skeleton search category specific object recognition and segmentation using a skeletal shape model we describe a top down object detection and segmentation approach that uses a skeleton based shape model and that works directly on real images the approach is based on three components first we propose a fragment based generative model for shape that is based on the shock graph and has minimal dependency among its shape fragments the model is capable of generating a wide variation of shapes as instances of a given object category second we develop a progressive selection mechanism to search among the generated shapes for the category instances that are present in the image the search begins with a large pool of candidates identified by a dynamic programming dp algorithm and progressively reduces it in size by applying series of criteria namely local minimum criterion extent of shape overlap and thresholding of the objective function to select the final object candidates third we propose the partitioned chamfer matching pcm measure to capture the support of image edges for a hypothesized shape this measure overcomes the shortcomings of the oriented chamfer matching and is robust against spurious edges missing edges and accidental alignment between the image edges and the shape boundary contour we have evaluated our approach on the ethz dataset and found it to perform well in both object detection and object segmentation tasks

a shape reconstructability measure of object part importance with applications to object detection and localization we propose a computational model which computes the importance of 2 d object shape parts and we apply it to detect and localize objects with and without occlusions the importance of a shape part a localized contour fragment is considered from the perspective of its contribution to the perception and recognition of the global shape of the object accordingly the part importance measure is defined based on the ability to estimate recall the global shapes of objects from the local part namely the part s shape reconstructability more precisely the shape reconstructability of a part is determined by two factors part variation and part uniqueness i part variation measures the precision of the global shape reconstruction i e the consistency of the reconstructed global shape with the true object shape and ii part uniqueness quantifies the ambiguity of matching the part to the object i e taking into account that the part could be matched to the object at several different locations taking both these factors into consideration an information theoretic formulation is proposed to measure part importance by the conditional entropy of the reconstruction of the object shape from the part experimental results demonstrate the benefit with the proposed part importance in object detection including the improvement of detection rate localization accuracy and detection efficiency by comparing with other state of the art object detectors in a challenging but common scenario object detection with occlusions we show a considerable improvement using the proposed importance measure with the detection rate increased over 10 10 on a subset of the challenging pascal dataset the interpolated average precision as used in the pascal voc challenge is improved by 4 8 moreover we perform a psychological experiment which provides evidence suggesting that humans use a similar measure for part importance when perceiving and recognizing shapes

shape based object detection via boundary structure segmentation we address the problem of object detection and segmentation using global holistic properties of object shape global shape representations are highly susceptible to clutter inevitably present in realistic images and thus can be applied robustly only using a precise segmentation of the object to this end we propose a figure ground segmentation method for extraction of image regions that resemble the global properties of a model boundary structure and are perceptually salient our shape representation called the chordiogram is based on geometric relationships of object boundary edges while the perceptual saliency cues we use favor coherent regions distinct from the background we formulate the segmentation problem as an integer quadratic program and use a semidefinite programming relaxation to solve it the obtained solutions provide a segmentation of the object as well as a detection score used for object recognition our single step approach achieves state of the art performance on several object detection and segmentation benchmarks

a graduated assignment algorithm for graph matching a graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise by combining graduated nonconvexity two way assignment constraints and sparsity large improvements in accuracy and speed are achieved its low order computational complexity o lm where l and m are the number of links in the two graphs and robustness in the presence of noise offer advantages over traditional combinatorial approaches the algorithm not restricted to any special class of graph is applied to subgraph isomorphism weighted graph matching and attributed relational graph matching to illustrate the performance of the algorithm attributed relational graphs derived from objects are matched then results from twenty five thousand experiments conducted on 100 mode random graphs of varying types graphs with only zero one links weighted graphs and graphs with node attributes and multiple link types are reported no comparable results have been reported by any other graph matching algorithm before in the research literature twenty five hundred control experiments are conducted using a relaxation labeling algorithm and large improvements in accuracy are demonstrated

comparing images using the hausdorff distance the hausdorff distance measures the extent to which each point of a model set lies near some point of an image set and vice versa thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another efficient algorithms for computing the hausdorff distance between all possible relative positions of a binary image and a model are presented the focus is primarily on the case in which the model is only allowed to translate with respect to the image the techniques are extended to rigid motion the hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived the method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods it is shown that the method extends naturally to the problem of comparing a portion of a model against an image

groups of adjacent contour segments for object detection we present a family of scale invariant local shape features formed by chains of k connected roughly straight contour segments kas and their use for object class detection kas are able to cleanly encode pure fragments of an object boundary without including nearby clutter moreover they offer an attractive compromise between information content and repeatability and encompass a wide variety of local shape structures we also define a translation and scale invariant descriptor encoding the geometric configuration of the segments within a kas making kas easy to reuse in other frameworks for example as a replacement or addition to interest points ips software for detecting and describing kas is released at http lear inrialpes fr software we demonstrate the high performance of kas within a simple but powerful sliding window object detection scheme through extensive evaluations involving eight diverse object classes and more than 1 400 images we 1 study the evolution of performance as the degree of feature complexity k varies and determine the best degree 2 show that kas substantially outperform ips for detecting shape based classes and 3 compare our object detector to the recent state of the art system by dalal and triggs 2005

robust object detection with interleaved categorization and segmentation this paper presents a novel method for detecting and localizing objects of a visual category in cluttered real world scenes our approach considers object categorization and figure ground segmentation as two interleaved processes that closely collaborate towards a common goal as shown in our work the tight coupling between those two processes allows them to benefit from each other and improve the combined performance the core part of our approach is a highly flexible learned representation for object shape that can combine the information observed on different training examples in a probabilistic extension of the generalized hough transform the resulting approach can detect categorical objects in novel images and automatically infer a probabilistic segmentation from the recognition result this segmentation is then in turn used to again improve recognition by allowing the system to focus its efforts on object pixels and to discard misleading influences from the background moreover the information from where in the image a hypothesis draws its support is employed in an mdl based hypothesis verification stage to resolve ambiguities between overlapping hypotheses and factor out the effects of partial occlusion an extensive evaluation on several large data sets shows that the proposed system is applicable to a range of different object categories including both rigid and articulated objects in addition its flexible representation allows it to achieve competitive object detection performance already from training sets that are between one and two orders of magnitude smaller than those used in comparable systems

shape based detection and top down delineation using image segments we introduce a segmentation based detection and top down figure ground delineation algorithm unlike common methods which use appearance for detection our method relies primarily on the shape of objects as is reflected by their bottom up segmentation our algorithm receives as input an image along with its bottom up hierarchical segmentation the shape of each segment is then described both by its significant boundary sections and by regional dense orientation information derived from the segment s shape using the poisson equation our method then examines multiple overlapping segmentation hypotheses using their shape and color in an attempt to find a coherent whole i e a collection of segments that consistently vote for an object at a single location in the image once an object is detected we propose a novel pixel level top down figure ground segmentation by competitive coverage process to accurately delineate the boundaries of the object in this process given a particular detection hypothesis we let the voting segments compete for interpreting covering each of the semantic parts of an object incorporating competition in the process allows us to resolve ambiguities that arise when two different regions are matched to the same object part and to discard nearby false regions that participated in the voting process we provide quantitative and qualitative experimental results on challenging datasets these experiments demonstrate that our method can accurately detect and segment objects with complex shapes obtaining results comparable to those of existing state of the art methods moreover our method allows us to simultaneously detect multiple instances of class objects in images and to cope with challenging types of occlusions such as occlusions by a bar of varying size or by another object of the same class that are difficult to handle with other existing class specific top down segmentation methods

algebras associated to elliptic curves this paper completes the classification of artin schelter regular algebras of global dimension three for algebras generated by elements of degree one this has been achieved by artin schelter tate and van den bergh we are therefore concerned with algebras which are not generated in degree one we show that there exist some exceptional algebras each of which has geometric data consisting of an elliptic curve together with an automorphism just as in the case where the algebras are assumed to be generated in degree one in particular we study the elliptic algebras a a and a a where a p2 which were first defined in an earlier paper we omit a set s p2 consisting of 11 specified points where the algebras a a become too degenerate to be regular theorem let a represent a a or a a where a p2 s then a is an artin schelter regular algebra of global dimension three moreover a is a noetherian domain with the same hilbert series as the appropriately graded commutative polynomial ring in three variables this combined with our earlier results completes the classification

the normalized numerical range and the davis wielandt shell abstract for a given n by n matrix a its normalized numerical range f n a is defined as the range of the function f n a x x a x a x x on the complement of ker a we provide an explicit description of this set for the case when a is normal or n 2 this extension of earlier results for particular cases of 2 by 2 matrices by gevorgyan and essentially hermitian matrices of arbitrary size by a stoica and one of the authors was achieved due to the fresh point of view at f n a as the image of the davis wielandt shell dw a under a certain non linear mapping h r 3 c

sacoseg object cosegmentation by shape conformability in this paper an object cosegmentation method based on shape conformability is proposed different from the previous object cosegmentation methods which are based on the region feature similarity of the common objects in image set our proposed sacoseg cosegmentation algorithm focuses on the shape consistency of the foreground objects in image set in the proposed method given an image set where the implied foreground objects may be varied in appearance but share similar shape structures the implied common shape pattern in the image set can be automatically mined and regarded as the shape prior of those unsatisfactorily segmented images the sacoseg algorithm mainly consists of four steps 1 the initial grabcut segmentation 2 the shape mapping by coherent point drift registration 3 the common shape pattern discovery by affinity propagation clustering and 4 the refinement by grabcut with common shape constraint to testify our proposed algorithm and establish a benchmark for future work we built the coshape data set to evaluate the shape based cosegmentation the experiments on coshape data set and the comparison with some related cosegmentation algorithms demonstrate the good performance of the proposed sacoseg algorithm

shape classification using the inner distance part structure and articulation are of fundamental importance in computer and human vision we propose using the inner distance to build shape descriptors that are robust to articulation and capture part structure the inner distance is defined as the length of the shortest path between landmark points within the shape silhouette we show that it is articulation insensitive and more effective at capturing part structures than the euclidean distance this suggests that the inner distance can be used as a replacement for the euclidean distance to build more accurate descriptors for complex shapes especially for those with articulated parts in addition texture information along the shortest path can be used to further improve shape classification with this idea we propose three approaches to using the inner distance the first method combines the inner distance and multidimensional scaling mds to build articulation invariant signatures for articulated shapes the second method uses the inner distance to build a new shape descriptor based on shape contexts the third one extends the second one by considering the texture information along shortest paths the proposed approaches have been tested on a variety of shape databases including an articulated shape data set mpeg7 ce shape 1 kimia silhouettes the eth 80 data set two leaf data sets and a human motion silhouette data set in all the experiments our methods demonstrate effective performance compared with other algorithms

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

an eigendecomposition approach to weighted graph matching problems an approximate solution to the weighted graph matching problem is discussed for both undirected and directed graphs the weighted graph matching problem is that of finding the optimum matching between two weighted graphs which are graphs with weights at each arc the proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem using the eigendecompositions of the adjacency matrices in the case of the undirected graph matching problem or hermitian matrices derived from the adjacency matrices in the case of the directed graph matching problem a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other simulation results are given to evaluate the performance of the proposed method

twisted multi homogeneous coordinate rings abstract artin and van den bergh have constructed noncommutative analogues of the homogeneous coordinate ring of a projective scheme we generalize their results to the multiprojective setting such multi homogeneous coordinate rings include tensor products of twisted homogeneous coordinate rings as well as their rees algebras finally we show that these last two examples are noetherian assuming ampleness conditions though the coordinate ring in general is not

segmentation registration and measurement of shape variation via image object shape a model of object shape by nets of medial and boundary primitives is justified as richly capturing multiple aspects of shape and yet requiring representation space and image analysis work proportional to the number of primitives metrics are described that compute an object representation s prior probability of local geometry by reflecting variabilities in the net s node and link parameter values and that compute a likelihood function measuring the degree of match of an image to that object representation a paradigm for image analysis of deforming such a model to optimize a posteriori probability is described and this paradigm is shown to be usable as a uniform approach for object definition object based registration between images of the same or different imaging modalities and measurement of shape variation of an abnormal anatomical object compared with a normal anatomical object examples of applications of these methods in radiotherapy surgery and psychiatry are given

shape matching and object recognition using shape contexts we present a novel approach to measuring similarity between shapes and exploit it for object recognition in our framework the measurement of similarity is preceded by 1 solving for correspondences between points on the two shapes 2 using the correspondences to estimate an aligning transform in order to solve the correspondence problem we attach a descriptor the shape context to each point the shape context at a reference point captures the distribution of the remaining points relative to it thus offering a globally discriminative characterization corresponding points on two similar shapes will have similar shape contexts enabling us to solve for correspondences as an optimal assignment problem given the point correspondences we estimate the transformation that best aligns the two shapes regularized thin plate splines provide a flexible class of transformation maps for this purpose the dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points together with a term measuring the magnitude of the aligning transform we treat recognition in a nearest neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image results are presented for silhouettes trademarks handwritten digits and the coil data set

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

between the von neumann inequality and the crouzeix conjecture abstract a new concept of a deformed numerical range w t is introduced here t is a bounded linear operator or a matrix and 1 is a parameter each w t is a closed convex set that contains the spectrum of t furthermore w t is decreasing with respect to and w 2 t coincides with the numerical range it is also shown that w t is contained in the closed unit disc if and only if t has a unitary dilation in the sense of nagy foias the spectral constant of w t is investigated it is shown that it is monotone and continuous with respect to the parameter

ample filters of invertible sheaves abstract let x be a scheme proper over a commutative noetherian ring a we introduce the concept of an ample filter of invertible sheaves on x and generalize the most important equivalent criteria for ampleness of an invertible sheaf we also prove the theorem of the base for x and generalize serre s vanishing theorem we then generalize results for twisted homogeneous coordinate rings which were previously known only when x was projective over an algebraically closed field specifically we show that the concepts of left and right ampleness are equivalent and that the associated twisted homogeneous coordinate ring must be noetherian

parameter free modelling of 2d shapes with ellipses our goal is to represent a given 2d shape with an automatically determined number of ellipses so that the total area covered by the ellipses is equal to the area of the original shape without any assumption or prior knowledge about the object structure to solve this interesting theoretical problem first we employ the skeleton of the 2d shape which provides important information on the parameters of the ellipses that could approximate the original shape for a given number of such ellipses the hard expectation maximisation em algorithm is employed to maximise the shape coverage under the equal area constraint different models i e solutions involving different numbers of ellipses are evaluated based on the akaike information criterion aic this considers a novel entropy based shape complexity measure that balances the model complexity and the model approximation error in order to minimise the aic criterion two variants are proposed and evaluated a the augmentative method that gradually increases the number of considered ellipses starting from a single one and b the decremental method that decreases the number of ellipses starting from a large automatically defined set the obtained quantitative results on more than 4000 2d shapes included in standard as well as in custom datasets quantify the performance of the proposed methods and illustrate that their solutions agree with human intuition highlights2d shape representation with an automatically determined number of ellipses we propose a novel definition of shape complexity that exploits the shape skeleton good balance between model complexity and shape coverage experiments on more than 4000 2d shapes show the effectiveness of the proposed methods the solutions proposed by aefa and defa seem to agree with human intuition

noncommutative graded domains with quadratic growth letk be an algebraically closed field and letr be a finitely generated connected gradedk algebra which is a domain of gelfand kirillov dimension two write the graded quotient ringq r ofr asd z z 1 for some automorphism of the division ringd we prove thatd is a finitely generated field extension ofk of transcendence degree one moreover we describer in terms of geometric data ifr is generated in degree one then up to a finite dimensional vector space r is isomorphic to the twisted homogeneous coordinate ring of an invertible sheaf over a projective curvey this implies in particular thatr is noetherian thatr is primitive when and thatr is a finite module over its centre when ifr is not generated in degree one thenr will still be noetherian and primitive if has infinite order butr need not be noetherian when has finite order

noncommutative ampleness for multiple divisors abstract the twisted homogeneous coordinate ring is one of the basic constructions of the noncommutative projective geometry of artin van den bergh and others chan generalized this construction to the multi homogeneous case using a concept of right ampleness for a finite collection of invertible sheaves and automorphisms of a projective scheme from this he derives that certain multi homogeneous rings such as tensor products of twisted homogeneous coordinate rings are right noetherian we show that right and left ampleness are equivalent and that there is a simple criterion for such ampleness thus we find under natural hypotheses that multi homogeneous coordinate rings are noetherian and have integer gk dimension

shapes shocks and deformations i the components of two dimensional shape and the reaction diffusion space we undertake to develop a general theory of two dimensional shape by elucidating several principles which any such theory should meet the principles are organized around two basic intuitions first if a boundary were changed only slightly then in general its shape would change only slightly this leads us to propose an operational theory of shape based on incremental contour deformations the second intuition is that not all contours are shapes but rather only those that can enclose physical material a theory of contour deformation is derived from these principles based on abstract conservation principles and hamilton jacobi theory these principles are based on the work of sethian 1985a c the osher sethian 1988 level set formulation the classical shock theory of lax 1971 1973 as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of gage hamilton grayson 1986 1989 the result is a characterization of the computational elements of shape deformations parts bends and seeds which show where to place the components of a shape the theory unifies many of the diverse aspects of shapes and leads to a space of shapes the reaction diffusion space which places shapes within a neighborhood of similar ones such similarity relationships underlie descriptions suitable for recognition

shape similarity measure based on correspondence of visual parts a cognitively motivated similarity measure is presented and its properties are analyzed with respect to retrieval of similar objects in image databases of silhouettes of 2d objects to reduce influence of digitization noise as well as segmentation errors the shapes are simplified by a novel process of digital curve evolution to compute our similarity measure we first establish the best possible correspondence of visual parts without explicitly computing the visual parts then the similarity between corresponding parts is computed and aggregated we applied our similarity measure to shape matching of object contours in various image databases and compared it to well known approaches in the literature the experimental results justify that our shape matching procedure gives an intuitive shape correspondence and is stable with respect to noise distortions

convexity of the joint numerical range topological and differential geometric viewpoints abstract we investigate the convexity of the joint numerical range of m tuples of n n hermitian matrices the methods come from differential geometry and the differential and algebraic topology our main result is a sufficient condition for convexity of the joint numerical range for arbitrary m and n modulo a mild technical assumption this condition is formulated in terms of the largest eigenvalue of an associated family of hermitian matrices parameterized by the m 1 dimensional unit sphere the condition is that the eigenvalue has constant multiplicity we show that the constant multiplicity condition is in fact a criterion for the stable convexity of numerical ranges as a byproduct of our main result we obtain a new proof of the celebrated toeplitz hausdorff theorem and of its extension the numerical range of any triple of hermitian n n matrices is convex if n 2

geometric idealizer rings let b b x be the twisted homogeneous coordinate ring of a projective variety x over an algebraically closed field k we construct and investigate a large class of interesting and highly noncommutative noetherian subrings of b specifically let z be a closed subscheme of x and let i b be the corresponding right ideal of b we study the subalgebra r k i of b under mild conditions on z and aut k x r is the idealizer of i in b the maximal subring of b in which i is a two sided ideal our main result gives geometric conditions on z and that determine the algebraic properties of r we say that n z is critically transverse if for any closed subscheme y of z for n 0 the sub schemes y and n z are homologically transverse we show that if n z is critically transverse then r is left and right noetherian has finite left and right cohomological dimension is strongly right noetherian but not strongly left noetherian and satisfies right d where d codim z but fails left 1 this generalizes results of rogalski in the case that z is a point in d we also give an example of a right noetherian ring with infinite right cohomological dimension partially answering a question of stafford and van den bergh further we study the geometry of critical transversality and show that it is often generic behavior in a sense that we make precise