shape matching and object recognition using shape contexts

Shape Matching and Object

Recognition Using Shape Contexts Serge Belongie,Member,IEEE,Jitendra Malik,Member,IEEE,and Jan Puzicha

AbstractDWe present a novel approach to measuring similarity between shapes and exploit it for object recognition.In our

framework,the measurement of similarity is preceded by1)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.

Index TermsDShape,object recognition,digit recognition,correspondence problem,MPEG7,image registration,deformable templates.

?

1I NTRODUCTION

C ONSIDER the two handwritten digits in Fig.1.Regarded

as vectors of pixel brightness values and compared using L P norms,they are very different.However,regarded as shapes they appear rather similar to a human observer. Our objective in this paper is to operationalize this notion of shape similarity,with the ultimate goal of using it as a basis for category-level recognition.We approach this as a three-stage process:

1.solve the correspondence problembetween the two

shapes,

https://www.wendangku.net/doc/bb18285121.html,e the correspondences to estimate an aligning

transform,and

https://www.wendangku.net/doc/bb18285121.html,pute the distance between the two shapes as a

sumof m atching errors between corresponding

points,together with a term measuring the magni-

tude of the aligning transformation.

At the heart of our approach is a tradition of matching shapes by deformation that can be traced at least as far back as D'Arcy Thompson.In his classic work,On Growth and Form[55],Thompson observed that related but not identical shapes can often be deformed into alignment using simple coordinate transformations,as illustrated in Fig.2.In the computer vision literature,Fischler and Elschlager[15] operationalized such an idea by means of energy mini-mization in a mass-spring model.Grenander et al.[21] developed these ideas in a probabilistic setting.Yuille[61] developed another variant of the deformable template concept by means of fitting hand-crafted parametrized models,e.g.,for eyes,in the image domain using gradient descent.Another well-known computational approach in this vein was developed by Lades et al.[31]using elastic graph matching.

Our primary contribution in this work is a robust and simple algorithm for finding correspondences between shapes.Shapes are represented by a set of points sampled fromthe shape contours(typically100or so pixel locations sampled from the output of an edge detector are used). There is nothing special about the points.They are not required to be landmarks or curvature extrema,etc.;as we use more samples,we obtain better approximations to the underlying shape.We introduce a shape descriptor,the shape context,to describe the coarse distribution of the rest of the shape with respect to a given point on the shape. Finding correspondences between two shapes is then equivalent to finding for each sample point on one shape the sample point on the other shape that has the most similar shape context.Maximizing similarities and enfor-cing uniqueness naturally leads to a setup as a bipartite graph matching(equivalently,optimal assignment)pro-blem.As desired,we can incorporate other sources of matching information readily, e.g.,similarity of local appearance at corresponding points.

Given the correspondences at sample points,we extend the correspondence to the complete shape by estimating an aligning transformation that maps one shape onto the other.

.S.Belongie is with the Department of Computer Science and Engineering,

AP&M Building,Room4832,University of California,San Diego,La

Jolla,CA92093-0114.E-mail:sjb@https://www.wendangku.net/doc/bb18285121.html,.

.J.Malik is with the Computer Science Division,University of California at Berkeley,725Soda Hall,Berkeley,CA94720-1776.

E-mail:malik@https://www.wendangku.net/doc/bb18285121.html,.

.J.Puzicha is with RecomMind,Inc.,1001Camelia St.,Berkeley,CA

94710.E-mail:jan@https://www.wendangku.net/doc/bb18285121.html,.

Manuscript received09Apr.2001;revised13Aug.2001;accepted14Aug.

2001.

Recommended for acceptance by J.Weng.

For information on obtaining reprints of this article,please send e-mail to:

tpami@https://www.wendangku.net/doc/bb18285121.html,,and reference IEEECS Log Number113957.

0162-8828/02/$17.00?2002IEEE

A classic illustration of this idea is provided in Fig.2.The transformations can be picked from any of a number of familiesDwe have used Euclidean,affine,and regularized thin plate splines in various applications.Aligning shapes enables us to define a simple,yet general,measure of shape similarity.The dissimilarity between the two shapes can now be computed as a sum of matching errors between corresponding points,together with a termm easuring the magnitude of the aligning transform.

Given such a dissimilarity measure,we can use nearest-neighbor techniques for object recognition.Philo-sophically,nearest-neighbor techniques can be related to prototype-based recognition as developed by Rosch [47]and Rosch et al.[48].They have the advantage that a vector space structure is not requiredDonly a pairwise dissimilarity measure.

We demonstrate object recognition in a wide variety of settings.We deal with 2D objects,e.g.,the MNIST data set of handwritten digits (Fig.8),silhouettes (Figs.11and 13)and trademarks (Fig.12),as well as 3D objects from the Columbia COIL data set,modeled using multiple views (Fig.10).These are widely used benchmarks and our approach turns out to be the leading performer on all the problems for which there is comparative data.

We have also developed a technique for selecting the number of stored views for each object category based on its visual complexity.As an illustration,we show that for the 3D objects in the COIL-20data set,one can obtain as low as 2.5percent misclassification error using only an average of four views per object (see Figs.9and 10).

The structure of this paper is as follows:We discuss related work in Section 2.In Section 3,we describe our shape-matching method in detail.Our transformation model is presented in Section 4.We then discuss the problem of measuring shape similarity in Section 5and demonstrate our proposed measure on a variety of

databases including handwritten digits and pictures of 3D objects in Section 6.We conclude in Section 7.

2

P RIOR W ORK

ON

S HAPE M ATCHING

Mathematicians typically define shape as an equivalence class under a group of transformations.This definition is incomplete in the context of visual analysis.This only tells us when two shapes are exactly the same.We need more than that for a theory of shape similarity or shape distance.The statistician's definition of shape,e.g.,Bookstein [6]or Kendall [29],addresses the problemof shape distance,but assumes that correspondences are known.Other statistical approaches to shape comparison do not require correspon-dencesDe.g.,one could compare feature vectors containing descriptors such as area or momentsDbut such techniques often discard detailed shape information in the process.Shape similarity has also been studied in the psychology literature,an early example being Goldmeier [20].

An extensive survey of shape matching in computer vision can be found in [58],[22].Broadly speaking,there are two approaches:1)feature-based,which involve the use of spatial arrangements of extracted features such as edge elements or junctions,and 2)brightness-based,which make more direct use of pixel brightnesses.

2.1Feature-Based Methods

A great deal of research on shape similarity has been done using the boundaries of silhouette images.Since silhouettes do not have holes or internal markings,the associated boundaries are conveniently represented by a single-closed curve which can be parametrized by arclength.Early work used Fourier descriptors,e.g.,[62],[43].Blum's medial axis transformhas led to attem pts to capture the part structure of the shape in the graph structure of the skeleton by Kimia,Zucker and collaborators,e.g.,Sharvit et al.[53].The 1D nature of silhouette curves leads naturally to dynamic programming approaches for matching,e.g.,[17],which uses the edit distance between curves.This algorithmis fast and invariant to several kinds of transformation including some articulation and occlusion.A comprehensive comparison of different shape descriptors for comparing silhouettes was done as part of the MPEG-7standard activity [33],with the leading approaches being those due to Latecki et al.[33]and Mokhtarian et al.[39].

Fig.1.Examples of two handwritten digits.In terms of pixel-to-pixel comparisons,these two images are quite different,but to the human observer,the shapes appear to be

similar.

Fig.2.Example of coordinate transformations relating two fish,from D'Arcy Thompson's On Growth and Form [55].Thompson observed that similar biological forms could be related by means of simple mathematical transformations between homologous (i.e.,corresponding)features.Examples of homologous features include center of eye,tip of dorsal fin,etc.

Silhouettes are fundamentally limited as shape descrip-tors for general objects;they ignore internal contours and are difficult to extract from real images.More promising are approaches that treat the shape as a set of points in the 2D image.Extracting these from an image is less of a problemDe.g.,one can just use an edge detector.Hutten-locher et al.developed methods in this category based on the Hausdorff distance[23];this can be extended to deal with partial matching and clutter.A drawback for our purposes is that the method does not return correspon-dences.Methods based on Distance Transforms,such as [16],are similar in spirit and behavior in practice.

The work of Sclaroff and Pentland[50]is representative of the eigenvector-or modal-matching based approaches; see also[52],[51],[57].In this approach,sample points in the image are cast into a finite element spring-mass model and correspondences are found by comparing modes of vibration.Most closely related to our approach is the work of Gold et al.[19]and Chui and Rangarajan[9],which is discussed in Section3.4.

There have been several approaches to shape recognition based on spatial configurations of a small number of keypoints or landmarks.In geometric hashing[32],these configurations are used to vote for a model without explicitly solving for correspondences.Amit et al.[1]train decision trees for recognition by learning discriminative spatial configurations of keypoints.Leung et al.[35], Schmid and Mohr[49],and Lowe[36]additionally use gray-level information at the keypoints to provide greater discriminative power.It should be noted that not all objects have distinguished key points(think of a circle for instance),and using key points alone sacrifices the shape information available in smooth portions of object contours.

2.2Brightness-Based Methods

Brightness-based(or appearance-based)methods offer a complementary view to feature-based methods.Instead of focusing on the shape of the occluding contour or other extracted features,these approaches make direct use of the gray values within the visible portion of the object.One can use brightness information in one of two frameworks.

In the first category,we have the methods that explicitly find correspondences/alignment using grayscale values. Yuille[61]presents a very flexible approach in that invariance to certain kinds of transformations can be built into the measure of model similarity,but it suffers from the need for human-designed templates and the sensitivity to initialization when searching via gradient https://www.wendangku.net/doc/bb18285121.html,des et al.[31]use elastic graph matching,an approach that involves both geometry and photometric features in the formof local descriptors based on Gaussian derivative jets. Vetter et al.[59]and Cootes et al.[10]compare brightness values but first attempt to warp the images onto one another using a dense correspondence field.

The second category includes those methods that build classifiers without explicitly finding correspondences.In such approaches,one relies on a learning algorithmhaving enough examples to acquire the appropriate invariances.In the area of face recognition,good results were obtained using principal components analysis(PCA)[54],[56]particularly when used in a probabilistic framework[38].Murase and Nayar applied these ideas to3D object recognition[40]. Several authors have applied discriminative classification methods in the appearance-based shape matching frame-work.Some examples are the LeNet classifier[34],a convolutional neural network for handwritten digit recogni-tion,and the Support Vector Machine(SVM)-based methods of[41](for discriminating between templates of pedestrians based on2D wavelet coefficients)and[11],[7](for hand-written digit recognition).The MNIST database of hand-written digits is a particularly important data set as many different pattern recognition algorithms have been tested on it.We will show our results on MNIST in Section6.1.

3M ATCHING WITH S HAPE C ONTEXTS

In our approach,we treat an object as a(possibly infinite) point set and we assume that the shape of an object is essentially captured by a finite subset of its points.More practically,a shape is represented by a discrete set of points sampled from the internal or external contours on the object.These can be obtained as locations of edge pixels as found by an edge detector,giving us a set f p I;F F F;p n g, p i P s P,of n points.They need not,and typically will not, correspond to key-points such as maxima of curvature or inflection points.We prefer to sample the shape with roughly uniformspacing,though this is also not critical.1 Figs.3a and3b show sample points for two shapes. Assuming contours are piecewise smooth,we can obtain as good an approximation to the underlying continuous shapes as desired by picking n to be sufficiently large. 3.1Shape Context

For each point p i on the first shape,we want to find the abestomatching point q j on the second shape.This is a correspondence problemsim ilar to that in stereopsis. Experience there suggests that matching is easier if one uses a rich local descriptor,e.g.,a gray-scale window or a vector of filter outputs[27],instead of just the brightness at a single pixel or edge location.Rich descriptors reduce the ambiguity in matching.

As a key contribution,we propose a novel descriptor,the shape context,that could play such a role in shape matching. Consider the set of vectors originating froma point to all other sample points on a shape.These vectors express the configuration of the entire shape relative to the reference point.Obviously,this set of nàI vectors is a rich description,since as n gets large,the representation of the shape becomes exact.

The full set of vectors as a shape descriptor is much too detailed since shapes and their sampled representation may vary fromone instance to another in a category.We identify the distribution over relative positions as a more robust and compact,yet highly discriminative descriptor.For a point p i on the shape,we compute a coarse histogram h i of the relative coordinates of the remaining nàI points,

h i k 5q p i X qàp i P in k

f g: I

BELONGIE ET AL.:SHAPE MATCHING AND OBJECT RECOGNITION USING SHAPE CONTEXTS511

1.Sampling considerations are discussed in Appendix B.

This histogramis defined to be the shape context of p i.We use bins that are uniformin log-polar2space,making the descriptor more sensitive to positions of nearby sample points than to those of points farther away.An example is shown in Fig.3c.

Consider a point p i on the first shape and a point q j on the second shape.Let C ij C p i;q j denote the cost of matching these two points.As shape contexts are distributions represented as histograms,it is natural to use the P test statistic:

C ij C p i;q j I

P

K

k I

h i k àh j k P

h i k h j k

;

where h i k and h j k denote the K E in normalized histogramat p i and q j,respectively.3

The cost C ij for matching points can include an additional termbased on the local appearance similarity at points p i and q j.This is particularly useful when we are comparing shapes derived from gray-level images instead of line drawings.For example,one can add a cost based on normalized correlation scores between small gray-scale patches centered at p i and q j,distances between vectors of filter outputs at p i and q j,tangent orientation difference between p i and q j,and so on.The choice of this appearance similarity term is application dependent,and is driven by the necessary invariance and robustness requirements,e.g., varying lighting conditions make reliance on gray-scale brightness values risky.3.2Bipartite Graph Matching

Given the set of costs C ij between all pairs of points p i on the first shape and q j on the second shape,we want to minimize the total cost of matching,

H

i

C p i;q i

àá

P

subject to the constraint that the matching be one-to-one,i.e., is a permutation.This is an instance of the square assignment (or weighted bipartite matching)problem,which can be solved in O N Q time using the Hungarian method[42].In our experiments,we use the more efficient algorithm of[28].The input to the assignment problem is a square cost matrix with entries C ij.The result is a permutation i such that(2)is minimized.

In order to have robust handling of outliers,one can add adummyonodes to each point set with a constant matching cost of d.In this case,a point will be matched to a adummyowhenever there is no real match available at smaller cost than d.Thus, d can be regarded as a threshold parameter for outlier detection.Similarly,when the number of sample points on two shapes is not equal,the cost matrix can be made square by adding dummy nodes to the smaller point set.

3.3Invariance and Robustness

A matching approach should be1)invariant under scaling and translation,and2)robust under small geometrical distortions,occlusion and presence of outliers.In certain applications,one may want complete invariance under rotation,or perhaps even the full group of affine transfor-mations.We now evaluate shape context matching by these criteria.

512IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,VOL.24,NO.24,APRIL

2002

Fig.3.Shape context computation and matching.(a)and(b)Sampled edge points of two shapes.(c)Diagram of log-polar histogram bins used in computing the shape contexts.We use five bins for log r and12bins for .(d),(e),and(f)Example shape contexts for reference samples marked by ;?;/in(a)and(b).Each shape context is a log-polar histogram of the coordinates of the rest of the point set measured using the reference point as the origin.(Dark=large value.)Note the visual similarity of the shape contexts for and?,which were computed for relatively similar points on the two shapes.By contrast,the shape context for/is quite different.(g)Correspondences found using bipartite matching,with costs defined by the P distance between histograms.

2.This choice corresponds to a linearly increasing positional uncertainty

with distance from p i,a reasonable result if the transformation between the

shapes around p i can be locally approximated as affine.

3.Alternatives include Bickel's generalization of the Kolmogorov-

Smirnov test for2D distributions[4],which does not require binning.

Invariance to translation is intrinsic to the shape context definition since all measurements are taken with respect to points on the object.To achieve scale invariance we normalize all radial distances by the mean distance between the n P point pairs in the shape.

Since shape contexts are extremely rich descriptors,they are inherently insensitive to small perturbations of parts of the shape.While we have no theoretical guarantees here, robustness to small nonlinear transformations,occlusions and presence of outliers is evaluated experimentally in Section4.2.

In the shape context framework,we can provide for complete rotation invariance,if this is desirable for an application.Instead of using the absolute frame for computing the shape context at each point,one can use a relative frame,based on treating the tangent vector at each point as the positive x E xis.In this way,the reference frame turns with the tangent angle,and the result is a completely rotation invariant descriptor.In Appendix A,we demon-strate this experimentally.It should be emphasized though that,in many applications,complete invariance impedes recognition performance,e.g.,when distinguishing6from9 rotation invariance would be completely inappropriate. Another drawback is that many points will not have well-defined or reliable tangents.Moreover,many local appear-ance features lose their discriminative power if they are not measured in the same coordinate system.

Additional robustness to outliers can be obtained by excluding the estimated outliers from the shape context computation.More specifically,consider a set of points that have been labeled as outliers on a given iteration.We render these pointsainvisibleoby not allowing themto contribute to any histogram.However,we still assign them shape contexts,taking into account only the surrounding inlier points,so that at a later iteration they have a chance of reemerging as an inlier.

3.4Related Work

The most comprehensive body of work on shape corre-spondence in this general setting is the work of Gold et al.

[19]and Chui and Rangarajan[9].They developed an iterative optimization algorithm to determine point corre-spondences and underlying image transformations jointly, where typically some generic transformation class is assumed,e.g.,affine or thin plate splines.The cost function that is being minimized is the sum of Euclidean distances between a point on the first shape and the transformed second shape.This sets up a chicken-and-egg problem:The distances make sense only when there is at least a rough alignment of shape.Joint estimation of correspondences and shape transformation leads to a difficult,highly non-convex optimization problem,which is solved using deterministic annealing[19].The shape context is a very discriminative point descriptor,facilitating easy and robust correspondence recovery by incorporating global shape information into a local descriptor.

As far as we are aware,the shape context descriptor and its use for matching2D shapes is novel.The most closely related idea in past work is that due to Johnson and Hebert [26]in their work on range images.They introduced a representation for matching dense clouds of oriented 3D points called theaspin image.oA spin image is a 2D histogram formed by spinning a plane around a normal vector on the surface of the object and counting the points that fall inside bins in the plane.As the size of this plane is relatively small,the resulting signature is not as informative as a shape context for purposes of recovering correspon-dences.This characteristic,however,might have the trade-off of additional robustness to occlusion.In another related work,Carlsson[8]has exploited the concept of order structure for characterizing local shape configurations.In this work,the relationships between points and tangent lines in a shape are used for recovering correspondences.

4M ODELING T RANSFORMATIONS

Given a finite set of correspondences between points on two shapes,one can proceed to estimate a plane transformation T X s Pà3s P that may be used to map arbitrary points from one shape to the other.This idea is illustrated by the warped gridlines in Fig.2,wherein the specified corre-spondences consisted of a small number of landmark points such as the centers of the eyes,the tips of the dorsal fins, etc.,and T extends the correspondences to arbitrary points. We need to choose T froma suitable fam ily of transformations.A standard choice is the affine model,i.e.,

T x Ax o Q with some matrix A and a translational offset vector o parameterizing the set of all allowed transformations.Then, the least squares solution T A; o is obtained by

o

I

n

n

i I

p iàq i

àá

; R

A Q P t; S where P and Q contain the homogeneous coordinates of and ,respectively,i.e.,

P

I p II p IP

F F F F F F F F F

I p n I p n P

H

f d

I

g e: T

Here,Q denotes the pseudoinverse of Q.

In this work,we mostly use the thin plate spline(TPS) model[14],[37],which is commonly used for representing flexible coordinate transformations.Bookstein[6]found it to be highly effective for modeling changes in biological forms.Powell applied the TPS model to recover transfor-mations between curves[44].The thin plate spline is the 2D generalization of the cubic spline.In its regularized form,which is discussed below,the TPS model includes the affine model as a special case.We will now provide some background information on the TPS model.

We start with the1D interpolation problem.Let v i denote the target function values at corresponding locations p i x i;y i in the plane,with i I;P;F F F;n.In particular,we will set v i equal to x H i and y H i in turn to obtain one continuous transformation for each coordinate.We assume that the locations x i;y i are all different and are not collinear.The TPS interpolant f x;y minimizes the bending energy

BELONGIE ET AL.:SHAPE MATCHING AND OBJECT RECOGNITION USING SHAPE CONTEXTS513

I f

s

P

@P f

@x P

P

P @P f @x@y P @P f @y P

P

dxdy

and has the form:

f x;y a I a x x a y y

n i I

w i U x i ;y i à x;y k k ;

where the kernel function U r is defined by U r r P log r P and U H H as usual.In order for f x;y to have square integrable second derivatives,we require that

n i I

w i H nd

n i I

w i x i

n i I

w i y i H : U

Together with the interpolation conditions,f x i ;y i v i ,

this yields a linear systemfor the TPS

coefficients:

where K ij U k x i ;y i à x j ;y j k ,the i th row of P is I ;x i ;y i ,w and v are column vectors formed from w i and v i ,respectively,and a is the column vector with elements a I ;a x ;a y .We will denote the n Q ? n Q matrix of this systemby L .As discussed,e.g.,in [44],L is nonsingular and we can find the solution by inverting L .If we denote the upper left n ?n block of L àI by A ,then it can be shown that

I f G v T Av w T Kw:

W

4.1Regularization and Scaling Behavior

When there is noise in the specified values v i ,one may wish to relax the exact interpolation requirement by means of regularization.This is accomplished by minimizing

H f

n i I

v i àf x i ;y i P I f :

IH

The regularization parameter ,a positive scalar,controls the amount of smoothing;the limiting case of H reduces to exact interpolation.As demonstrated in [60],[18],we can solve for the TPS coefficients in the regularized case by replacing the matrix K by K I ,where I is the n ?n identity matrix.It is interesting to note that the highly regularized TPS model degenerates to the least-squares affine model.

To address the dependence of on the data scale,suppose x i ;y i and x H i ;y H i are replaced by x i ; y i and x H i ; y H i ,respectively,for some positive constant .Then,it can be shown that the parameters w;a;I f of the optimal thin plate spline are unaffected if is replaced by P .This simple scaling behavior suggests a normalized definition of the regularization parameter.Let again represent the scale of the point set as estimated by the mean edge length between two points in the set.Then,we can define in terms of and o ,a scale-independent regularization parameter,via the simple relation P o .

We use two separate TPS functions to model a coordinate

transformation,

T x;y f x x;y ;f y x;y àá

II which yields a displacement field that maps any position in

the first image to its interpolated location in the second image.

In many cases,the initial estimate of the correspondences contains some errors which could degrade the quality of the transformation estimate.The steps of recovering correspon-dences and estimating transformations can be iterated to overcome this problem.We usually use a fixed number of iterations,typically three in large-scale experiments,but more refined schemes are possible.However,experimental experiences show that the algorithmic performance is independent of the details.An example of the iterative algorithmis illustrated in Fig.4.

4.2Empirical Robustness Evaluation

In order to study the robustness of our proposed method,we performed the synthetic point set matching experiments described in [9].The experiments are broken into three parts designed to measure robustness to deformation,noise,and outliers.(The latter tests each include a amoderateoamount of deformation.)In each test,we subjected the model point set to one of the above distortions to create a atargetopoint set;see Fig.5.We then ran our algorithmto find the best warping between the model and the target.Finally,the performance is quantified by computing the average distance between the coordinates of the warped model and those of the target.The results are shown in Fig.6.In the most challenging part of the testDthe outlier experimentDour approach shows robustness even up to a level of 100percent outlier-to-data ratio.

In practice,we will need robustness to occlusion and segmentation errors which can be explored only in the context of a complete recognition system,though these experiments provide at least some guidelines.

4.3Computational Demands

In our implementation on a regular Pentium III /500MHz workstation,a single comparison including computation of shape context for 100sample points,set-up of the full matching matrix,bipartite graph matching,computation of the TPS coefficients,and image warping for three cycles takes roughly 200ms.The runtime is dominated by the number of sample points for each shape,with most components of the algorithm exhibiting between quadratic and cubic scaling https://www.wendangku.net/doc/bb18285121.html,ing a sparse representation throughout,once the shapes are roughly aligned,the complexity could be made close to linear.

5

O BJECT R ECOGNITION AND

P ROTOTYPE

S ELECTION

Given a measure of dissimilarity between shapes,which we will make precise shortly,we can proceed to apply it to the task of object recognition.Our approach falls into the category of prototype-based recognition.In this framework,pioneered by Rosch et al.[48],categories are represented by ideal

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examples rather than a set of formal logical rules.As an example,a sparrow is a likely prototype for the category of birds;a less likely choice might be an penguin.The idea of prototypes allows for soft category membership,meaning that as one moves farther away from the ideal example in some suitably defined similarity space,one's association with that prototype falls off.When one is sufficiently far away from that prototype,the distance becomes meaningless,but by then one is most likely near a different prototype.As an example,one can talk about good or so-so examples of the color red,but when the color becomes sufficiently different,the level of dissimilarity saturates at some maximum level rather than continuing on indefinitely.

Prototype-based recognition translates readily into the computational framework of nearest-neighbor methods using multiple stored views.Nearest-neighbor classifiers have the property [46]that as the number of examples n in the training set goes to infinity,the IExx error converges to a value P E ?,where E ?is the Bayes Risk (for K Exx ,K 3

I and K=n 3H ,the error 3E ?).This is interesting because it shows that the humble nearest-neighbor classifier is asymptotically optimal,a property not possessed by several considerably more complicated techniques.Of course,what matters in practice is the performance for small n ,and this gives us a way to compare different similarity/distance measures.

5.1Shape Distance

In this section,we make precise our definition of shape distance and apply it to several practical problems.We used a regularized TPS transformation model and three iterations of shape context matching and TPS reestimation.After matching,we estimated shape distances as the weighted sum of three terms:shape context distance,image appear-ance distance,and bending energy.

We measure shape context distance between shapes and as the symmetric sum of shape context matching costs over best matching points,i.e.,

BELONGIE

ET AL.:SHAPE MATCHING AND OBJECT RECOGNITION USING SHAPE CONTEXTS 515

Fig.5.Testing data for empirical robustness evaluation,following Chui and Rangarajan [9].The model pointsets are shown in the first column.Columns 2-4show examples

of target point sets for the deformation,noise,and outlier tests,respectively.

Fig.4.Illustration of the matching process applied to the example of Fig.1.Top row:1st iteration.Bottom row:5th iteration.Left column:estimated correspondences shown relative to the transformed model,with tangent vectors shown.Middle column:estimated correspondences shown relative to the untransformed model.Right column:result of transforming the model based on the current correspondences;this is the input to the next iteration.The grid points illustrate the interpolated transformation over s P .Here,we have used a regularized TPS model with o I .

h s ;

I n

p P

rg min q P C p;T q

I m

q P

rg min p P C p;T q ; IP

where T á denotes the estimated TPS shape transformation.

In many applications there is additional appearance information available that is not captured by our notion of shape, e.g.,the texture and color information in the grayscale image patches surrounding corresponding points.The reliability of appearance information often suffers substantially from geometric image distortions.However,after establishing image correspondences and recovery of underlying 2D image transformation the distorted image can be warped back into a normal form,thus correcting for distortions of the image appearance.

We used a term h ; for appearance cost,defined as the sumof squared brightness differences in Gaussian windows around corresponding image points,

h ;

I n

n i I áP Z P

G á I p i á àI T q i àá áàá??P ; IQ

where I and I are the gray-level images corresponding to and ,respectively.ádenotes some differential vector offset and G is a windowing function typically chosen to be a Gaussian,thus putting emphasis to pixels nearby.We thus sumover squared differences in windows around corresponding points,scoring the weighted gray-level similarity.

This score is computed after the thin plate spline transformation T has been applied to best warp the images into alignment.

The third term h e ; corresponds to the aamountoof transformation necessary to align the shapes.In the TPS case the bending energy (9)is a natural measure (see [5]).

5.2Choosing Prototypes

In a prototype-based approach,the key question is:what examples shall we store?Different categories need different numbers of views.For example,certain handwritten digits have more variability than others,e.g.,one typically sees more variations in fours than in zeros.In the category of 3D objects,a sphere needs only one view,for example,while a telephone needs several views to capture the variety of visual appearance.This idea is related to the aaspectoconcept as discussed in [30].We will now discuss how we approach the problemof prototype selection.

In the nearest-neighbor classifier literature,the problem of selecting exemplars is called editing .Extensive reviews of nearest-neighbor editing methods can be found in Ripley [46]and Dasarathy [12].We have developed a novel editing algorithmbased on shape distance and K Emedoids cluster-ing.K Emedoids can be seen as a variant of K Eme ns that restricts prototype positions to data points.First a matrix of pairwise similarities between all possible prototypes is computed.For a given number of K prototypes the K Emedoids algorithmthen iterates two steps:1)For a given assignment of points to (abstract)clusters a new prototype is selected for that cluster by minimizing the average distance of the prototype to all elements in the cluster,and 2)given the set of prototypes,points are then reassigned to clusters according to the nearest prototype.More formally,denote by c the (abstract)cluster of shape ,e.g.,represented by some number f I ;F F F ;k g and denote by p c the associated prototype.Thus,we have a class map

c X I & à

3f I ;F F F ;k g IR

and a prototype map

p X f I ;F F F ;k g à3 P & :

IS Here, I and P are some subsets of the set of all potential

shapes .Often, I P .K Emedoids proceeds by iterating two steps:

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https://www.wendangku.net/doc/bb18285121.html,parison of our results (u t )to Chui and Rangarajan (?)and iterated closest point ( )for the fish and Chinese character,respectively.The error bars indicate the standard deviation of the error over 100random trials.Here,we have used 5iterations with o I :H .In the deformation and noise tests no dummy nodes were added.In the outlier test,dummy nodes were added to the model point set such that the total number of nodes was equal to that of the target.In this case,the value of d does not affect the solution.

1.

group I into classes given the class prototypes p c ,and

2.identify a representative prototype for each class

given the elements in the cluster.

Basically,item1is solved by assigning each shape P I to the nearest prototype,thus

c rg min k

h ;p k :

IT

For given classes,in item2new prototypes are selected based on minimal mean dissimilarity,i.e.,

p k rg min p P P

X c shape k

h ;p : IU

Since both steps minimize the same cost function

H c;p

P I

h ;p c ;

IV

the algorithm necessarily converges to a (local)minimum.

As with most clustering methods,with k Emedoids one must have a strategy for choosing k .We select the number of prototypes using a greedy splitting strategy starting with one prototype per category.We choose the cluster to split based on the associated overall misclassification error.This continues until the overall misclassification error has dropped below a criterion level.Thus,the prototypes are automatically allocated to the different object classes,thus optimally using available resources.The application of this procedure to a set of views of 3D objects is explored in Section 6.2and illustrated in Fig.10.

6C ASE S TUDIES

6.1Digit Recognition

Here,we present results on the MNIST data set of hand-written digits,which consists of 60,000training and 10,000test digits [34].In the experiments,we used 100points sampled fromthe Canny edges to represent each digit.When computing the C ij 's for the bipartite matching,we included a termrepresenting the dissim ilarity of local tangent angles.Specifically,we defined the matching cost as

C ij I à C sc ij C tan ij ,where C sc

ij is the shape context cost,

C tan ij H :S I à os i à j measures tangent angle dissim-ilarity,and H :I .For recognition,we used a K Exx classifier with a distance function

h I :T h h s H :Q h e : IW

The weights in (19)have been optimized by a leave-one-out procedure on a Q ;HHH ?Q ;HHH subset of the training data.On the MNIST data set nearly 30algorithms have been compared (https://www.wendangku.net/doc/bb18285121.html,/~yann/exdb/mnist/index.html).The lowest test set error rate published at this time is 0.7percent for a boosted LeNet-4with a training set of size TH ;HHH ?IH synthetic distortions per training digit.Our error rate using 20,000training examples and QExx is 0.63percent.The 63errors are shown in Fig.8.4

As mentioned earlier,what matters in practical applica-tions of nearest-neighbor methods is the performance for small n ,and this gives us a way to compare different similarity/distance measures.In Fig.7(left),our shape distance is compared to SSD (sum of squared differences between pixel brightness values).In Fig.7(right),we compare the classification rates for different K .

6.23D Object Recognition

Our next experiment involves the 20common household objects fromthe COIL-20database [40].Each object was placed on a turntable and photographed every S for a total of 72views per object.We prepared our training sets by selecting a number of equally spaced views for each object and using the remaining views for testing.The matching algorithmis exactly the sam e as for digits.Recall,that the Canny edge detector responds both to external and internal contours,so the 100sample points are not restricted to the external boundary of the silhouette.

Fig.9shows the performance using IExx with the distance function D as given in (19)com pared to a

BELONGIE ET AL.:SHAPE MATCHING AND OBJECT RECOGNITION USING SHAPE CONTEXTS 517

4.DeCoste and Scho

èlkopf [13]report an error rate of 0.56percent on the same database using Virtual Support Vectors (VSV)with the full training set of 60,000.VSVs are found as follows:1)obtain SVs fromthe original training set using a standard SVM,2)subject the SVs to a set of

desired transformations (e.g.,translation),3)train another SVM on the generated examples.

Fig.7.Handwritten digit recognition on the MNIST data set.Left:Test set errors of a 1-NN classifier using SSD and Shape Distance (SD)measures.Right:Detail of performance curve for Shape Distance,including results with training set sizes of 15,000and 20,000.Results are shown on a semilog-x scale for K I ;Q ;S nearest-neighbors.

straightforward sumof squared differences (SSD).SSD performs very well on this easy database due to the lack of variation in lighting [24](PCA just makes it faster).

The prototype selection algorithmis illustrated in Fig.10.As seen,views are allocated mainly for more complex categories with high within class variability.The curve marked SC-proto in Fig.9shows the improved classification performance using this prototype selection strategy instead of equally-spaced views.Note that we obtain a 2.4percent

error rate with an average of only four two-dimensional views for each three-dimensional object,thanks to the flexibility provided by the matching algorithm.

6.3MPEG-7Shape Silhouette Database

Our next experiment involves the MPEG-7shape silhouette database,specifically Core Experiment CE-Shape-1part B,which measures performance of similarity-based retrieval [25].The database consists of 1,400images:70shape categories,20images per category.The performance is measured using the so-called abullseye test,oin which each

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Fig.8.All of the misclassified MNIST test digits using our method (63out of 10,000).The text above each digit indicates the example number followed by the true label and the assigned

label.

Fig.9.3D object recognition using the COIL-20data https://www.wendangku.net/doc/bb18285121.html,parison of test set error for SSD,Shape Distance (SD),and Shape Distance with k Emedoids prototypes (SD-proto)versus number of prototype views.For SSD and SD,we varied the number of prototypes uniformly for all objects.For SD-proto,the number of prototypes per object depended on the within-object variation as well as the between-object

similarity.

Fig.10.Prototype views selected for two different 3D objects from the COIL data set using the algorithm described in Section 5.2.With this approach,views are allocated adaptively depending on the visual complexity of an object with respect to viewing angle.

image is used as a query and one counts the number of correct images in the top 40matches.

As this experiment involves intricate shapes we in-creased the number of samples from 100to 300.In some categories,the shapes appear rotated and flipped,which we address using a modified distance function.The distance dist R;Q between a reference shape R and a query shape Q is defined as

dist Q;R min f dist Q;R a ;dist Q;R b ;dist Q;R c g ;where R a ;R b ,and R c denote three versions of R :un-changed,vertically flipped,and horizontally flipped.

With these changes in place but otherwise using the same approach as in the MNIST digit experiments,we obtain a retrieval rate of 76.51percent.Currently the best published performance is achieved by Latecki et al.[33],with a retrieval rate of 76.45percent,followed by Mokhtar-ian et al.at 75.44percent.

6.4Trademark Retrieval

Trademarks are visually often best described by their shape information,and,in many cases,shape provides the only source of information.The automatic identification of trademark infringement has interesting industrial applica-tions,since with the current state of the art trademarks are broadly categorized according to the Vienna code,and then manually classified according to their perceptual similarity.Even though shape context matching does not provide a full solution to the trademark similarity problem (other poten-tial cues are text and texture),it still serves well to illustrate the capability of our approach to capture the essence of shape similarity.In Fig.12,we depict retrieval results for a database of 300trademarks.In this experiment,we relied on an affine transformation model as given by (3),and as in the previous case,we used 300sample points.

We experimented with eight different query trademarks for each of which the database contained at least one potential infringement.We depict the top four hits as well as their similarity score.It is clearly seen that the potential infringe-ments are easily detected and appear as most similar in the top ranks despite substantial variation of the actual shapes.It has been manually verified that no visually similar trademark has been missed by the algorithm.

7C ONCLUSION

We have presented a new approach to shape matching.A key characteristic of our approach is the estimation of shape similarity and correspondences based on a novel descriptor,the shape context.Our approach is simple and easy to apply,yet provides a rich descriptor for point sets that greatly improves point set registration,shape matching and shape recognition.In our experiments,we have demonstrated

BELONGIE

ET AL.:SHAPE MATCHING AND OBJECT RECOGNITION USING SHAPE CONTEXTS 519

Fig.11.

Examples of shapes in the MPEG7database for three different categories.

Fig.12.Trademark retrieval results based on a database of 300different real-world trademarks.We used an affine transformation model and a weighted combination of shape context similarity D s and the sum over local tangent orientation differences.

invariance to several common image transformations,in-cluding significant 3D rotations of real-world objects.

A PPENDIX A

C OMPLETE R OTATION I NVARIANT R ECOGNITION

In this appendix,we demonstrate the use of the relative frame in our approach as a means of obtaining complete rotation invariance.To demonstrate this idea,we have used the database provided by Sharvit et al.[53]shown in Fig.13.In this experiment,we used n IHH sample points and,as mentioned above,we used the relative frame (Section 3.3)when computing the shape contexts.We used five bins for log r over the range H :IPS to P and 12equally spaced radial bins in these and all other experiments in this paper.No transformation model at all was used.As a similarity

score,we used the matching cost function

i C i; i after one iteration with no transformation step.Thus,this experiment is specifically designed solely to evaluate the power of the shape descriptor in the face of rotation.

In [53]and [17],the authors summarize their results on this data set by stating the number of 1st,2nd,and 3rd nearest-neighbors that fall into the correct category.Our results are 25/25,24/25,22/25.In [53]and [17],the results quoted are 23/25,21/25,20/25and 25/25,21/25,19/25,respectively.

A PPENDIX B

S AMPLING C ONSIDERATIONS

In our approach,a shape is represented by a set of sample points drawn fromthe internal and external contours of an object.Operationally,one runs an edge detector on the

gray-scale image and selects a subset of the edge pixels found.The selection could be uniformly at random,but we have found it to be advantageous to ensure that the sample points have a certain minimum distance between them as this makes sure that the sampling along the contours is somewhat uniform.(This corresponds to sampling from a point process which is a hard-core model [45].)

Since the sample points are drawn randomly and independently fromthe two shapes,there is inevitably jitter noise in the output of the matching algorithm which finds correspondences between these two sets of sample points.However,when the transformation between the shapes is estimated as a regularized thin plate spline,the effect of this jitter is smoothed away.

A CKNOWLEDGMENTS

This research is supported by the Army Research Office (ARO)DAAH04-96-1-0341,the Digital Library Grant IRI-9411334,a US National Science Foundation Graduate Fellowship for S.Belongie,and the German Research Foundation by DFG grant PU-165/1.Parts of this work have appeared in [3],[2].The authors wish to thank H.Chui and A.Rangarajan for providing the synthetic testing data used in Section 4.2.We would also like to thank themand various members of the Berkeley computer vision group,particularly A.Berg,A.Efros,D.Forsyth,T.Leung,J.Shi,and Y.Weiss,for useful discussions.This work was carried out while the authors were with the Department of Electrical Engineering and Computer Science Division,University of California at Berkeley.

R EFERENCES

[1]

Y.Amit,D.Geman,and K.Wilder,aJoint Induction of Shape Features and Tree Classifiers,oIEEE Trans.Pattern Analysis and Machine Intelligence,vol.19,no.11,pp.1300-1305,Nov.1997.[2]S.Belongie,J.Malik,and J.Puzicha,aMatching Shapes,oProc.

Eighth Int'https://www.wendangku.net/doc/bb18285121.html,puter Vision,pp.454-461,July 2001.

[3]S.Belongie,J.Malik,and J.Puzicha,aShape Context:A New

Descriptor for Shape Matching and Object Recognition,oAdvances in Neural Information Processing Systems 13:Proc.2000Conf.,T.K.Leen,T.G.Dietterich,and V.Tresp,eds..pp.831-837,2001.

[4]P.J.Bickel,aA Distribution Free Version of the Smirnov Two-Sample Test in the Multivariate Case,oAnnals of Math.Statistics,vol.40,pp.1-23,1969.

[5] F.L.Bookstein,aPrincipal Warps:Thin-Plate Splines and Decom-position of Deformations,oIEEE Trans.Pattern Analysis and Machine Intelligence,vol.11,no.6,pp.567-585,June 1989.

[6] F.L.Bookstein,Morphometric Tools for Landmark Data:Geometry and

Biology.Cambridge Univ.Press,1991.

[7] C.Burges and B.Scho

èlkopf,aImproving the Accuracy and Speed of Support Vector Machines,oAdvances in Neural Information Processing Systems 9:Proc.1996Conf.,D.S.Touretzky,M.C.Mozer,and M.E.Hasselmo,eds.pp.375-381,1997.

[8]S.Carlsson,aOrder Structure,Correspondence and Shape Based

Categories,oInt'l Workshop Shape,Contour and Grouping,May 1999.[9]H.Chui and A.Rangarajan,aA New Algorithmfor Non-Rigid

Point Matching,oProc.IEEE https://www.wendangku.net/doc/bb18285121.html,puter Vision and Pattern Recognition,pp.44-51,June 2000.

[10]T.Cootes,D.Cooper,C.Taylor,and J.Graham,aActive Shape

ModelsDTheir Training and Application,oComputer Vision and Image Understanding (CVIU),vol.61,no.1,pp.38-59,Jan.1995.[11] C.Cortes and V.Vapnik,aSupport Vector Networks,oMachine

Learning,vol.20,pp.273-297,1995.

[12]Nearest Neighbor (NN)Norms:(NN)Pattern Classification Techniques.

B.V.Dasarathy,ed.,IEEE Computer Soc.,1991.520IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,VOL.24,NO.24,APRIL

2002

Fig.13.Kimia data set:each row shows instances of a different object category.Performance is measured by the number of closest matches with the correct category label.Note that several of the categories require rotation invariant matching for effective recognition.All of the 1st ranked closest matches were correct using our method.Of the 2nd ranked matches,one error occurred in 1versus 8.In the 3rd ranked matches,confusions arose from 2versus 8,8versus 1,and 15versus 17.

[13] D.DeCoste and B.Schoèlkopf,aTraining Invariant Support Vector

Machines,oMachine Learning,to appear in2002.

[14]J.Duchon,aSplines Minimizing Rotation-Invariant Semi-Norms in

Sobolev Spaces,oConstructive Theory of Functions of Several Variables,W.Schempp and K.Zeller,eds.,pp.85-100,Berlin: Springer-Verlag,1977.

[15]M.Fischler and R.Elschlager,aThe Representation and Matching

of Pictorial Structures,oIEEE https://www.wendangku.net/doc/bb18285121.html,puters,vol.22,no.1, pp.67-92,1973.

[16] D.Gavrila and V.Philomin,aReal-Time Object Detection for

Smart Vehicles,oProc.Seventh Int'https://www.wendangku.net/doc/bb18285121.html,puter Vision,pp.87-93,1999.

[17]Y.Gdalyahu and D.Weinshall,aFlexible Syntactic Matching of

Curves and its Application to Automatic Hierarchical Classifica-tion of Silhouettes,oIEEE Trans.Pattern Analysis and Machine Intelligence,vol.21,no.12,pp.1312-1328,Dec.1999.

[18] F.Girosi,M.Jones,and T.Poggio,aRegularization Theory and

Neural Networks Architectures,oNeural Computation,vol.7,no.2, pp.219-269,1995.

[19]S.Gold,A.Rangarajan,C.-P.Lu,S.Pappu,and E.Mjolsness,

aNew Algorithms for2D and3D Point Matching:Pose Estimation and Correspondence,oPattern Recognition,vol.31,no.8,1998. [20] E.Goldmeier,aSimilarity in Visually Perceived Forms,oPsycho-

logical Issues,vol.8,no.1,pp.1-135,1936/1972.

[21]U.Grenander,Y.Chow,and D.Keenan,HANDS:A Pattern

Theoretic Study Of Biological Shapes.Springer,1991.

[22]M.Hagedoorn,aPattern Matching Using Similarity Measures,o

PhD thesis,Universiteit Utrecht,2000.

[23] D.Huttenlocher,G.Klanderman,and W.Rucklidge,aComparing

Images Using the Hausdorff Distance,oIEEE Trans.Pattern Analysis and Machine Intelligence,vol.15,no.9,pp.850-863,Sept.

1993.

[24] D.Huttenlocher,R.Lilien,and C.Olson,aView-Based Recogni-

tion Using an Eigenspace Approximation to the Hausdorff Measure,oIEEE Trans.Pattern Analysis and Machine Intelligence, vol.21,no.9,pp.951-955,Sept.1999.

[25]S.Jeannin and M.Bober,aDescription of Core Experiments for

MPEG-7Motion/Shape,oTechnical Report ISO/IEC JTC1/SC 29/WG11MPEG99/N2690,MPEG-7,Seoul,Mar.1999. [26] A.E.Johnson and M.Hebert,aRecognizing Objects by Matching

Oriented Points,oProc.IEEE https://www.wendangku.net/doc/bb18285121.html,puter Vision and Pattern Recognition,pp.684-689,1997.

[27] D.Jones and J.Malik,aComputational Framework to Determining

Stereo Correspondence froma Set of Linear Spatial Filters,oImage and Vision Computing,vol.10,no.10,pp.699-708,Dec.1992. [28]R.Jonker and A.Volgenant,aA Shortest Augmenting Path

Algorithmfor Dense and Sparse Linear Assignm ent Problem s,oComputing,vol.38,pp.325-340,1987.

[29] D.Kendall,aShape Manifolds,Procrustean Metrics and Complex

Projective Spaces,oBull.London Math.Soc.,vol.16,pp.81-121, 1984.

[30]J.J.Koenderink and A.J.van Doorn,aThe Internal Representation

of Solid Shape with Respect to Vision,oBiological Cybernetics, vol.32,pp.211-216,1979.

[31]https://www.wendangku.net/doc/bb18285121.html,des,C.Vorbuèggen,J.Buhmann,https://www.wendangku.net/doc/bb18285121.html,nge,C.von der

Malsburg,R.Wurtz,and W.Konen,aDistortion Invariant Object Recognition in the Dynamic Link Architecture,oIEEE Trans.

Computers,vol.42,no.3,pp.300-311,Mar.1993.

[32]https://www.wendangku.net/doc/bb18285121.html,mdan,J.Schwartz,and H.Wolfson,aAffine Invariant Model-

Based Object Recognition,oIEEE Trans.Robotics and Automation, vol.6,pp.578-589,1990.

[33]https://www.wendangku.net/doc/bb18285121.html,tecki,https://www.wendangku.net/doc/bb18285121.html,kaèmper,and U.Eckhardt,aShape Descriptors for

Non-Rigid Shapes with a Single Closed Contour,oProc.IEEE Conf.

Computer Vision and Pattern Recognition,pp.424-429,2000. [34]Y.LeCun,L.Bottou,Y.Bengio,and P.Haffner,aGradient-Based

Learning Applied to Document Recognition,oProc.IEEE,vol.86, no.11,pp.2278-2324,Nov.1998.

[35]T.K.Leung,M.C.Burl,and P.Perona,aFinding Faces in Cluttered

Scenes Using RandomLabelled Graph M atching,oProc.Fifth Int'l.

https://www.wendangku.net/doc/bb18285121.html,puter Vision,pp.637-644,1995.

[36] D.G.Lowe,aObject Recognition fromLocal Scale-Invariant

Features,oProc.Seventh Int'https://www.wendangku.net/doc/bb18285121.html,puter Vision,pp.1150-1157,Sept.1999.

[37]J.Meinguet,aMultivariate Interpolation at Arbitrary Points Made

Simple,oJ.Applied Math.Physics(ZAMP),vol.5,pp.439-468,1979.[38] B.Moghaddam,T.Jebara,and A.Pentland,aBayesian Face

Recognition,oPattern Recognition,vol.33,no.11,pp.1771-1782, Nov,2000.

[39] F.Mokhtarian,S.Abbasi,and J.Kittler,aEfficient and Robust

Retrieval by Shape Content Through Curvature Scale Space,oImage Databases and Multi-Media Search,A.W.M.Smeulders and R.Jain,eds.,pp.51-58,World Scientific,1997.

[40]H.Murase and S.Nayar,aVisual Learning and Recognition of3-D

Objects fromOppearance,oInt'https://www.wendangku.net/doc/bb18285121.html,puter Vision,vol.14,no.1, pp.5-24,Jan.1995.

[41]M.Oren,C.Papageorgiou,P.Sinha,E.Osuna,and T.Poggio,

aPedestrian Detection Using Wavelet Templates,oProc.IEEE Conf.

Computer Vision and Pattern Recognition,pp.193-199,June1997.

[42] C.Papadimitriou and K.Stieglitz,Combinatorial Optimization:

Algorithms and Complexity.Prentice Hall,1982.

[43] E.Persoon and K.Fu,aShape Discrimination Using Fourier

Descriptors,oIEEE Trans.Systems,Man and Cybernetics,vol.7,no.3, pp.170-179,Mar.1977.

[44]M.J.D.Powell,aA Thin Plate Spline Method for Mapping Curves

into Curves in Two Dimensions,oComputational Techniques and Applications(CTAC'95),1995.

[45] B.D.Ripley,aModelling Spatial Patterns,oJ.Royal Statistical

Society,Series B,vol.39,pp.172-212,1977.

[46] B.D.Ripley,Pattern Recognition and Neural Networks.Cambridge

Univ.Press,1996.

[47] E.Rosch,aNatural Categories,oCognitive Psychology,vol.4,no.3,

pp.328-350,1973.

[48] E.Rosch,C.B.Mervis,W.D.Gray,D.M.Johnson,and P.Boyes-

Braem,aBasic Objects in Natural Categories,oCognitive Psychol-ogy,vol.8,no.3,pp.382-439,1976.

[49] C.Schmid and R.Mohr,aLocal Grayvalue Invariants for Image

Retrieval,oIEEE Trans.Pattern Analysis and Machine Intelligence, vol.19,no.5,pp.530-535,May1997.

[50]S.Sclaroff and A.Pentland,aModal Matching for Correspondence

and Recognition,oIEEE Trans.Pattern Analysis and Machine Intelligence,vol.17,no.6,pp.545-561,June1995.

[51]G.Scott and H.Longuet-Higgins,aAn Algorithmfor Associating

the Features of Two Images,oProc.Royal Soc.London,vol.244, pp.21-26,1991.

[52]L.S.Shapiro and J.M.Brady,aFeature-Based Correspondence:An

Eigenvector Approach,oImage and Vision Computing,vol.10,no.5, pp.283-288,June1992.

[53] D.Sharvit,J.Chan,H.Tek,and B.Kimia,aSymmetry-Based

Indexing of Image Databases,oJ.Visual Comm.and Image Representation,vol.9,no.4,pp.366-380,Dec.1998.

[54]L.Sirovich and M.Kirby,aLow Dimensional Procedure for the

Characterization of Human Faces,oJ.Optical Soc.Am.A,vol.4, no.3,pp.519-524,1987.

[55] D.W.Thompson,On Growth and Form,Cambridge Univ.Press,

1917.

[56]M.Turk and A.Pentland,aEigenfaces for Recognition,oJ.Cognitive

Neuroscience,vol.3,no.1,pp.71-96,1991.

[57]S.Umeyama,aAn Eigen Decomposition Approach to Weighted

Graph Matching Problems,oIEEE Trans.Pattern Analysis and Machine Intelligence,vol.10,no.5,pp.695-703,Sept.1988. [58]R.C.Veltkamp and M.Hagedoorn,aState of the Art in Shape

Matching,oTechnical Report UU-CS-1999-27,Utrecht,1999. [59]T.Vetter,M.J.Jones,and T.Poggio,aA Bootstrapping Algorithm

for Learning Linear Models of Object Classes,oProc.IEEE Conf.

Computer Vision and Pattern Recognition,pp.40-46,1997. [60]G.Wahba,Spline Models for Observational Data.Soc.Industrial and

Applied Math.,1990.

[61] A.Yuille,aDeformable Templates for Face Recognition,o

J.Cognitive Neuroscience,vol.3,no.1,pp.59-71,1991.

[62] C.Zahn and R.Roskies,aFourier Descriptors for Plane Closed

Curves,oIEEE https://www.wendangku.net/doc/bb18285121.html,puters,vol.21,no.3,pp.269-281,Mar.

1972.

BELONGIE ET AL.:SHAPE MATCHING AND OBJECT RECOGNITION USING SHAPE CONTEXTS521

Serge Belongie received the BS degree(with

honor)in electrical engineering from the California

Institute of Technology,Pasadena,California,in

1995,and the MS and PhD degrees in electrical

engineering and computer sciences(EECS)at

the University of California at Berkeley,in1997

and2000,respectively.While at Berkeley,his

research was supported by a National Science

Foundation Graduate Research Fellowship and

the Chancellor's Opportunity Predoctoral Fellow-ship.He is also a cofounder of Digital Persona,Inc.,and the principal architect of the Digital Persona fingerprint recognition algorithm.He is currently an assistant professor in the Computer Science and Engineering Department at the University of California at San Diego.His research interests include computer vision,pattern recognition,and digital signal processing.He is a member of the IEEE.

Jitendra Malik received the BTech degree in

electrical engineering from Indian Institute of

Technology,Kanpur in1980and the PhD

degree in computer science from Stanford

University,Stanford,California,in1986.In

January1986,he joined the faculty of the

Computer Science Division,Department of

EECS,University of California at Berkeley,

where he is currently a professor.During1995-

1998,he also served as vice-chair for Graduate Matters.He is a member of the Cognitive Science and Vision Science groups at UC Berkeley.His research interests are in computer vision and computational modeling of human vision.His work spans a range of topics in vision including image segmentation and grouping,texture, stereopsis,object recognition,image-based modeling and rendering, content-based image querying,and intelligent vehicle highway systems. He has authored or coauthored more than100research papers on these topics.He received the gold medal for the best graduating student in electrical engineering from IIT Kanpur in1980,a Presidential Young Investigator Award in1989,and the Rosenbaum fellowship for the Computer Vision Programme at the Newton Institute of Mathematical Sciences,University of Cambridge in1993.He received the Diane S. McEntyre Award for Excellence in Teaching from the Computer Science Division,University of California at Berkeley,in2000.He is an Editor-in-Chief of the International Journal of Computer Vision.He is a member of the IEEE.

Jan Puzicha received the Diploma degree in

1995and the PhD degree in computer science in

1999,both from the University of Bonn,Bonn,

Germany.He was with the Computer Vision and

Pattern Recognition Group,University of Bonn,

from1995to1999.In September1999,he

joined the Computer Science Department,Uni-

versity of California,Berkeley,as an Emmy

Noether Fellow of the German Science Founda-

tion,where he is currently working on optimiza-tion methods for perceptual grouping and image segmentation.His research interests include computer vision,image processing,unsu-pervised learning,data analysis,and data mining.

.For more information on this or any other computing topic, please visit our Digital Library at https://www.wendangku.net/doc/bb18285121.html,/publications/dilb.

522IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE,VOL.24,NO.24,APRIL

2002

最小二乘法及其应用..

最小二乘法及其应用 1． 引言 最小二乘法在19世纪初发明后,很快得到欧洲一些国家的天文学家和测地学家的广泛关注。据不完全统计,自1805年至1864年的60年间,有关最小二乘法的研究论文达256篇,一些百科全书包括1837年出版的大不列颠百科全书第7版,亦收入有关方法的介绍。同时,误差的分布是“正态”的,也立刻得到天文学家的关注及大量经验的支持。如贝塞尔( F. W. Bessel, 1784—1846)对几百颗星球作了三组观测,并比较了按照正态规律在给定范围内的理论误差值和实际值,对比表明它们非常接近一致。拉普拉斯在1810年也给出了正态规律的一个新的理论推导并写入其《分析概论》中。正态分布作为一种统计模型,在19世纪极为流行,一些学者甚至把19世纪的数理统计学称为正态分布的统治时代。在其影响下,最小二乘法也脱出测量数据意义之外而发展成为一个包罗极大,应用及其广泛的统计模型。到20世纪正态小样本理论充分发展后,高斯研究成果的影响更加显著。最小二乘法不仅是19世纪最重要的统计方法,而且还可以称为数理统计学之灵魂。相关回归分析、方差分析和线性模型理论等数理统计学的几大分支都以最小二乘法为理论基础。正如美国统计学家斯蒂格勒( S. M. Stigler)所说,“最小二乘法之于数理统计学犹如微积分之于数学”。最小二乘法是参数回归的最基本得方法所以研究最小二乘法原理及其应用对于统计的学习有很重要的意义。 2. 最小二乘法 所谓最小二乘法就是：选择参数10,b b ,使得全部观测的残差平方和最小. 用数学公式表示为： 21022)()(m in i i i i i x b b Y Y Y e --=-=∑∑∑∧ 为了说明这个方法，先解释一下最小二乘原理，以一元线性回归方程为例. i i i x B B Y μ++=10 （一元线性回归方程）

数据库死锁问题总结

数据库死锁问题总结 1、死锁（Deadlock） 所谓死锁：是指两个或两个以上的进程在执行过程中，因争夺资源而造 成的一种互相等待的现象，若无外力作用，它们都将无法推进下去。此时称系 统处于死锁状态或系统产生了死锁，这些永远在互相等待的进程称为死锁进程。由于资源占用是互斥的，当某个进程提出申请资源后，使得有关进程在无外力 协助下，永远分配不到必需的资源而无法继续运行，这就产生了一种特殊现象 死锁。一种情形，此时执行程序中两个或多个线程发生永久堵塞（等待），每 个线程都在等待被其他线程占用并堵塞了的资源。例如，如果线程A锁住了记 录1并等待记录2，而线程B锁住了记录2并等待记录1，这样两个线程就发 生了死锁现象。计算机系统中,如果系统的资源分配策略不当，更常见的可能是 程序员写的程序有错误等，则会导致进程因竞争资源不当而产生死锁的现象。 锁有多种实现方式，比如意向锁，共享－排他锁，锁表，树形协议，时间戳协 议等等。锁还有多种粒度，比如可以在表上加锁，也可以在记录上加锁。(回滚 一个，让另一个进程顺利进行) 产生死锁的原因主要是： （1）系统资源不足。 （2）进程运行推进的顺序不合适。 （3）资源分配不当等。 如果系统资源充足，进程的资源请求都能够得到满足，死锁出现的可能 性就很低，否则就会因争夺有限的资源而陷入死锁。其次，进程运行推进顺序 与速度不同，也可能产生死锁。 产生死锁的四个必要条件： （1）互斥条件：一个资源每次只能被一个进程使用。 （2）请求与保持条件：一个进程因请求资源而阻塞时，对已获得的资源保持不放。 破解：静态分配(分配全部资源) （3）不剥夺条件:进程已获得的资源，在末使用完之前，不能强行剥夺。 破解：可剥夺 （4）循环等待条件:若干进程之间形成一种头尾相接的循环等待资源关系。 破解：有序分配 这四个条件是死锁的必要条件，只要系统发生死锁，这些条件必然成立，而只要上述条件之一不满足，就不会发生死锁。 死锁的预防和解除：

1、曲线拟合及其应用综述

曲线拟合及其应用综述 摘要：本文首先分析了曲线拟合方法的背景及在各个领域中的应用，然后详细介绍了曲线拟合方法的基本原理及实现方法，并结合一个具体实例，分析了曲线拟合方法在柴油机故障诊断中的应用，最后对全文内容进行了总结，并对曲线拟合方法的发展进行了思考和展望。 关键词：曲线拟合最小二乘法故障模式识别柴油机故障诊断 1背景及应用 在科学技术的许多领域中，常常需要根据实际测试所得到的一系列数据，求出它们的函数关系。理论上讲，可以根据插值原则构造n 次多项式Pn(x)，使得Pn(x)在各测试点的数据正好通过实测点。可是, 在一般情况下，我们为了尽量反映实际情况而采集了很多样点，造成了插值多项式Pn(x)的次数很高，这不仅增大了计算量，而且影响了函数的逼近程度；再就是由于插值多项式经过每一实测样点，这样就会保留测量误差，从而影响逼近函数的精度，不易反映实际的函数关系。因此，我们一般根据已知实际测试样点，找出被测试量之间的函数关系，使得找出的近似函数曲线能够充分反映实际测试量之间的关系，这就是曲线拟合。 曲线拟合技术在图像处理、逆向工程、计算机辅助设计以及测试数据的处理显示及故障模式诊断等领域中都得到了广泛的应用。 2 基本原理 2.1 曲线拟合的定义 解决曲线拟合问题常用的方法有很多，总体上可以分为两大类：一类是有理论模型的曲线拟合，也就是由与数据的背景资料规律相适应的解析表达式约束的曲线拟合；另一类是无理论模型的曲线拟合，也就是由几何方法或神经网络的拓扑结构确定数据关系的曲线拟合。 2.2 曲线拟合的方法 解决曲线拟合问题常用的方法有很多，总体上可以分为两大类：一类是有理论模型的曲线拟合，也就是由与数据的背景资料规律相适应的解析表达式约束的曲线拟合；另一类是无理论模型的曲线拟合，也就是由几何方法或神经网络的拓扑结构确定数据关系的曲线拟合。 2.2.1 有理论模型的曲线拟合 有理论模型的曲线拟合适用于处理有一定背景资料、规律性较强的拟合问题。通过实验或者观测得到的数据对（x i,y i）（i=1,2, …,n），可以用与背景资料规律相适应的解析表达式y=f(x,c)来反映x、y之间的依赖关系，y=f(x,c)称为拟合的理论模型，式中c=c0,c1,…c n是待定参数。当c在f中线性出现时，称为线性模型，否则称为非线性模型。有许多衡量拟合优度的标准，最常用的方法是最小二乘法。 2.2.1.1 线性模型的曲线拟合 线性模型中与背景资料相适应的解析表达式为： ε β β+ + =x y 1 （1） 式中，β0，β1未知参数，ε服从N(0，σ2)。 将n个实验点分别带入表达式（1）得到： i i i x yε β β+ + = 1 （2） 式中i=1,2,…n，ε1, ε2,…, εn相互独立并且服从N(0，σ2)。 根据最小二乘原理，拟合得到的参数应使曲线与试验点之间的误差的平方和达到最小，也就是使如下的目标函数达到最小： 2 1 1 ) ( i i n i i x y Jε β β- - - =∑ = （3） 将试验点数据点入之后，求目标函数的最大值问题就变成了求取使目标函数对待求参数的偏导数为零时的参数值问题，即： ) ( 2 1 1 = - - - - = ? ?∑ = i i n i i x y J ε β β β （4）

死锁问题解决方法

Sqlcode -244 死锁问题解决 版本说明 事件日期作者说明 创建09年4月16日Alan 创建文档 一、分析产生死锁的原因 这个问题通常是因为锁表产生的。要么是多个用户同时访问数据库导致该问题，要么是因为某个进程死了以后资源未释放导致的。 如果是前一种情况，可以考虑将数据库表的锁级别改为行锁，来减少撞锁的机会；或在应用程序中，用set lock mode wait 3这样的语句，在撞锁后等待若干秒重试。 如果是后一种情况，可以在数据库端用onstat -g ses/onstat -g sql/onstat -k等命令找出锁表的进程，用onmode -z命令结束进程；如果不行，就需要重新启动数据库来释放资源。 二、方法一 onmode -u 将数据库服务器强行进入单用户模式，来释放被锁的表。注意：生产环境不适合。 三、方法二 1、onstat -k |grep HDR+X 说明：HDR+X为排他锁，HDR 头，X 互斥。返回信息里面的owner项是正持有锁的线程的共享内存地址。 2、onstat -u |grep c60a363c 说明：c60a363c为1中查到的owner内容。sessid是会话标识符编号。 3、onstat -g ses 20287 说明：20287为2中查到的sessid内容。Pid为与此会话的前端关联的进程标识符。 4、onstat -g sql 20287

说明：20287为2中查到的sessid内容。通过上面的命令可以查看执行的sql语句。 5、ps -ef |grep 409918 说明：409918为4中查到的pid内容。由此，我们可以得到锁表的进程。可以根据锁表进程的重要程度采取相应的处理方法。对于重要且该进程可以自动重联数据库的进程，可以用onmode -z sessid的方法杀掉锁表session。否则也可以直接杀掉锁表的进程 kill -9 pid。 四、避免锁表频繁发生的方法 4.1将页锁改为行锁 1、执行下面sql语句可以查询当前库中所有为页锁的表名： select tabname from systables where locklevel='P' and tabid > 99 2、执行下面语句将页锁改为行锁 alter table tabname lock mode(row) 4.2统计更新 UPDATE STATISTICS; 4.3修改数据库配置onconfig OPTCOMPIND参数帮助优化程序为应用选择合适的访问方法。 ?如果OPTCOMPIND等于0，优化程序给予现存索引优先权，即使在表扫描比较快时。 ?如果OPTCOMPIND设置为1，给定查询的隔离级设置为Repeatable Read时，优化程序才使用索引。 ?如果OPTCOMPIND等于2，优化程序选择基于开销选择查询方式。，即使表扫描可以临时锁定整个表。 *建议设置：OPTCOMPIND 0 # To hint the optimizer 五、起停informix数据库 停掉informix数据库 onmode -ky 启动informix数据库 oninit 注意千万别加-i参数，这样会初始化表空间，造成数据完全丢失且无法挽回。

最小二乘法原理及应用【文献综述】

毕业论文文献综述 信息与计算科学 最小二乘法的原理及应用 一、国内外状况 国际统计学会第56届大会于2007年8月22-29日在美丽的大西洋海滨城市、葡萄牙首都里斯本如期召开。应大会组委会的邀请，以会长李德水为团长的中国统计学会代表团一行29人注册参加了这次大会。北京市统计学会、山东省统计学会，分别组团参加了这次大会。中国统计界（不含港澳台地区）共有58名代表参加了这次盛会。本届大会的特邀论文会议共涉及94个主题，每个主题一般至少有3-5位代表做学术演讲和讨论。通过对大会论文按研究内容进行归纳，特邀论文大致可以分为四类：即数理统计，经济、社会统计和官方统计，统计教育和统计应用。 数理统计方面。数理统计作为统计科学的一个重要部分，特别是随机过程和回归分析依然展现着古老理论的活力，一直受到统计界的重视并吸引着众多的研究者。本届大会也不例外。 二、进展情况 数理统计学19世纪的数理统计学史, 就是最小二乘法向各个应用领域拓展的历史席卷了统计大部分应用的几个分支——相关回归分析, 方差分析和线性模型理论等, 其灵魂都在于最小二乘法; 不少近代的统计学研究是在此法的基础上衍生出来, 作为其进一步发展或纠正其不足之处而采取的对策, 这包括回归分析中一系列修正最小二乘法而导致的估计方法。 数理统计学的发展大致可分 3 个时期。① 20 世纪以前。这个时期又可分成两段，大致上可以把高斯和勒让德关于最小二乘法用于观测数据的误差分析的工作作为分界线，前段属萌芽时期，基本上没有超出描述性统计量的范围。后一阶段可算作是数理统计学的幼年阶段。首先，强调了推断的地位，而摆脱了单纯描述的性质。由于高斯等的工作揭示了最小二乘法的重要性，学者们普遍认为，在实际问题中遇见的几乎所有的连续变量，都可以满意地用最小二乘法来刻画。这种观点使关于最小二乘法得到了深入的发展，②20世纪初到第二次世界大战结束。这是数理统计学蓬勃发展达到成熟的时期。许多重要的基本观点和方法，以及数理统计学的主要分支学科，都是在这个时期建立和发展起来的。这个时期的成就，包含了至今仍在广泛使用的大多数统计方法。在其发展中，以英国统计学家、生物学家费希尔为代表的英国学派起了主导作用。③战后时期。这一时期中，数理统计学在应用和理论两方面继续获得很大的进展。

最小二乘法综述及举例

最小二乘法综述及算例 一最小二乘法的历史简介 1801年，意大利天文学家朱赛普·皮亚齐发现了第一颗小行星谷神星。经过40天的跟踪观测后，由于谷神星运行至太阳背后，使得皮亚齐失去了谷神星的位置。随后全世界的科学家利用皮亚齐的观测数据开始寻找谷神星，但是根据大多数人计算的结果来寻找谷神星都没有结果。时年24岁的高斯也计算了谷神星的轨道。奥地利天文学家海因里希·奥尔伯斯根据高斯计算出来的轨道重新发现了谷神星。 高斯使用的最小二乘法的方法发表于1809年他的著作《天体运动论》中。 经过两百余年后，最小二乘法已广泛应用与科学实验和工程技术中，随着现代电子计算机的普及与发展，这个方法更加显示出其强大的生命力。 二最小二乘法原理 最小二乘法的基本原理是：成对等精度测得的一组数据),...,2,1(,n i y x i i =，是找出一条最佳的拟合曲线，似的这条曲线上的个点的值与测量值的差的平方和在所有拟合曲线中最小。 设物理量y 与1个变量l x x x ,...,2,1间的依赖关系式为:)(,...,1,0;,...,2,1n l a a a x x x f y =。 其中n a a a ,...,1,0是n +l 个待定参数,记()2 1 ∑=- = m i i i y v s 其中 是测量值, 是由己求 得的n a a a ,...,1,0以及实验点),...,2,1)(,...,(;,2,1m i v x x x i il i i =得出的函数值 )(,...,1,0;,...,2,1n il i i a a a x x x f y =。 在设计实验时, 为了减小误差, 常进行多点测量, 使方程式个数大于待定参数的个数, 此时构成的方程组称为矛盾方程组。通过最小二乘法转化后的方程组称为正规方程组(此时方程式的个数与待定参数的个数相等) 。我们可以通过正规方程组求出a 最小二乘法又称曲线拟合, 所谓“ 拟合” 即不要求所作的曲线完全通过所有的数据点, 只要求所得的曲线能反映数据的基本趋势。 三曲线拟合 曲线拟合的几何解释: 求一条曲线, 使数据点均在离此曲线的上方或下方不远处。 （1）一元线性拟合 设变量y 与x 成线性关系x a a y 10+=,先已知m 个实验点),...,2,1(,m i v x i i =，求两个未知参数1,0a a 。 令()2 1 10∑ =--=m i i i x a a y s ，则1,0a a 应满足1,0,0==??i a s i 。 即 i v i v

《操作系统原理》5资源管理(死锁)习题

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题目:最小二乘法的综述及算例院系：航天学院自动化 班级： 学号： 学生签名： 指导教师签名： 日期：2011年12月6日

目录 1．综述 (3) 2．概念 (3) 3．原理 (4) 4．算例 (6) 5．总结 (10) 参考文献 (10)

1．综述 最小二乘法最早是由高斯提出的，这是数据处理的一种很有效的统计方法。高斯用这种方法解决了天文学方面的问题，特别是确定了某些行星和彗星的天体轨迹。这类天体的椭圆轨迹由5个参数确定，原则上，只要对它的位置做5次测量就足以确定它的整个轨迹。但由于存在测量误差，由5次测量所确定的运行轨迹极不可靠，相反，要进行多次测量，用最小二乘法消除测量误差，得到有关轨迹参数的更精确的值。最小二乘法近似将几十次甚至上百次的观察所产生的高维空间问题降到了椭圆轨迹模型的五维参数空间。 最小二乘法普遍适用于各个科学领域，它在解决实际问题中发挥了重要的作用。它在生产实践、科学实验及经济活动中均有广泛应用。比如说，我们引入等效时间的概念,根据Arrhenius 函数和指数函数研究水化热化学反应速率随温度的变化,最后采用最小二乘法回归分析试验数据,确定绝热温升和等效时间的关系式。 为了更好地掌握最小二乘法，我们引入以下两个问题： (1)假设已知一组二维数据（i i y x ,），（i=1,2,3···n ），怎样确定它的拟合曲线y=f(x)（假设为多项式形式f(x)=n n x a x a a +++...10）,使得这些点与曲线总体来说尽量接近？ (2)若拟合模型为非多项式形式bx ae y =，怎样根据已知的二维数据用最小二乘线性拟合确定其系数，求出曲线拟合函数？ 怎样从给定的二维数据出发，寻找一个简单合理的函数来拟合给定的一组看上去杂乱无章的数据，正是我们要解决的问题。 2．概念 在科学实验的统计方法研究中，往往要从一组实验数（i i y x ,）（i=1,2,3···m ）中寻找自变量x 与y 之间的函数关系y=F(x).由于观测数据往往不准确，此时不要求y=F(x)经过所有点（i i y x ,），而只要求在给定i x 上误差i δ=F （i x ）i y -（i=1,2,3···m ）按某种标准最小。 若记δ=( )δδδm T 2 ,1,就是要求向量δ的范数δ 最小。如果用最大范数，计算上困 难较大，通常就采用Euclid 范数2 δ 作为误差度量的标准。 关于最小二乘法的一般提法是：对于给定的一组数据（i i y x ,） (i=0,1,…m)要求在函数空间Φ=span{ n ???,....,,10}中找一个函数S*(x)，使加权的误差平方和22 δ =

死锁原因和解决方法

1 简单的死锁（不同表,相同资源竞争） 连接1 Set nocount on; Use testdb; Go Begin tran Update dbo.T1 set col1 = col1 + 1 where keycol = 2; 目前链接1获取排它锁，并且一直保持。 连接2 Set nocount on; Use testdb; Begin tran Update dbo.T2 set col1 = col1 + 1 where keycol = 2; 链接2获取排它锁，并且一直保持。 连接1 Select col1 from dbo.T2 where keycol = 2; Commit tran 连接1被阻塞,但是这样还不算死锁，可能连接2也许会在某一时刻结束事务，释放连接1需要资源上的锁。 连接2 Select col1 from dbo.T1 where keycol = 2; Commit tran 这样产生死锁，因为每个进程都在等待另外一个进程释放他们所需要的锁。 解决方法： 如果交换事务中访问表的顺序，并假定这种变化不影响应用程序的逻辑，就可以避免这种死锁。如果两个事务按相同的顺序访问表，就不会放生这样的死锁。当你开发以特定顺序访问表的事务时，可以联系这样做，只要有必要这样做而且不影响程序的逻辑就可以。

2 因缺少索引导致的死锁(不同表不同资源无索引竞争) 当筛选列上缺少索引时就会出现这种情况。如果被筛选列上没有索引，SQLSERVER 必须扫描所有的行。因此当一个进程保持了某一行的锁时，其他的进程扫描所有的行已检查他们是否符合筛选器，而不是通过索引直接找到期望的行，这样就会发生冲突。 T1.col1和T1.col2上都没有索引 连接1 Begin tran Update dbo.T1 set col2 = col2 + 1 where col1 = 101; 连接2 Begin tran Update dbo.T2 set col2 = col2 + 1 where col1 = 203; 连接 1 Select col2 from dbo.T2 where col1 = 201; Commit tran 由于col1没有索引，SQL SERVER必须扫描所有行并获取共享锁以检查这些行是否符合筛选器。所以被连接2阻塞。 连接2 Select col2 from dbo.T1 where col1 = 103; Commit tran 同样也给阻塞，并且发生死锁。 解决方法 通过在被筛选列上创建索引，你可以避免死锁。当然，如果两个进程尝试访问相同的资源还是可能发生死锁。

【文献综述】最小二乘法原理及应用

文献综述 信息与计算科学 最小二乘法的原理及应用 一、国内外状况 国际统计学会第56届大会于2007年8月22-29日在美丽的大西洋海滨城市、葡萄牙首都里斯本如期召开。应大会组委会的邀请，以会长李德水为团长的中国统计学会代表团一行29人注册参加了这次大会。北京市统计学会、山东省统计学会，分别组团参加了这次大会。中国统计界（不含港澳台地区）共有58名代表参加了这次盛会。本届大会的特邀论文会议共涉及94个主题，每个主题一般至少有3-5位代表做学术演讲和讨论。通过对大会论文按研究内容进行归纳，特邀论文大致可以分为四类：即数理统计，经济、社会统计和官方统计，统计教育和统计应用。 数理统计方面。数理统计作为统计科学的一个重要部分，特别是随机过程和回归分析依然展现着古老理论的活力，一直受到统计界的重视并吸引着众多的研究者。本届大会也不例外。 二、进展情况 数理统计学19世纪的数理统计学史, 就是最小二乘法向各个应用领域拓展的历史席卷了统计大部分应用的几个分支——相关回归分析, 方差分析和线性模型理论等, 其灵魂都在于最小二乘法; 不少近代的统计学研究是在此法的基础上衍生出来, 作为其进一步发展或纠正其不足之处而采取的对策, 这包括回归分析中一系列修正最小二乘法而导致的估计方法。 数理统计学的发展大致可分 3 个时期。① 20 世纪以前。这个时期又可分成两段，大致上可以把高斯和勒让德关于最小二乘法用于观测数据的误差分析的工作作为分界线，前段属萌芽时期，基本上没有超出描述性统计量的范围。后一阶段可算作是数理统计学的幼年阶段。首先，强调了推断的地位，而摆脱了单纯描述的性质。由于高斯等的工作揭示了最小二乘法的重要性，学者们普遍认为，在实际问题中遇见的几乎所有的连续变量，都可以满意地用最小二乘法来刻画。这种观点使关于最小二乘法得到了深入的发展，②20世纪初到第二次世界大战结束。这是数理统计学蓬勃发展达到成熟的时期。许多重要的基本观点和方法，以及数理统计学的主要分支学科，都是在这个时期建立和发展起来的。这个时期的成就，包含了至今仍在广泛使用的大多数统计方法。在其发展中，以英国统计学家、生物学家费希尔为代表的英国学派起了主导作用。③战后时期。这一时期中，数理统计学在应用和理论两方面继续获得很大的进展。

浅谈操作系统中的死锁问题

浅谈操作系统中的死锁问题 学院：数学与计算机科学学院 姓名 学号：

摘要：进程死锁问题是操作系统的主要问题之一，很多学者专家一直在研究怎样解决这个问题。本文针对操作系统中经常出现的死锁问题进行了讨论，阐述了死锁出现的原因、四个必要条件，以及死锁的处理方法。 关键词：死锁；死锁产生的原因；死锁产生的条件；死锁的解除与预防；银行家算法。 一、死锁的概述： 死锁是进程死锁的简称，是由Dijkstra于1965年研究银行家算法时首先提出的。所谓死锁是指两个或两个以上的进程在执行过程中，因争夺资源而造成的一种互相等待的现象，若无外力作用，它们都将无法推进下去.此时称系统处于死锁状态或系统产生了死锁，这些永远在互相等待的进程称为死锁进程。 二、产生死锁的原因： 因为系统资源不足；进程运行推进的顺序不合适；资源分配不当等。如果系统资源充足，进程的资源请求都能够得到满足，死锁出现的可能性就很低，否则就会因争夺有限的资源而陷入死锁。其次，进程运行推进顺序与速度不同，也可能产生死锁 三、产生死锁的四个必要条件： 互斥条件：一个资源每次只能被一个进程使用。请求与保持条件（占有等待）：一个进程因请求资源而阻塞时，对已获得的资源保持不放。不剥夺条件（不可抢占）：进程已获得的资源，在未使用完之前，不能强行剥夺。循环等待条件：若干进程之间形成一种头尾相接的循环

等待资源关系。 四、死锁的解除与预防： 理解了死锁的原因，尤其是产生死锁的四个必要条件，就可以最大可能地避免、预防和解除死锁。在系统设计、进程调度等方面注意如何不让这四个必要条件成立，如何确定资源的合理分配算法，避免进程永久占据系统资源。 ⑴有序资源分配法。这种算法资源按某种规则系统中的所有资源统一编号（例如打印机为1、磁带机为2、磁盘为3、等等），申请时必须以上升的次序。 采用有序资源分配法：R1的编号为1，R2的编号为2；PA：申请次序应是：R1，R2；PB：申请次序应是：R1，R2；这样就破坏了环路条件，避免了死锁的发生。 ⑵银行算法。避免死锁算法中最有代表性的算法是DijkstraE.W于1968年提出的银行家算法。该算法需要检查申请者对资源的最大需求量，如果系统现存的各类资源可以满足申请者的请求，就满足申请者的请求。这样申请者就可很快完成其计算，然后释放它占用的资源，从而保证了系统中的所有进程都能完成，所以可避免死锁的发生。五、死锁排除的方法： 撤消陷于死锁的全部进程；逐个撤消陷于死锁的进程，直到死锁不存在；从陷于死锁的进程中逐个强迫放弃所占用的资源，直至死锁消失；从另外一些进程那里强行剥夺足够数量的资源分配给死锁进程，以解除死锁状态。死锁是网络中最容易发生的故障之一，即使在网络负荷

关于进程中死锁问题的研究

关于进程中死锁问题的研究 摘要 死锁问题是Dijkstra于1965年研究银行家算法时首先提出的，也是计算机操作系统乃至并发程序设计中非常重要但又最难处理的问题之一。实际上死锁问题是一种具有普遍性的现象。不仅在计算机系统中，就是在其它各个领域乃至日常生活中，也都是屡见不鲜的。掌握对死锁的处理方法，对于指导我们的现实生活，都会有积极地意义。本文研究的是操作系统进程中的死锁问题。从理论上说，死锁问题的研究涉及到计算机科学中一个基本问题，即并行程序的终止性问题。本文将通过对死锁的基本概念、产生的原因和产生死锁的四个必要条件的了解，找出合理的预防、避免、检测和解除的有效方法，并将其运用到实际问题中去。 关键字：死锁的预防死锁的避免银行家算法死锁的检测死锁的解除 一、死锁的基本概念 1.1 死锁的概念 当两个或两个以上的进程因竞争系统资源而无休止的相互等待时，我们就称这些进程是死锁的，或者说它们处于死锁状态。 1.2 死锁产生的原因 1、各进程竞争有限的资源。 2、进程推进顺序不当。 1.3 产生死锁的四个必要条件 1、互斥条件。指在一段时间内，一个资源只能由一个进程独占使用，若别的进程也要求该资源，则须等待直至其占用者释放。 2、请求和保持条件。指进程已经保持了至少一个资源，但又提出新的请求，而该资源已被其他进程占用，此时请求进程阻塞，但又不释放自己已获得的资源。 3、不可剥夺条件。进程所获得的资源在未使用完之前，不能被其他进程强行夺走，而只能由其自身释放。

4、环路条件。指存在一个等待进程集合{}n P P P P ,,,,210 ，0P 正在等待一个1P 占用的资源，1P 正在等待一个2P 占用的资源，…，n P 正在的等待一个由0P 占用的资源。这些进程及其请求的资源构成一个“进程——资源”的有向循环图。 二、死锁的处理 2.1 死锁的预防 死锁的预防是排除死锁的静态策略，因为我们已经知道了导致死锁产生的四个必要条件，那么我们只须破坏这四个条件中的一个即可预防死锁。为此介绍如下4种方法。 1、共享使用法 允许一个资源部件可以由多个进程“同时”使用。这种方法在早期曾使用过，但实践证明这种方法对有些资源是行不通的。如对宽行就是由各个进程“同时”使用，结果在打印纸上交替出现了不同进程的不同信息，从而给用户带来很大的不便，故对此类资源一般都采用独占方式。由于对大多数资源来说互斥使用是完全必要的，所以通过破坏互斥条件来防止死锁是不现实的。 2、预先静态分配法 在进程调度程序选择进程时，仅当进程所需要的全部资源都能满足时，才调度它进入内存运行。或者说，在进程尚处于运行前的静态情况下，就为它分配了所需要的全部资源。显然这是一种简单而安全的预防死锁的方法，但是，若资源搭配不当，就会导致进程将延迟运行，资源利用率低。 3、采用剥夺式调度法 这种方法主要用在处理器和存储器资源调度上，是调度进程自身的开销，以及主存和磁盘的对换进程、数据的开销。但对于需要由操作员装卸私有数据的外围设备，此法就不宜使用。这种方法实现起来比较复杂，且要付出很大的代价，还可能导致反复地请求和释放资源，而使进程的执行无限延迟。这不仅延长了进程的周转时间，还增加了系统的开销，降低了系统的吞吐量。 4、有序资源使用法 系统设计者把系统中所有资源都赋予一个唯一的编号。如令输入机为1，