on the controllability of some equations of sobolev galpern type abstract in this paper we deal with the controllability problem for some sobolev type equations we show that the equations cannot be driven to zero if the control region is strictly supported within the domain nevertheless we also prove that it is possible to control the equations using controls which have a moving support under some assumptions on their movement

view variation of point set and line segment features the variation with respect to view of 2d features defined for projections of 3d point sets and line segments is studied it is established that general case view invariants do not exist for any number of points given true perspective weak perspective or orthographic projection models feature variation under the weak perspective approximation is then addressed though there are no general case weak perspective invariants there are special case invariants of practical importance those cited in the literature are derived from linear dependence relations and the invariance of this type of relation to linear transformation the variation with respect to view is studied for an important set of 2d line segment features the relative orientation size and position of one line segment with respect to another the analysis includes an evaluation criterion for feature utility in terms of view variation this relationship is a function of both the feature and the particular configuration of 3d line segments the use of this information in objection recognition is demonstrated for difficult discrimination tasks

an algorithm for computing some heegaard floer homologies in this paper we give an algorithm to compute the hat version of heegaard floer homology of a closed oriented three manifold this method also allows us to compute the filtration coming from a null homologous link in a three manifold

recovering surface shape and orientation from texture texture provides an important source of information about the three dimensional structure of visible surfaces particularly for stationary monocular views to recover 3d structure the distorting effects of projection must be distinguished from properties of the texture on which the distortion acts this requires that assumptions must be made about the texture yet the unpredictability of natural textures precludes the use of highly restrictive assumptions the recovery method reported in this paper exploits the minimal assumption that textures do not mimic projective effects this assumption determines the strategy of attributing as much as possible of the variation observed in the image to projection equivalently the interpretation is chosen for which the texture prior to projection is made as uniform as possible this strategy was implemented using statistical methods first for the restricted case of planar surfaces and then by extension for curved surfaces the technique was applied successfully to natural images

shape from texture and contour by weak isotropy abstract a unified framework for shape from texture and contour is proposed it is based on the assumption that the surface markings are not systematically compressed or formally that they are weakly isotropic the weak isotropy principle is based on analysis of the directional statistics of the projected surface markings it builds on several previous theories in particular by witkin 25 and kanatani 15 it extends these theories in various ways most notably to perspective projection the theory also provides an exact solution to an estimation problem earlier solved approximately by kanatani the weak isotropy principle leads to a computationally efficient algorithm wisp for estimation of surface orientation wisp uses simple image observables that are shown to be direct correlates of the surface orientation to compute an initial approximate estimate in a single step in certain simple cases this first estimate is exact and in experiments with natural images it is typically within 5 of the final estimate furthermore a proof is given that a rotationally symmetric contour of order three or higher is weakly isotropic hence the wisp algorithm will without modification recover the orientation of any such contour from a perspective view of it

mobile point controls versus locally distributed ones for the controllability of the semilinear parabolic equation it is well known now that a rather general semilinear parabolic equation with globally lipschitz nonlinear term is both approximately and exactly null controllable in l2 omega when governed in a bounded domain by the locally distributed controls in this paper we intend to show that in fact in one space dimension omega 0 1 the very same results can be achieved by employing em at most two mobile point controls with support on the curves properly selected within an arbitrary subdomain of qt 0 1 0 t we will show that such curves can be described by a certain differential inequality and the explicit examples are provided we also discuss some extensions of our main results to the superlinear terms and to the case of several dimensions

determining camera parameters from the perspective projection of a rectangle abstract in this note we show how to use the 2d perspective projection of a rectangle of unknown size and position in 3d space to determine the camera look angle parameters relative to the plans of the rectangle all equations are simple in addition if the size of the rectangle is known it is possible to compute the exact 3d coordinates of the rectangle

null controllability of the structurally damped wave equation with moving control we investigate the internal controllability of the wave equation with structural damping on the one dimensional torus we assume that the control is acting on a moving point or on a moving small interval with a constant velocity we prove that the null controllability holds in some suitable sobolev space and after a fixed positive time independent of the initial conditions

comments on symmetry as a continuous feature we point out the existence of a theoretical difficulty that underlies the symmetry detection studied by zabrodsky et al 1995 and present a possible solution to it

motion and structure from point correspondences with error estimation planar surfaces the determination of motion and structure of a planar scene from monocular image sequences is studied a new and simpler linear algorithm that gives closed form solutions for motion and structure parameters using point correspondences between two images assuming that the coplanar points undergo a rigid motion in 3 d space is presented a series of analytical results is established from two perspective views of a planar scene which is undergoing a rigid motion there are generally two normalized interpretations for motion parameters and the positions of the object plane these two interpretations one vertical and the other illusive are both valid in the sense that they render the same pair of images the authors identify all the special cases in which the number of interpretations is not two and derive necessary and sufficient geometrical conditions for those special cases to occur the approach to error estimation is based on the first order perturbation the estimated errors provide quantitative assessment for the accuracy of the solutions they also indicate degenerate or nearly degenerate configurations in the presence of noise

on the controllability of the linearized benjamin bona mahony equation we study the boundary controllability properties of the linearized benjamin bona mahony equation left begin array ll u t u xxt u x 0 x in 0 1 t 0 u t 0 0 u 1 t f t t 0 end array right we show that the equation is approximately controllable but not spectrally controllable no finite linear combination of eigenfunctions other than zero is controllable next we prove a finite controllability result and we estimate the norms of the controls needed in this case

monopoles and lens space surgeries monopole floer homology is used to prove that real projective three space cannot be obtained from dehn surgery on a nontrivial knot in the three sphere to obtain this result we use a surgery long exact sequence for monopole floer homology together with a nonvanishing theorem which shows that monopole floer homology detects the unknot in addition we apply these techniques to give information about knots which admit lens space surgeries and to exhibit families of three manifolds which do not admit taut foliations

equivalence of heegaard floer homology and embedded contact homology via open book decompositions we sketch the proof of the equivalence between the hat versions of heegaard floer homology and embedded contact homology ech the key point is to express these two floer homology theories in terms of an open book decomposition of the ambient manifold

3d symmetry detection using the extended gaussian image symmetry detection is important in the area of computer vision a 3d symmetry detection algorithm is presented in this paper the symmetry detection problem is converted to the correlation of the gaussian image once the gaussian image of the object has been obtained the algorithm is independent of the input format the algorithm can handle different kinds of images or objects simulated and real images have been tested in a variety of formats and the results show that the symmetry can be determined using the gaussian image

analyzing skewed symmetries symmetry is pervasive in both man made objects and nature since symmetries project to skew symmetries finding axes of skew symmetry is an important vision task this paper presents a linear time algorithm for finding the axes of skew symmetry where the degree of symmetry is known first we present a review and critique of current methods for finding the axes of skew symmetry next we decompose the problem of finding skew symmetry into the subproblems of solving for the rotational parameter of a shear symmetry and recovering the shear parameter of a reflexive symmetry using this approach the authors derive a direct non heuristic moment based technique for finding the axes of skew symmetry for skew symmetric figures with degree of symmetry less than five we obtain a closed form solution the method does not rely on continuous contours but assumes there is no occlusion and requires knowing the contour s degree of symmetry it is the first algorithm to find the axes of skew symmetry ino n time where n is the number of contour points the method is especially suited to industrial applications where the degree of symmetry is often knowna priori examples of the method are presented for both real and synthetic images and an error analysis of the method is given

chiral coefficient a measure of the amount of structural chirality a new concept of quantitative measurement of chiral structure is introduced and labelled as chiral coefficient chi a distinction is made between geometric and physical chiralities and chi is defined for various physical cases few general geometrical features are discussed and it is shown that for every chiral body there exists a natural z direction depending on the physical property treated possible practical applications of this concept are discussed a few simple examples of the chiral coefficient of mass chi m for chiral molecules are treated

projective reconstruction and invariants from multiple images this correspondence investigates projective reconstruction of geometric configurations seen in two or more perspective views and the computation of projective invariants of these configurations from their images a basic tool in this investigation is the fundamental matrix that describes the epipolar correspondence between image pairs it is proven that once the epipolar geometry is known the configurations of many geometric structures for instance sets of points or lines are determined up to a collineation of projective 3 space spl pscrsup 3 by their projection in two independent images this theorem is the key to a method for the computation of invariants of the geometry invariants of six points in spl pscrsup 3 and of four lines in spl pscrsup 3 are defined and discussed an example with real images shows that they are effective in distinguishing different geometrical configurations since the fundamental matrix is a basic tool in the computation of these invariants new methods of computing the fundamental matrix from seven point correspondences in two images or six point correspondences in three images are given

motion estimation with more than two frames the development of a general motion estimation system based on using three or more frames is reported the relevant portion of the sequence is treated as a whole thus simplifying the process of estimating the motion parameters and making possible the computation of the motion parameters in terms of the natural center of motion a general description of this motion estimation method is presented with the derivation of motion equations for three cases three points in three frames two points in four frames and one point in five frames results are given for real and synthetic images for the case of one point in five and six frames on the average the program converged quickly to the right answer for noiseless data for noisy data the answers were reasonable and their accuracy was directly a function of the amount of noise in the disparity vector

space and time bounds on indexing 3d models from 2d images model based visual recognition systems often match groups of image features to groups of model features to form initial hypotheses which are then verified in order to accelerate recognition considerably the model groups can be arranged in an index space hashed offline such that feasible matches are found by indexing into this space for the case of 2d images and 3d models consisting of point features bounds on the space required for indexing and on the speedup that such indexing can achieve are demonstrated it is proved that even in the absence of image error each model must be represented by a 2d surface in the index space this places an unexpected lower bound on the space required to implement indexing and proves that no quantity is invariant for all projections of a model into the image theoretical bounds on the speedup achieved by indexing in the presence of image error are also determined and an implementation of indexing for measuring this speedup empirically is presented it is found that indexing can produce only a minimal speedup on its own however when accompanied by a grouping operation indexing can provide significant speedups that grow exponentially with the number of features in the groups

when is it possible to identify 3d objects from single images using class constraints one approach to recognizing objects seen from arbitrary viewpoint is by extracting invariant properties of the objects from single images such properties are found in images of 3d objects only when the objects are constrained to belong to certain classes e g bilaterally symmetric objects existing studies that follow this approach propose how to compute invariant representations for a handful of classes of objects a fundamental question regarding the invariance approach is whether it can be applied to a wide range of classes to answer this question it is essential to study the set of classes for which invariance exists this paper introduces a new method for determining the existence of invariant functions for classes of objects together with the set of images from which these invariants can be computed we develop algebraic tests that determine whether the objects in a given class can be identified from single images these tests apply to classes of objects undergoing affine projection in addition these tests allow us to determine the set of views of the objects which are degenerate we apply these tests to several classes of objects and determine which of them is identifiable and which of their views are degenerate

on symmetry detection a straight line is an axis ofsymmetry of a planar figure if the figure is invariant to reflection with respect to that line the purpose of this correspondence is to describe an o n log n time algorithm for enumerating all the axes of symmetry of a planar figure which is made up of possibly intersecting segments circles points etc the solution involves a reduction of the problem to a combinatorial question on words our algorithm is optimal since we can establish an n log n time lower bound for this problem

invariants of six points and projective reconstruction from three uncalibrated images there are three projective invariants of a set of six points in general position in space it is well known that these invariants cannot be recovered from one image however an invariant relationship does exist between space invariants and image invariants this invariant relationship is first derived for a single image then this invariant relationship is used to derive the space invariants when multiple images are available this paper establishes that the minimum number of images for computing these invariants is three and the computation of invariants of six points from three images can have as many as three solutions algorithms are presented for computing these invariants in closed form the accuracy and stability with respect to image noise selection of the triplets of images and distance between viewing positions are studied both through real and simulated images applications of these invariants are also presented both the results of faugeras 1992 and hartley et al 1992 for projective reconstruction and sturm s method 1869 for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

null controllability of a pseudo parabolic equation with moving control abstract in this paper we study the internal controllability of the pseudo parabolic equation on the one dimensional torus our control function is acting on a moving small interval with a constant velocity with this moving distributed control we obtain the system is null controllable for given data with certain regularity

tour of bordered floer theory heegaard floer theory is a kind of topological quantum field theory tqft assigning graded groups to closed connected oriented 3 manifolds and group homomorphisms to smooth oriented four dimensional cobordisms bordered heegaard floer homology is an extension of heegaard floer homology to 3 manifolds with boundary with extended tqft type gluing properties in this survey we explain the formal structure and construction of bordered floer homology and sketch how it can be used to compute some aspects of heegaard floer theory

self calibration of catadioptric camera with two planar mirrors from silhouettes if an object is interreflected between two planar mirrors we may take an image containing both the object and its multiple reflections i e simultaneously imaging multiple views of an object by a single pinhole camera this paper emphasizes the problem of recovering both the intrinsic and extrinsic parameters of the camera using multiple silhouettes from one single image view pairs among views in a single image can be divided into two kinds by the relationship between the two views in the pair reflected by some mirror real or virtual and in a circular motion epipoles in the first kind of pairs can be easily determined from intersections of common tangent lines of silhouettes based on the projective properties of these epipoles efficient methods are proposed to recover both the imaged circular points and the included angle between two mirrors epipoles in the second kind of pairs can be recovered simultaneously with the projection of intersection line between two mirrors by solving a simple 1d optimization problem using the consistency constraint of epipolar tangent lines fundamental matrices among views in a single image are all recovered using the estimated intrinsic and extrinsic parameters of the camera a euclidean reconstruction can be obtained experiments validate the proposed approach

from image quadrilaterals to symmetrical trapezia abstract this paper concerns the 3 d interpretation of image quadrilaterals as the perspective projections of bilateral symmetric trapezia simple algorithms are described for reconstructing a symmetric trapezium from a given image quadrilateral and for determining the 3 d motion of a symmetric trapezium from two matched image quadrilaterals several results are established and or further verified including the necker reversal ambiguity in the interpretation of image quadrilaterals as the perspective projection of bilateral symmetric trapezia experiments with both synthetic and real images are included to demonstrate the validity of the theoretic results

3d object recognition using invariance abstract the systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years invariance overcomes one of the fundamental difficulties in recognising objects from images that the appearance of an object depends on viewpoint this problem is entirely avoided if the geometric description is unaffected by the imaging transformation such invariant descriptions can be measured from images without any prior knowledge of the position orientation and calibration of the camera these invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification object models can be acquired directly from images allowing efficient construction of model libraries without manual intervention a significant part of the paper is a summary of recent results on the construction of invariants for 3d objects from a single perspective view a proposed recognition architecture is described which enables the integration of multiple general object classes and provides a means for enforcing global scene consistency various criticisms of the invariant approach are articulated and addressed

3 d reconstruction using mirror images based on a plane symmetry recovering method three dimensional reconstruction from a perspective 2d image using mirrors is addressed the mirrors are used to form symmetrical relations between the direct image and mirror images by finding correspondences between them the 3d shape can be reconstructed by means of plane symmetry recovering method using the vanishing point two constraints are used in determining the correspondence in the case where only one mirror is used invisible parts both in the direct image and in the mirror image may still remain using multiple mirrors however occluded parts will decrease or disappear and occlusion free object reconstruction becomes possible

on view likelihood and stability we define two measures on views view likelihood and view stability view likelihood measures the probability that a certain view of a given 3d object is observed it may be used to identify typical or characteristic views view stability measures how little the image changes as the viewpoint is slightly perturbed it may be used to identify generic views both definitions are shown to be identical up to the prior probability of camera orientations and determined by the 2d metric used to compare images we analytically derive the stability and likelihood measures for two feature based 2d metrics where the most stable and most likely view is shown to be the flattest view of the 3d shape incorporating view likelihood or stability in 3d object recognition and 3d reconstruction increases the chance of robust performance in particular we propose to use these measures to enhance 3d object recognition and 3d reconstruction algorithms by adding a second step where the most likely solution is selected among all feasible solutions these applications are demonstrated using simulated and real images

symmetry based photo editing in this paper we demonstrate how to edit digital photos based on the understanding of high level geometric knowledge imposed upon objects in the photos this is achieved by the correct recovery of the 3 d shape and relationships of the objects without explicitly performing full 3 d reconstruction symmetry is proposed as the central notion that unifies both conceptually and algorithmically all types of geometric regularities such as parallelism orthogonality and similarity the methods are extremely simple accurate easy to implement and they demonstrate the utility of applying scene knowledge to image understanding and editing

unique continuation property and control for the benjamin bona mahony equation on a periodic domain abstract we consider the benjamin bona mahony bbm equation on the one dimensional torus t r 2 z we prove a unique continuation property ucp for small data in h 1 t with nonnegative zero means next we extend the ucp to certain bbm like equations including the equal width wave equation and the kdv bbm equation applications to the stabilization of the above equations are given in particular we show that when an internal control acting on a moving interval is applied in the bbm equation then a semiglobal exponential stabilization can be derived in h s t for any s 1 furthermore we prove that the bbm equation with a moving control is also locally exactly controllable in h s t for any s 0 and globally exactly controllable in h s t for any s 1 in a sufficiently large time depending on the h s norms of the initial and terminal states

admissible transverse surgery does not preserve tightness we produce the first examples of closed tight contact 3 manifolds which become overtwisted after performing admissible transverse surgeries along the way we clarify the relationship between admissible transverse surgery and legendrian surgery we use this clarification to study a new invariant of transverse knots namely the range of slopes on which admissible transverse surgery preserves tightness and to provide some new examples of knot types which are not uniformly thick our examples also illuminate several interesting new phenomena including the existence of hyperbolic universally tight contact 3 manifolds whose heegaard floer contact invariants vanish and which are not weakly fillable and the existence of open books with arbitrarily high fractional dehn twist coefficients whose compatible contact structures are not deformations of co orientable taut foliations

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

computing local surface orientation and shape from texture forcurved surfaces shape from texture is best analyzed in two stages analogous to stereopsis and structure from motion a computing the texture distortion from the image and b interpreting the texture distortion to infer the orientation and shape of the surface in the scene we model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters we have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis one need not explicitly identify texels or make restrictive assumptions about the nature of the texture such as isotropy we use non linear minimization of a least squares error criterion to recover the surface orientation slant and tilt and shape principal curvatures and directions based on the estimated affine transforms in a number of different directions a simple linear algorithm based on singular value decomposition of the linear parts of the affine transforms provides the initial guess for the minimization procedure experimental results on both planar and curved surfaces under perspective projection demonstrate good estimates for both orientation and shape a sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture

single view metrology we describe how 3d affine measurements may be computed from a single perspective view of a scene given only minimal geometric information determined from the image this minimal information is typically the vanishing line of a reference plane and a vanishing point for a direction not parallel to the plane it is shown that affine scene structure may then be determined from the image without knowledge of the camera s internal calibration e g focal length nor of the explicit relation between camera and world pose in particular we show how to i compute the distance between planes parallel to the reference plane up to a common scale factor s ii compute area and length ratios on any plane parallel to the reference planes iii determine the camera s location simple geometric derivations are given for these results we also develop an algebraic representation which unifies the three types of measurement and amongst other advantages permits a first order error propagation analysis to be performed associating an uncertainty with each measurement we demonstrate the technique for a variety of applications including height measurements in forensic images and 3d graphical modelling from single images

paraperspective affine it is shown that the set of all paraperspective images with arbitrary reference point and the set of affine images of a 3 d object are identical consequently all uncalibrated paraperspective images of an object can be constructed from a 3 d model of the object by applying an affine transformation to the model and every affine image of the object represents some uncalibrated paraperspective image of the object it follows that the paraperspective images of an object can be expressed as linear combinations of any two non degenerate images of the object when the image position of the reference point is given the parameters of the affine transformation and likewise the coefficients of the linear combinations satisfy two quadratic constraints conversely when the values of parameters are given the image position of the reference point is determined by solving a bi quadratic equation

effect of aggregation on population recovery modeled by a forward backward pseudoparabolic equation in this paper we study the equation u t u f u u t f u in a bounded domain of r d d 1 with homogeneous boundary conditions of the neumann type as a model of aggregating population with a migration rate determined by and total birth and mortality rates characterized by f we will show that the aggregating mechanism induced by u allows the survival of a species in danger of extinction numerical simulations suggest that the solutions stabilize asymptotically in time to a not necessarily homogeneous stationary solution this is shown to be the case for a particular version of the function u

conic reconstruction and correspondence from two views conics are widely accepted as one of the most fundamental image features together with points and line segments the problem of space reconstruction and correspondence of two conics from two views is addressed in this paper it is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views given the relative orientation of the two views these two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics a unified closed form solution is also developed for both projective reconstruction of conics in space from two uncalibrated camera views and metric reconstruction from two calibrated camera views experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images

an extremum principle for shape from contour an extremum principle is developed that determines three dimensional surface orientation from a two dimensional contour the principle maximizes the ratio of the area to the square of the perimeter a measure of the compactness or symmetry of the three dimensional surface the principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries the maximum likelihood method approximates the principle on irregular figures but we show that it consistently overestimates the slant of an ellipse

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

recognizing solid objects by alignment with an image in this paper we consider the problem of recognizing solid objects from a single two dimensional image of a three dimensional scene we develop a new method for computing a transformation from a three dimensional model coordinate frame to the two dimensional image coordinate frame using three pairs of model and image points we show that this transformation always exists for three noncollinear points and is unique up to a reflective ambiguity the solution method is closed form and only involves second order equations we have implemented a recognition system that uses this transformation method to determine possible alignments of a model with an image each of these hypothesized matches is verified by comparing the entire edge contours of the aligned object with the image edges using the entire edge contours for verification rather than a few local feature points reduces the chance of finding false matches the system has been tested on partly occluded objects in highly cluttered scenes

on symmetry perspectivity and level set based segmentation we introduce a novel variational method for the extraction of objects with either bilateral or rotational symmetry in the presence of perspective distortion information on the symmetry axis of the object and the distorting transformation is obtained as a by product of the segmentation process the key idea is the use of a flip or a rotation of the image to segment as if it were another view of the object we call this generated image the symmetrical counterpart image we show that the symmetrical counterpart image and the source image are related by planar projective homography this homography is determined by the unknown planar projective transformation that distorts the object symmetry the proposed segmentation method uses a level set based curve evolution technique the extraction of the object boundaries is based on the symmetry constraint and the image data the symmetrical counterpart of the evolving level set function provides a dynamic shape prior it supports the segmentation by resolving possible ambiguities due to noise clutter occlusions and assimilation with the background the homography that aligns the symmetrical counterpart to the source level set is recovered via a registration process carried out concurrently with the segmentation promising segmentation results of various images of approximately symmetrical objects are shown

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

recognition by linear combinations of models an approach to visual object recognition in which a 3d object is represented by the linear combination of 2d images of the object is proposed it is shown that for objects with sharp edges as well as with smooth bounding contours the set of possible images of a given object is embedded in a linear space spanned by a small number of views for objects with sharp edges the linear combination representation is exact for objects with smooth boundaries it is an approximation that often holds over a wide range of viewing angles rigid transformations with or without scaling can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations three alternative methods of determining the transformation that matches a model to a given image are proposed

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

least squares fitting of two 3 d point sets two point sets pi and p i i 1 2 n are related by p i rpi t ni where r is a rotation matrix t a translation vector and ni a noise vector given pi and p i we present an algorithm for finding the least squares solution of r and t which is based on the singular value decomposition svd of a 3 3 matrix this new algorithm is compared to two earlier algorithms with respect to computer time requirements

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

on the detection of the axes of symmetry of symmetric and almost symmetric planar images a simple algorithm is presented for finding all the axes of symmetry of symmetric and almost symmetric planar images having nonuniform gray level intensity images the technique which can also be used in conjunction with planar curves is based on the identification of the centroids of the given image and other related sets of points followed by a maximization of a specially defined coefficient of symmetry owing to the nature of the required procedures which are strictly based on the computation of mean values the method is not particularly affected by the presence of noise and is especially suited for application in conjunction with digitized figures

on symmetry and multiple view geometry structure pose and calibration from a single image in this paper we provide a principled explanation of how knowledge in global 3 d structural invariants typically captured by a group action on a symmetric structure can dramatically facilitate the task of reconstructing a 3 d scene from one or more images more importantly since every symmetric structure admits a canonical coordinate frame with respect to which the group action can be naturally represented the canonical pose between the viewer and this canonical frame can be recovered too which explains why symmetric objects e g buildings provide us overwhelming clues to their orientation and position we give the necessary and sufficient conditions in terms of the symmetry group admitted by a structure under which this pose can be uniquely determined we also characterize when such conditions are not satisfied to what extent this pose can be recovered we show how algorithms from conventional multiple view geometry after properly modified and extended can be directly applied to perform such recovery from all hidden images of one image of the symmetric structure we also apply our results to a wide range of applications in computer vision and image processing such as camera self calibration image segmentation and global orientation large baseline feature matching image rendering and photo editing as well as visual illusions caused by symmetry if incorrectly assumed

initial boundary value problem for a class of semilinear pseudo parabolic equations with logarithmic nonlinearity abstract in this paper we study the initial boundary value problem for a class of semilinear pseudo parabolic equations with logarithmic nonlinearity by using the logarithmic sobolev inequality and a family of potential wells we obtain the existence of global solution blow up at and behavior of vacuum isolation of solutions on the other hand the asymptotic behavior of solutions is also discussed our result implies that the polynomial nonlinearity is important for the solutions of such kinds of semilinear pseudo parabolic equations to be blow up in finite time

3 d modeling from a single view of a symmetric object 3 d technologies are considered as the next generation of multimedia applications currently one of the challenges faced by 3 d applications is the shortage of 3 d resources to solve this problem many 3 d modeling methods are proposed to directly recover 3 d geometry from 2 d images however these methods on single view modeling either require intensive user interaction or are restricted to a specific kind of object in this paper we propose a novel 3 d modeling approach to recover 3 d geometry from a single image of a symmetric object with minimal user interaction symmetry is one of the most common properties of natural or manmade objects given a single view of a symmetric object the user marks some symmetric lines and depth discontinuity regions on the image our algorithm first finds a set of planes to approximately fit to the object and then a rough 3 d point cloud is generated by an optimization procedure the occluded part of the object is further recovered using symmetry information experimental results on various indoor and outdoor objects show that the proposed system can obtain 3 d models from single images with only a little user interaction

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

a combinatorial spanning tree model for knot floer homology abstract we iterate manolescu s unoriented skein exact triangle in knot floer homology with coefficients in the field of rational functions over z 2 z the result is a spectral sequence which converges to a stabilized version of graded knot floer homology the e 2 d 2 page of this spectral sequence is an algorithmically computable chain complex expressed in terms of spanning trees and we show that there are no higher differentials this gives the first combinatorial spanning tree model for knot floer homology

knot floer homology detects genus one fibred knots ozsv ath and szab o conjectured that knot floer homology detects fibred knots we propose a strategy to approach this conjecture based on contact topology and gabai s theory of sutured manifold decomposition we implement this strategy for genus one knots obtaining as a corollary that if rational surgery on a knot k gives the poincar e homology sphere sigma 2 3 5 then k is the left handed trefoil knot

recovery of the three dimensional shape of an object from a single view given a single picture which is a projection of a three dimensional scene onto the two dimensional picture plane we usually have definite ideas about the 3 d shapes of objects to do this we need to use assumptions about the world and the image formation process since there exist a large number of shapes which can produce the same picture the purpose of this paper is to identify some of these assumptions mostly geometrical ones by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape recovery method the method consists of two parts the first is the application of the origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively the second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair given a single image the method recovers the 3 d shapes of an object in it and generates images of the same object as we would see it from other directions

the unique solution of projective invariants of six points from four uncalibrated images in this paper we show that four uncalibrated images are sufficient to uniquely determine the 3d projective invariants of a set of six points in general position in space an algorithm for computing the unique solution is proposed it computes by solving a set of linear equations for its two linear independent solutions and is simpler than other algorithms which compute the three possible solutions of 3d projective invariants by solving a set of nonlinear equations however a fourth image is needed to get the linear unique solution finally experimental results have shown the feasibility of this algorithm