations of curves given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines instead we suggest assessing an algorithm s results relative to an optimal polygon and describe a measure which combines the relative fidelity and efficiency of a curve segmentation we use this measure to compare the application of 23 algorithms to a curve first used by teh and chin 1989 their integral square errors ises are assessed relative to the optimal ise in addition using an example of pose estimation it is shown how goal directed evaluation can be used to select an appropriate assessment criterion

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

fibertract segmentation in position orientation space from high angular resolution diffusion mri in diffusion mri standard approaches for fibertract identification are based on algorithms that generate lines of coherent diffusion currently known as tractography a tract is then identified as a set of such lines selected on some criteria in the present study we investigate whether fibertract identification can be formulated as a segmentation task that recognizes a fibertract as a region where diffusion is intense and coherent indeed we show that it is possible to segment efficiently well known fibertracts with classical image processing methods provided that the problem is formulated in a five dimensional space of position and orientation as an example we choose to adapt to this newly defined high dimensional non euclidean space called position orientation space an algorithm based on the hidden markov random field framework structures such as the cerebellar peduncles corticospinal tract association bundles can be identified and represented in three dimensions by a back projection technique similar to maximum intensity projection potential advantages and drawbacks as compared to classical tractography are discussed for example it appears that our formulation handles naturally crossing tracts and is not biased by human intervention

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

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

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

image filtering using multiresolution representations it is shown how multiresolution representations can be used for filter design and implementation these representations provide a coarse frequency decomposition of the image which forms the basis for two filtering techniques the first method based on image pyramids is used for approximating the convolution of an image with a given mask in this technique a filter is designed using a least squares procedure based on filters synthesized from the basic pyramid equivalent filters the second method is an adaptive noise reduction algorithm an optimally filtered image is synthesized from the multiresolution levels which in this case are maintained at the original sampling density individual pixels of the image representation are linearly combined under a minimum mean square error criterion this uses a local signal to noise ratio estimate to provide the best compromise between noise removal and resolution loss

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

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 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

on the graded group u 1 1 a noncanonical parametrization for the graded group u 1 1 is introduced similar to the euler angles for the ordinary group su 2 two differential representations for the underlying algebra of u 1 1 are constructed on the full and the restricted i e coset parameter space respectively a space of functions living on the latter is found exhibiting close formal similarities to a hilbert space remarkably the indices of those functions and thus the orthogonality and completeness relations involve anticommuting variables using this hilbert space a representation of u 1 1 is evaluated which shows analogies to the wigner functions for su 2

equilateral polygon approximation of closed contours numerous algorithms have been suggested for computing polygonal approximations of closed contours we present an algorithm which as a unique feature creates polygons which are equilateral that is whose edges are all of the same length this allows one dimensional shape descriptions to be derived using the interior polygon angles conceptually the algorithm is an optimization framework for finding the minimum energy configuration of a mechanical system of particles and springs that represent the contour points the polygon vertices and their interaction in practice the dominant points are detected on the gaussian smoothed contour and used to seed an initial polygon nonlinear programming is then used to minimize the system energy subject to the constraint that adjacent vertices must be equidistant the objective function is the sum of a curvature weighted distance between each vertex and a set of contour points associated therewith experimental results are given for closed contours obtained from grey scale images

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

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

atlas based fiber bundle segmentation using principal diffusion directions and spherical harmonic coefficients abstract purpose to develop an automatic atlas based method for segmentation of fiber bundles using high angular resolution diffusion imaging hardi data hypothesis quantitative evaluation of diffusion characteristics inside specific fiber bundles provides new insights into disease developments evolutions therapy effects and surgical interventions background most of previous segmentation methods use similarity measures and strategies that do not lead to accurate segmentation results they also suffer from subjectivity of initial seeds and regions of interest roi defined by operator materials and methods we propose a novel method that uses spherical harmonic coefficients shc of hardi diffusion signals to compute orientation distribution function odf and to extract principal diffusion directions pdds the proposed method selects most collinear pdd of neighbors of each voxel then based on shc and selected pdd a similarity measure is proposed and used as a speed function in the level set framework that segments fiber bundles to automate the process an atlas based method is used to select initial seeds for fiber bundles to generate data for evaluation of the proposed method an artificial pattern consisting of three crossing bundles intersected by a circular bundle is created also two normal controls are imaged by two different hardi protocols results segmentation results for different fiber bundles in simulated data and normal control data are presented influence of threshold selection on the proposed segmentation method is evaluated using dice coefficient also effect of increasing the number of gradient directions on accuracy of extracted pdds is evaluated conclusion the proposed segmentation method has advantages over previous methods especially those that use similarity measures based on diffusion tensor imaging dti data these advantages are achieved by proper propagation of a hyper surface in fiber crossing areas without making assumptions about diffusivity profile and selection of initial seeds or roi

extraction of dominant points by estimation of the contour fluctuations a new method of dominant points dps extraction is presented for each boundary point the method assigns a support region whose length is individually limited two steps are used to detect dps firstly points having higher curvature value than the estimated fluctuations over the support region are extracted as candidates secondly adjacent candidates are merged and a final elimination step is performed on each region additionally a new error measurement scheme is introduced which takes into account the error due to the polygonalisation and the deviation brought by each dp this error is used to compare our algorithm to other methods

clustering method for estimating principal diffusion directions diffusion tensor magnetic resonance imaging dtmri is a non invasive tool for the investigation of white matter structure within the brain however the traditional tensor model is unable to characterize anisotropies of orders higher than two in heterogeneous areas containing more than one fiber population to resolve this issue high angular resolution diffusion imaging hardi with a large number of diffusion encoding gradients is used along with reconstruction methods such as q ball using hardi data the fiber orientation distribution function odf on the unit sphere is calculated and used to extract the principal diffusion directions pdds fast and accurate estimation of pdds is a prerequisite for tracking algorithms that deal with fiber crossings in this paper the pdds are defined as the directions around which the odf data is concentrated estimates of the pdds based on this definition are less sensitive to noise in comparison with the previous approaches a clustering approach to estimate the pdds is proposed which is an extension of fuzzy c means clustering developed for orientation of points on a sphere mdl minimum description length principle is proposed to estimate the number of pdds using both simulated and real diffusion data the proposed method has been evaluated and compared with some previous protocols experimental results show that the proposed clustering algorithm is more accurate more resistant to noise and faster than some of techniques currently being utilized

dti segmentation by statistical surface evolution we address the problem of the segmentation of cerebral white matter structures from diffusion tensor images dti a dti produces from a set of diffusion weighted mr images tensor valued images where each voxel is assigned with a 3 times 3 symmetric positive definite matrix this second order tensor is simply the covariance matrix of a local gaussian process with zero mean modeling the average motion of water molecules as we will show in this paper the definition of a dissimilarity measure and statistics between such quantities is a nontrivial task which must be tackled carefully we claim and demonstrate that by using the theoretically well founded differential geometrical properties of the manifold of multivariate normal distributions it is possible to improve the quality of the segmentation results obtained with other dissimilarity measures such as the euclidean distance or the kullback leibler divergence the main goal of this paper is to prove that the choice of the probability metric i e the dissimilarity measure has a deep impact on the tensor statistics and hence on the achieved results we introduce a variational formulation in the level set framework to estimate the optimal segmentation of a dti according to the following hypothesis diffusion tensors exhibit a gaussian distribution in the different partitions we must also respect the geometric constraints imposed by the interfaces existing among the cerebral structures and detected by the gradient of the dti we show how to express all the statistical quantities for the different probability metrics we validate and compare the results obtained on various synthetic data sets a biological rat spinal cord phantom and human brain dtis

corner detection and curve segmentation by multiresolution chain code linking in this paper we propose a new method to characterise a curve by means of the hierarchical computation of a multiresolution structure this structure consisting of successive lower resolution versions of the same object is processed using the linked pyramid approach we adapt the multiresolution pixel linking algorithm to the processing of curve contours which are described by their chain code we also introduce a selective class selection process which allows application of the algorithm to segmentation and detection of contour features the resulting framework presents good performance for a wide range of object sizes without the need of any parameter tweaking and allows detection of shape detail at different scales

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

nonuniform image representation in area of interest systems this paper is concerned with image representation by data distributed nonuniformly and in particular with a representation scheme suitable for area of interest imaging the class of signals under consideration whose information density varies with position can be represented according to a nonuniform sampling scheme position varying projection operators are presented as simple low pass filtering operations in a fourier like domain sequential projections are used for pyramidal representation of nonuniformly sampled images it is shown that irregular random sampling prevents under certain mild restrictions aliasing effects

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

a rotationally invariant two phase scheme for corner detection a rotationally invariant two phase scheme is proposed for the detection of corners in the first phase the curvature of each point on the curve is calculated based on the coordinates of five consecutive skipped points and the assumption that thes five points form a b spline curve the points with significant curvatures are collected as candidate corners during the second phase the candidate corners are verified for deviations in the global trend of the curve and the candidate corners due to quantization are removed using a self adjusting dot product window application of the propsed method on the examples given in the literature shows that it is both minimal in computation time and accurate and stable in the detected position of corners with the proposed method recognition of an object can be convenient since the corners detected are rotationally invariant

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