some koszul rings from geometry abstract we give examples of koszul rings that arise naturally in algebraic geometry in the first part we prove a general result on koszul property associated to an ample line bundle on a projective variety specifically we show how koszul property of multiples of a base point free ample line bundle depends on its castelnuovo mumford regularity in the second part we give examples of koszul rings that come from adjoint line bundles on minimal irregular surfaces of general type

linear free resolutions and minimal multiplicity let s k x x be a polynomial ring over a field and let a4 a m be a finitely generated graded module in the most interesting case a4 is an ideal of s for a given natural number p there is a great interest in the question can m be generated by homogeneous elements of degree p no simple answer say in terms of the local cohomology of m is known but somewhat surprisingly the stronger question can the jth syzygy of m be generated by elements of degree qp j for all j 0 l n does admit a simple response the following is neither new nor difficult to prove though it seems not well known

local well posedness for the maxwell schrodinger equation time local well posedness for the maxwell schrodinger equation in the coulomb gauge is studied in sobolev spaces by the contraction mapping principle the lorentz gauge and the temporal gauge cases are also treated by the gauge transform

complete solution classification for the perspective three point problem we use two approaches to solve the perspective three point p3p problem the algebraic approach and the geometric approach in the algebraic approach we use wu ritt s zero decomposition algorithm to give a complete triangular decomposition for the p3p equation system this decomposition provides the first complete analytical solution to the p3p problem we also give a complete solution classification for the p3p equation system i e we give explicit criteria for the p3p problem to have one two three and four solutions combining the analytical solutions with the criteria we provide an algorithm cassc which may be used to find complete and robust numerical solutions to the p3p problem in the geometric approach we give some pure geometric criteria for the number of real physical solutions

on syzygies of veronese embedding of arbitrary projective varieties abstract for a very ample line bundle l on a projective scheme x let l l x p h 0 x l l l 1 be the embedding defined by the complete linear series l l in this paper we study the problem how the castelnuovo mumford regularity of l x effects on the defining equations of l l x and the syzygies among them we show that if l x p h 0 x l is m regular then x l l satisfies property n 2 l m 1 for m 2 l m 2 and x l l satisfies property n l for all l m 1

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

castelnuovo mumford regularity of projected roth varieties abstract we work over an algebraically closed field of characteristic zero the purpose of this paper is to study the castelnuovo mumford regularity of projected roth varieties which are divisors of rational scrolls of certain types these varieties appear as an exceptional case in the study of finding whether a projective variety is defined by equations of the expected low degree

multigraded regularity and the koszul property abstract we give a criterion for the section ring of an ample line bundle to be koszul in terms of multigraded regularity we discuss applications to adjoint bundles on toric varieties as well as to polytopal semigroup rings

syzygies using vector bundles this paper studies syzygies of curves that have been embedded in projective space by line bundles of large degree the proofs take advantage of the relationship between syzygies and spaces of section of vector bundles associated to the given line bundles

two efficient solutions for visual odometry using directional correspondence this paper presents two new efficient solutions to the two view relative pose problem from three image point correspondences and one common reference direction this three plus one problem can be used either as a substitute for the classic five point algorithm using a vanishing point for the reference direction or to make use of an inertial measurement unit commonly available on robots and mobile devices where the gravity vector becomes the reference direction we provide a simple closed form solution and a solution based on algebraic geometry which offers numerical advantages in addition we introduce a new method for computing visual odometry with ransac and four point correspondences per hypothesis in a set of real experiments we demonstrate the power of our approach by comparing it to the five point method in a hypothesize and test visual odometry setting

global schrodinger maps in dimensions d 2 small data in the critical sobolev spaces we consider the schrodinger map initial value problem t on r d r 0 0 where r d r s 2 r 3 is a smooth function in all dimensions d 2 we prove that the schrodinger map initial value problem admits a unique global smooth solution 2 c r h 1 q q2 s 2 provided that the data 02 h 1 q is smooth and satises the smallness condition

a bound on the castelnuovo mumford regularity for curves recall that a projective curve in bbb p r with ideal sheaf cal i is said to be n regular if h i bbb p r cal i otimes cal o bbb p r n i 0 for every integer i 0 and that in this case it is cut out scheme theoretically by equations of degree at most n the purpose here is to show that an irreducible reduced projective curve of degree d and large arithmetic genus p a satisfies a smaller regularity bound than the optimal one d r 2 for example if p a geq r 2 then a curve is d 2r 4 regular unless it is embedded by a complete linear system of degree 2p a 2

higher syzygies of ruled varieties over a curve let x be a ruled variety over a smooth projective curve c with the projection morphism x c in this paper we study higher syzygies of very ample line bundles on x each embedding of x is fiberwise a veronese embedding and our first result is to clarify the relation between property np of very ample line bundles on x and that of the veronese embedding more precisely letting h be the tautological line bundle of x assume that the a uple veronese embedding of a fiber satisfies property np we prove that line bundles on x of the form ah b satisfy property np if deg b is sufficiently large theorem 1 1 also we get some partial answer for the converse corollary 3 7 from this observation we improve butler s result in d c butler normal generation of vector bundles over a curve j differential geom 39 1994 1 34 for ruled scrolls ruled surfaces and veronese surface fibrations

on the projective normality of double coverings over a rational surface abstract we study the projective normality of a minimal surface x which is a ramified double covering over a rational surface s with dim k s 1 in particular horikawa surfaces the minimal surfaces of general type with k x 2 2 p g x 4 are of this type up to resolution of singularities let be the covering map from x to s we show that the z 2 invariant adjoint divisors k x r a are normally generated where the integer r 3 and a is an ample divisor on s

green lazarsfeld condition for toric edge ideals of bipartite graphs abstract previously ohsugi and hibi gave a combinatorial description of bipartite graphs g whose toric edge ideal i g is generated by quadrics showing that every cycle of g of length at least 6 must have a chord this corresponds to the green lazarsfeld condition n 1 in this paper we investigate the higher syzygies of i g and give combinatorial descriptions of the green lazarsfeld conditions n p of toric edge ideals of bipartite graphs for all p 1 in particular we show that i g is linearly presented i e satisfies condition n 2 if and only if the bipartite complement of g is a tree of diameter at most 3 we also investigate the regularity of linearly presented toric edge ideals and give criteria for polyomino ideals to satisfy the green lazarsfeld conditions

higher linear syzygies of inner projections let x pr be a smooth projective variety embedded by the complete linear system associated to a very ample line bundle l on x in this paper we prove that if x satisfies property np for p 1 then every isomorphic inner projection x pr 1 of x satisfies np 1 we also give some applications of our results to various examples

global existence and asymptotic behavior of solutions for the maxwell schrodinger equations in three space dimensions in this paper we study the global existence and asymptotic behavior of solutions for the maxwell schrodinger equations under the coulomb gauge condition in three space dimensions with the final states given att this leads to the construction of the modified wave operator for certain scattered data it is also shown that for the initial data in the range of the modified wave operator the initial value problem of the maxwell schrodinger equations has the global solutions in time

dispersive estimates for principally normal pseudodifferential operators the aim of these notes is to describe some recent re sults concerning dispersive estimates for principally normal pseu dodifferential operators the main motivation for this comes from unique continuation problems such estimates can be used to prove l q carleman inequalities which in turn yield unique continuation results for various partial differential operators with rough poten tials dispersive estimates are l q estimates for nonelliptic partial differ ential operators which are a consequence of the decay properties of their fundamental solutions these decay properties follow from spa tial spreading of the singularities of the solutions since solutions prop agate in directions conormal to the characteristic set of the operator this spreading can be related to nonzero curvatures of the characteristic set dispersive estimates for constant coefficient operators are closely related to the restriction theorem in harmonic analysis various types of dispersive estimates are known to be true for op erators such as the wave operator the schrodinger operator and the linear kdv see ginibre velo 4 keel tao 11 they have proved to be useful in the study of nonlinear problems as well as of problems with unbounded potentials more recently similar estimates have been obtained for wave op erators with variable coefficients beginning with the smooth case in kapitanskii 10 mockenhaupt seeger and sogge 14 up to operators with c 2 coefficients in smith 15 and tataru 21 23 similar results were obtained for the schrodinger equation in staffilani tataru 19 c 2 coefficients and in burq gerard tzvetkov 1 smooth coeffic ients in the variable coefficient elliptic case one should also mention sogge s l q

some results on rational surfaces and fano varieties this is the publisher s version also available electronically from http www degruyter com view j crll 2001 2001 issue 538 crll 2001 068 crll 2001 068 xml

large data well posedness in the energy space of the chern simons schrodinger system abstract we consider the initial value problem for the chern simons schrodinger system which is a gauge covariant schrodinger system in r t r x 2 with a long range electromagnetic field we show that in the coulomb gauge it is locally well posed in h s for s 1 and the solution map satisfies a local in time weak lipschitz bound by energy conservation we also obtain a global regularity result the key is to retain the non perturbative part of the derivative nonlinearity in the principal operator and exploit the dispersive properties of the resulting paradifferential type principal operator using adapted u p and v p spaces

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

on syzygies of non complete embedding of projective varieties let x be a non degenerate not necessarily linearly normal projective variety in mathbb p r recently the generalization of property np to non linearly normal projective varieties have been considered and its algebraic and geometric properties are studied extensively one of the generalizations is the property nd p for the saturated ideal ix eisenbud et al in compos math 141 1460 1478 2005 and the other is the property n p s for the graded module of the twisted global sections of mathcal o x 1 kwak and park in j reine angew math 582 87 105 2005 in this paper we are interested in the algebraic and geometric meaning of properties n p s for every p 0 and the syzygetic behaviors of isomorphic projections and hyperplane sections of a given variety with property n p s

a castelnuovo mumford regularity bound for scrolls abstract let x p r be a scroll of codimension e and degree d over a smooth projective curve of genus g the purpose of this paper is to prove a linear castelnuovo mumford regularity bound that reg x d e 1 g e 1 this bound works over an algebraically closed field of arbitrary characteristic

graded mapping cone theorem multisecants and syzygies abstract let x be a reduced closed subscheme in p n as a slight generalization of property n p due to green lazarsfeld one says that x satisfies property n 2 p scheme theoretically if there is an ideal i generating the ideal sheaf i x p n such that i is generated by quadrics and there are only linear syzygies up to p th step cf eisenbud et al 2005 8 vermeire 2001 20 recently many algebraic and geometric results have been proved for projective varieties satisfying property n 2 p cf choi kwak and park 2008 6 eisenbud et al 2005 8 kwak and park 2005 15 in this case the castelnuovo regularity and normality can be obtained by the blowing up method as reg x e 1 where e is the codimension of a smooth variety x cf bertram ein and lazarsfeld 2003 3 on the other hand projection methods have been very useful and powerful in bounding castelnuovo regularity normality and other classical invariants in geometry cf beheshti and eisenbud 2010 2 kwak 1998 14 kwak and park 2005 15 lazarsfeld 1987 16 we first prove the graded mapping cone theorem on partial eliminations as a general algebraic tool to study syzygies of the non complete embedding of x for applications we give an optimal bound on the length of zero dimensional intersections of x and a linear space l in terms of graded betti numbers we also deduce several theorems about the relationship between x and its projections with respect to the geometry and syzygies for a projective scheme x satisfying property n 2 p scheme theoretically in addition we give not only interesting information on the regularity of fibers of the projection for the case of n d p d 2 but also geometric structures for projections according to moving the center

pose determination from line to plane correspondences existence condition and closed form solutions a class of pose determination problems in which the sensory data are lines and the corresponding reference data are planes is discussed the lines considered are different from edge lines in that they are not the intersection of boundary faces of the object the author describes a polynomial approach that does not require a priori knowledge about the object location closed form solutions for orthogonal parallel and coplanar feature configurations of critical importance in real applications are derived findings concerning the necessary and sufficient conditions under which the line to plane pose determination problem can be solved are described

regularity of modules over a koszul algebra abstract we prove that every module over a commutative homogeneous koszul algebra has regularity bounded by its regularity over a polynomial ring of which the koszul algebra is a homomorphic image from this we derive a result conjectured by george kempf to the effect that a sufficiently high truncation of any module over a homogeneous koszul algebra has a linear free resolution

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

determination of the attitude of 3d objects from a single perspective view a method for finding analytical solutions to the problem of determining the attitude of a 3d object in space from a single perspective image is presented its principle is based on the interpretation of a triplet of any image lines as the perspective projection of a triplet of linear ridges of the object model and on the search for the model attitude consistent with these projections the geometrical transformations to be applied to the model to bring it into the corresponding location are obtained by the resolution of an eight degree equation in the general case using simple logical rules it is shown on examples related to polyhedra that this approach leads to results useful for both location and recognition of 3d objects because few admissible hypotheses are retained from the interpolation of the three line segments line matching by the prediction verification procedure is thus less complex

on higher syzygies of ruled surfaces ii abstract in this article we continue the study of property n p of irrational ruled surfaces begun in e park on higher syzygies of ruled surfaces math ag 0401100 trans amer math soc in press let x be a ruled surface over a curve of genus g 1 with a minimal section c 0 and the numerical invariant e when x is an elliptic ruled surface with e 1 it is shown in f j gallego b p purnaprajna higher syzygies of elliptic ruled surfaces j algebra 186 1996 626 659 that there is a smooth elliptic curve e x such that e 2 c 0 f and we prove that if l pic x is in the numerical class of a c 0 b f and satisfies property n p then c l c 0 and e l e satisfy property n p and hence a b 3 p and a 2 b 3 p this gives a proof of the relevant part of gallego purnaprajna conjecture in f j gallego b p purnaprajna higher syzygies of elliptic ruled surfaces j algebra 186 1996 626 659 when g 2 and e 0 we prove some effective results about property n p let l pic x be a line bundle in the numerical class of a c 0 b f our main result is about the relation between higher syzygies of x l and those of c l c where l c is the restriction of l to c 0 in particular we show the followings 1 if e g 2 and b a e 3 g 2 then l satisfies property n p if and only if b a e 2 g 1 p 2 when c is a hyperelliptic curve of genus g 2 l is normally generated if and only if b a e 2 g 1 and normally presented if and only if b a e 2 g 2 also if e g 2 then l satisfies property n p if and only if a 1 and b a e 2 g 1 p

on syzygies of calabi yau varieties and varieties of general type abstract we establish projective normality property n p and effective very ampleness for line bundles on a calabi yau variety as well as for pluricanonical bundles of a variety of general type we also prove a result on the degrees of generators of canonical rings under the condition that the image of the canonical map has minimal degree

smooth varieties of almost minimal degree abstract in this article we study non linearly normal smooth projective varieties x p r of deg x codim x p r 2 we first give geometric characterizations for x theorem 1 1 indeed x is the image of an isomorphic projection of smooth varieties x p r 1 of minimal degree also if x is not the veronese surface then there exists a smooth rational normal scroll y p r which contains x as a divisor linearly equivalent to h 2 f where h is the hyperplane section of y and f is a fiber of the projection morphism y p 1 by using these characterizations 1 we determine all the possible types of y from the type of x theorem 1 2 and 2 we investigate the relation between the betti diagram of x and the type of y theorem 1 3 in particular we clarify the relation between the number of generators of the homogeneous ideal of x and the type of y as an application we construct non linearly normal examples where the converse to theorem 1 1 in d eisenbud m green k hulek s popescu restriction linear syzygies algebra and geometry compos math 141 2005 1460 1478 fails to hold remark 2

newton okounkov bodies on projective bundles over curves in this article we study newton okounkov bodies on projective vector bundles over curves inspired by wolfe s estimates used to compute the volume function on these varieties we compute all newton okounkov bodies with respect to linear flags moreover we characterize semi stable vector bundles over curves via newton okounkov bodies

four points in two or three calibrated views theory and practice suppose two perspective views of four world points are given and that the intrinsic parameters are known but the camera poses and the world point positions are not we prove that the epipole in each view is then constrained to lie on a curve of degree ten we derive the equation for the curve and establish many of the curve s properties for example we show that the curve has four branches through each of the image points and that it has four additional points on each conic of the pencil of conics through the four image points we show how to compute the four curve points on each conic in closed form we show that orientation constraints allow only parts of the curve and find that there are impossible configurations of four corresponding point pairs we give a novel algorithm that solves for the essential matrix given three corresponding points and one of the epipoles we then use the theory to create the most efficient solution yet to the notoriously difficult problem of solving for the pose of three views given four corresponding points the solution is a search over a one dimensional parameter domain where each point in the search can be evaluated in closed form the intended use for the solution is in a hypothesise and test architecture to solve for structure and motion

normal presentation on elliptic ruled surfaces from the introduction let x be an irreducible projective variety and l a very ample lline bundle on x whose complete linear series defines l x p h0 l let s 1 m 0 smh0 x l and let r l l1 n 0 h0 x l n be the homogeneous coordinate ring associated to l then r is a finitely generated graded module over s so it has a minimal graded free resolution we say that the line bundle l is normally generated if the natural maps smh0 x l h0 x l m are surjective for all m 2 if l is normally generated then we say that l satisfies property np if the matrices in the free resolution of r over s have linear entries until the p th stage in particular property n1 says that the homogeneous ideal i of x in p h0 l is generated by quadrics a line bundle satisfying property n1 is also called normally presented let r kr1r2 be a graded algebra over a field k the algebra r is a koszul ring iff torri k k has pure degree i for all i in this article we determine exactly theorem 4 2 which line bundles on an elliptic ruled surface x are normally presented as a corollary we show that mukai s conjecture is true for the normal presentation of the adjoint linear series for an elliptic ruled surface in section 5 of this article we show that if l is normally presented on x then the homogeneous coordinate ring associated to l is koszul we also give a new proof of the following result due to butler if deg l 2g 2 on a curve x of genus g then l embeds x with koszul homogeneous coordinate ring

smooth projective varieties with extremal or next to extremal curvilinear secant subspaces we intend to give a classification of smooth nondegenerate projective varieties admitting extremal or next to extremal curvilinear secant subspaces gruson lazarsfeld and peskine classified all projective integral curves with extremal secant lines on the other hand if a locally cohen macaulay variety x p n e of degree d meets with a linear subspace l of dimension at finite points then length x l d e as a finite scheme a linear subspace l for which the above length attains maximal possible value is called an extremal secant subspace and such l for which length x l d e 1 is called a next to extremal secant subspace in this paper we show that if a smooth variety x of degree d 6 has extremal or next to extremal curvilinear secant subspaces then it is either del pezzo or a scroll over a curve of genus g 1 this generalizes the results of gruson lazarsfeld and peskine 1983 for curves and the work of m a bertin 2002 who classified smooth higher dimensional varieties with extremal secant lines this is also motivated and closely related to establishing an upper bound for the castelnuovo mumford regularity and giving a classification of the varieties on the boundary

on higher syzygies of ruled surfaces we study higher syzygies of a ruled surface x over a curve of genus g with the numerical invariant e let l picx be a line bundle in the numerical class of ac 0 bf we prove that for 0 2g 1 p by using these facts we obtain mukai type results for ample line bundles at we show that k x a 1 a q satisfies property np when 0 e g 3 2 and q g 2e 1 p or when e g 3 2 and g p 4 therefore we prove mukai s conjecture for ruled surface with e g 3 2 we also prove that when x is an elliptic ruled surface with e 0 l satisfies property n p if and only if a 1 and b ae 3 p

long range scattering for the maxwell schrodinger system in the lorenz gauge without any restriction on the size of data abstract this paper concerns the scattering theory for the maxwell schrodinger ms system in the lorenz gauge or more precisely the existence of the modified wave operators for this system in r 3 1 space time we construct solutions to the ms system which behave as free maxwell and schrodinger waves with prescribed asymptotic states when t without any restriction on the size thereof since this system belongs to the borderline between the short range case and the long range case we need modification of phase for the schrodinger function

analysis on some infinite modules inner projection and applications a projective scheme x is called quadratic if x is scheme theoretically cut out by homogeneous equations of degree 2 furthermore we say that x satisfies property n2 p if it is quadratic and the quadratic ideal has only linear syzygies up to the first p th steps in the present paper we compare the linear syzygies of the inner projections with those of x and obtain a theorem on embedded linear syzygies as one of our main results this is the natural projection analogue of restricting linear syzygies in the linear section case as an immediate corollary we show that the inner projections of x satisfy property n2 p 1 for any reduced scheme x with property n2 p moreover we also obtain the neccessary lower bound codimx p p p 1 2 which is sharp on the number of quadrics vanishing on x in order to satisfy n2 p and show that the arithmetic depths of inner projections are equal to that of the quadratic scheme x these results admit an interesting syzygetic rigidity theorem on property n2 p which leads the classifications of extremal and next to extremal cases for these results we develop the elimination mapping cone theorem for infinitely generated graded modules and improve the partial elimination ideal theory initiated by m green this new method allows us to treat a wider class of projective schemes which cannot be covered by the koszul cohomology techniques because these are not projectively normal in general

on the projective normality and normal presentation on higher dimensional varieties with nef canonical bundle abstract in this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle as one of the consequences of the main theorem we give bounds on very ampleness and projective normality of pluricanonical linear systems on varieties of general type in dimensions three four and five these improve known such results

some effects of property n p on the higher normality and defining equations of nonlinearly normal varieties for a smooth projective variety x p embedded by the complete linear system property np has been studied for a long time 5 11 12 10 etc on the other hand castelnuovo mumford regularity conjecture and related problems have been focused for a projective variety which is not necessarily linearly normal 2 13 15 17 20 etc this paper aims to explain the influence of property np on higher normality and defining equations of a smooth variety embedded by sub linear system also we prove a claim about property np of surface scrolls which is a generalization of green s work in 11 about property np for curves

very ampleness and higher syzygies for calabi yau threefolds the authors prove various results concerning multiples of ample base point free linear systems on calabi yau threefolds suppose that b is an ample divisor on a calabi yau threefold x and that b has no base points then the authors prove that 3b is very ample and embeds x as a projectively normal variety if and only if b does not map x 2 1 onto p3 similarly they prove that 2b enjoys the same properties if and only if b does not map x onto a variety of minimal degree other than p3 nor maps x 2 1 onto p3 further results are proved giving conditions for when the linear system nb satisfies the condition np

accurately estimating rigid transformations in registration using a boosting inspired mechanism feature extraction and matching provide the basis of many methods for object registration modeling retrieval and recognition however this approach typically introduces false matches due to lack of features noise occlusion and cluttered backgrounds in registration these false matches lead to inaccurate estimation of the underlying transformation that brings the overlapping shapes into best possible alignment in this paper we propose a novel boosting inspired method to tackle this challenging task it includes three key steps i underlying transformation estimation in the weighted least squares sense ii boosting parameter estimation and regularization via tsallis entropy and iii weight re estimation and regularization via shannon entropy and update with a maximum fusion rule the process is iterated the final optimal underlying transformation is estimated as a weighted average of the transformations estimated from the latest iterations with weights given by the boosting parameters a comparative study based on real shape data shows that the proposed method outperforms four other state of the art methods for evaluating the established point matches enabling more accurate and stable estimation of the underlying transformation highlightswe provide a novel method for evaluating point matches established by typical methods real data based experimental results show that the method outperforms the state of the art under certain conditions the finally estimated underlying transformation is optimal the transformation can be recovered with an error as small as 5 from typical point matches

global wellposedness in the energy space for the maxwell schrodinger system we prove that the maxwell schrodinger system in mathbb r 3 1 is globally well posed in the energy space the key element of the proof is to obtain a short time wave packet parametrix for the magnetic schrodinger equation which leads to linear bilinear and trilinear estimates these in turn are extended to larger time scales via a bootstrap argument

a theory of minimal 3d point to 3d plane registration and its generalization registration of 3d data is a key problem in many applications in computer vision computer graphics and robotics this paper provides a family of minimal solutions for the 3d to 3d registration problem in which the 3d data are represented as points and planes such scenarios occur frequently when a 3d sensor provides 3d points and our goal is to register them to a 3d object represented by a set of planes in order to compute the 6 degrees of freedom transformation between the sensor and the object we need at least six points on three or more planes we systematically investigate and develop pose estimation algorithms for several configurations including all minimal configurations that arise from the distribution of points on planes we also identify the degenerate configurations in such registrations the underlying algebraic equations used in many registration problems are the same and we show that many 2d to 3d and 3d to 3d pose estimation registration algorithms involving points lines and planes can be mapped to the proposed framework we validate our theory in simulations as well as in three real world applications registration of a robotic arm with an object using a contact sensor registration of planar city models with 3d point clouds obtained using multi view reconstruction and registration between depth maps generated by a kinect sensor

a bound for castelnuovo mumford regularity by double point divisors abstract let x p r be a non degenerate smooth projective variety of dimension n codimension e and degree d defined over an algebraically closed field of characteristic zero in this paper we first show that reg o x d e and classify the extremal and the next to extremal cases our result reduces the eisenbud goto regularity conjecture for the smooth case to the problem finding a castelnuovo type bound for normality it is worth noting that mccullough peeva recently constructed counterexamples to the regularity conjecture by showing that reg o x is not even bounded above by any polynomial function of d when x is not smooth for a normality bound in the smooth case we establish that reg x n d 2 1 which improves previous results obtained by mumford bertram ein lazarsfeld and noma finally by generalizing mumford s method on double point divisors we prove that reg x d 1 m where m is an invariant arising from double point divisors associated to outer general projections using double point divisors associated to inner projections we also obtain a slightly better bound for reg x under suitable assumptions

review and analysis of solutions of the three point perspective pose estimation problem in this paper the major direct solutions to the three point perspective pose estimation problems are reviewed from a unified perspective beginning with the first solution which was published in 1841 by a german mathematician continuing through the solutions published in the german and then american photogrammetry literature and most recently in the current computer vision literature the numerical stability of these three point perspective solutions are also discussed we show that even in case where the solution is not near the geometric unstable region considerable care must be exercised in the calculation depending on the order of the substitutions utilized the relative error can change over a thousand to one this difference is due entirely to the way the calculations are performed and not due to any geometric structural instability of any problem instance we present an analysis method which produces a numerically stable calculation

the regularity of partial elimination ideals castelnuovo normality and syzygies abstract let x be a reduced closed subscheme in p n x x p n 1 be a projection from a point outside x and z i x x be the closed subscheme defined by the i th partial elimination ideal k i i x which is supported on the i 1 th multiple points of in this paper motivated from projection methods to prove eisenbud goto conjecture on regularity in many cases we describe the syzygetic behaviors and castelnuovo normality of the projection with a viewpoint of the regularity of the partial elimination ideal k i i x i 1 or that of the multiple locus z i x of we also give some applications to the syzygies and castelnuovo normality of successive projections which recover and generalize some known results in 1 3 15 16