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A$ne invariant detection of perceptually parallel

*Corresponding author.Tel.:#852-2788-8641;fax:#852-2784-4916.

E-mail addresses:dgshen @https://www.wendangku.net/doc/158654714.html, (D.Shen),cship @https://www.wendangku.net/doc/158654714.html,.hk (H.H.S.

Ip).

Pattern Recognition 33(2000)1909}1918

A $ne invariant detection of perceptually parallel

3D planar curves

Dinggang Shen ,Horace H.S.Ip *,Eam Khwang Teoh

Department of Radiology,School of Medicine,Johns Hopkins Uni v ersity,601N.Caroline Street,Baltimore,MD 21287,USA

Image Computing Group,Department of Computer Science,City Uni v ersity of Hong Kong,Kowloon,Hong Kong

School of Electrical and Electronic Engineering,Nanyang Technological Uni v ersity,Singapore 639798

Received 7January 1999;received in revised form 9July 1999;accepted 9July 1999

Abstract

The problem of parallelism detection between two curves has been formulated in this paper as a line detection problem within an a z ne-in v ariant local similarity matrix computed for the two curves.Each element of this matrix gives an a $ne invariant measure of local parallelism for any pair of curve segments along the two curves.This approach enables the detection of a pair of parallel 3D planar curves as well as parallel 2D curves under general a $ne transform.Two descriptors were also used here to provide a multi-resolution representation of a curve.Since these two descriptors provide su $cient local and semi-local shape information at every feature point on the curves,the process of detecting parallelism is thus robust against both noise and deformations.Moreover,the proposed technique allows all signi "cant pairs of parallel segments within any two curves in the scene to be detected.Experiments on detecting randomly a $ne-transformed curves,which are obtained from natural images or arti "cially generated images,have demonstrated the e !ectiveness of the technique. 2000Pattern Recognition Society.Published by Elsevier Science Ltd.All rights reserved.

Keywords:Parallelism detection;Local invariants;Semi-local invariants;A $ne invariant;Shape matching;Symmetry detection;3D parallel curves;Hand-written digit recognition

1.Introduction

The detection of symmetries is an essential step when inferring shapes from contours [1].Particularly,skewed symmetries and parallel symmetries have been shown to be useful in recovering the 3D structure of various types of objects from their 2D contours [2,3].Results from the study of perceptual organization in Ref.[4]also showed that primitive grouping in our vision system is done on proximity,collinearity,curvilinearity,parallelism ,sym-

metry,closure and repetitive patterns.Symmetries (in-cluding parallelism)have played important roles in shape perception [5].

The detection of skewed symmetries has been investi-gated by many researchers in the past [6,7].Depending on the nature of the features extracted from a shape,existing methods for symmetry detection can be roughly classi "ed into local and global approaches [6].There are advantages and disadvantages associated,respectively,with these two approaches.To overcome some of the disadvantages relating to both global and local ap-proaches,Sato and Cipolla [8]proposed integral invari-ant based on group invariant parameterization.They showed that integral invariant did not su !er from occlu-sion problem and is less sensitive to noise than di !eren-tial invariant.We also have developed techniques in Ref.[9]for the detection of both local and global symmetries

as well as skewed symmetries using the a$ne-invariant representation developed in Refs.[10,11].Based on this representation,in this paper,the detection of skewed symmetries has been simpli"ed and formulated as a line detection problem with known orientations within a local similarity matrix.

Parallelism is an important form of symmetries,and the detection of parallelism between two curves has at-tracted much attention in the vision community in the past.By representing the various properties of parallel-ism in terms of several distinctive forces,the second author has developed a force-driven model as a new optimization strategy to compute correspondence be-tween salient points extracted from the matching curves [12].This force-driven mechanism provides good coup-ling(or correspondence matching)results,which is the prerequisite for the correct detection of parallelism be-tween curves.

For curves to be parallel,certain point-wise corre-spondence between two curves must exist.Based on this observation,the research issues on parallelism detection are closely related to those for shape matching.Addition-ally,extra constraints like proximity and similarity in orientation should be added if parallelism detection is to be formulated as a shape matching problem.This is due to the fact that in shape matching the two input shapes may be under very di!erent orientation or even under severe a$ne transformation with respect to each other. Almost all solutions to shape(curve)matching were based on descriptor distance measures.Normally,local descriptors were favored since global descriptors could not handle partial matching,but local descriptors are sensitive to both noise and local deformation.Further-more,when the correspondence for the two matching curves are known,transformation parameters between these two curves can be estimated.

In this paper,we introduced two descriptors,namely, Semi-local shape descriptor and Tree-descriptor.Since these two descriptors extract both local and semi-local shape information from the curves,the process of detect-ing parallelism is thus robust against both noise and deformations.More importantly,the problem of parallel-ism detection can then be formulated as a line detection problem with known orientation within an a z ne-in v ari-ant local similarity matrix.Since the technique proposed here allows all signi"cant pairs of parallel segments con-tained in the two matching curves to be detected,partial matches for parallelism can also be detected.

We organize the paper as follows.The formulations of two descriptors are given in Section2.There,for every feature point,we establish(a)a feature vector which is able to capture both local and semi-local shape features, and(b)a set of Tree-like lines which connect the current feature point and its neighboring feature points for suc-cessive scales.Based on the two descriptors de"ned in Sections2and3describes a technique for detecting all signi"cant pairs of parallel segments contained in the two matching curves.In fact,the process of parallelism detec-tion is achieved by detecting lines of known orientations within an a z ne-in v ariant local similarity matrix,which contains the similarity measures calculated through the two descriptors for every pair of feature points along the two matching curves.A number of experiments on de-tecting randomly a$ne-transformed curves,which are obtained from natural or hand-drawn images,are given in Section4.This paper concludes in Section5.

2.Two new shape descriptors

Based on the de"nition of the parallelism given below, we provide two descriptors for detecting parallel seg-ments within two curves.These two descriptors were then combined to de"ne a set of similarity measures in the next section,and then used for parallelism detection for the two curves.

2.1.De x nition of parallelism

For curves to be parallel,certain point-wise corre-spondence between two curves must exist.Based on this requirement,the de"nition of parallelism from[1]is given below.

2.1.1.A de x nition of parallelism

Let r G(t)"[x G(t),y G(t)]2,for i"1,2,be two curves parameterized by arc length t.Let G(t)"arctan ((d y G(t)/d t)/(d x G(t)/d t)).Then r (t)and r (t)are said to be parallel symmetric if there exist a point-wise correspond-ence f(t)between them such that (t)" (f(t))for all values of t for which r and r are de"ned and f(t)is a continuous monotonous function.A useful special case is when f(t)is restricted to be a linear function.

To solve the parallelism detection problem for the discrete case,let us assume that+(x G ,y G ),(x G ,y G ) ,2,(x G,G,y G,G),,for i"1,2,is the set of feature points representing the curve r G in a particular scale.Here,N G is the total number of sampling points on the curve r G. These feature points can be extracted,for example,from the sample points,which are evenly distributed along the a z ne-length shape boundary[13].To render these fea-ture points robust against noise,we take the same num-ber of points from both sides of a sample point and average them to obtain a feature point.

Based on the above de"nition of parallelism,two shape descriptors can be de"ned as follows.

2.2.Semi-local shape descriptor

From the point of view of shape matching,the detec-tion of parallelism can be approached as the problem of matching between two shapes.An a$ne-invariant

1910 D.Shen et al./Pattern Recognition33(2000)1909}1918

feature vector for every feature point on the curve has been developed by the authors and applied to a number of problems:shape matching and indexing [10,14],model-based adaptive image segmentation [11],and de-tection of the skewed symmetries (both rotational sym-metry and re #ectional symmetry)[9].

In the following,we will use our a $ne-invariant feature vector as a semi-local shape descriptor for every feature point on the two curves.This way,corresponding feature points on a pair of parallel segments should have similar feature vectors.The de "nition of the a $ne-invari-ant feature vector has been presented in Ref.[11]but we will brie #y review it here for completeness.

Let r G (t )and r G (t )be the "rst and second derivatives of the curve r G (t ),where i "1,2.Their de "nitions are r G (t )"[x G (t )y G (t )]2" d x G (t )d t d y G (t )d t

r G (t )"[x G (t )y G (t )]2"

d x G (t )d t d y G (t )d t

Under general a $ne transformations,the following three

expressions are invariant up to a scale factor:

"(r G (t )!r G (t ))(r G (t )!r G (t ))","(r G (t )!r G (t

))r G (t )","r G (t )r (G (t )",

where ")"denotes the determinant of a matrix.That is,their values remain unchanged up to a factor which is equal to the determinant of the a $ne transformation.In this paper,we will use

"r G (t )r G (t )""

(x G (t )y G (t )!x G (t )y G (t ))to de "ne an a $ne-invariant feature vector for every point along the curve r G (t ).

The "rst and second derivatives of x G (t )and y G (t )with respect to t can be approximated as follows:x G (t )"d x G (t )d t &

x G (t )!x G (t ! t )x G (t )"d x G (t )d t &

x G (t )!2x G (t ! t )#x G (t !2 t )

t t y G (t )"d y G (t )d t &

y G (t )!y G (t ! t )

y G (t )"d y G (t )d t &

y G (t )!2y G (t ! t )#y G (t !2 t )

Using the above approximations,we can obtain 12"r G (t )r G (t )""1

x G (t !2 t )x G (t ! t )x G (t )

x G (t !2 t )y G (t ! t )y G (t )111

.The above expression indicates that the value of

"r G (t )r G (t )"denotes the area of a triangle,formed by three vertices (x G (t !2 t ),y G (t !2 t )),(x G (t ! t ),y G (t ! t ))

and (x G (t ),y G (t )).

In fact,the area of any triangle is relatively a $ne invariant and the ratios of such areas are a $ne invariant:area R R R "1

x G (t )x G (t )x G (t )y G (t )

y G (t )y G (t )1

,where area R R R

is the area of a triangle,whose three

vertices are (x G (t ),y G (t )),(x G (t ),y G (t ))and (x G (t ),y G (t

)).

Notice,t ,t and t

are the parameters of the curve.

Accordingly,an a $ne-invariant feature vector can be designed for every feature point of the given curves.For the k th feature point (x G I ,y G I

),its corresponding feature

vector is de "ned as F G I "[f G I f G I ....f G +I ]2,where f G HI "12

x G I \H x G I x G I>H y G I \H

y G I y G I>H 1

is the area of a triangle formed by (x G I \H ,y G I \H ),(x G I ,y G I

and (x G I>H ,y G I>H

).(Notice that the integer variables k

and l are in domains,M #1)k )N !M and M #1)l )N !M .)The size of M in e !ect determines the sampling resolution of the curve for our representa-tion.It should be noted that if j is close to 1,f G HI

denotes

local feature,i.e.f G HI

(for small j )extracts information of

local shape centered on the point (x G I ,y G I

),which is sensi-tive to noises.As j increases,f G HI

gradually captures the

semi-local features of the curve,i.e.f G HI

extracts low-fre-quency (smooth)information of the shape,which is less sensitive to digitization noise.In essence,f G HI

gives,after

suitable normalization,in a single feature vector,both local and semi-local a $ne-invariant information of the curve with respect to a single point on the curve.Fig.1shows the Semi-local shape descriptor for the k th feature point (x G I ,y G I

)on the i th curve.

F G I

can be made exactly a $ne-invariant by the follow-ing normalization:

F G I "F G I ,G I +H "f G HI

where F G I "[f G I f G I ....f G +I

]2.

The curve r G (t )can thus be described by a set of a $ne-invariant feature vectors,

+F G I

,k "M #1,M #2,2,N G !M and i "1,2,.In Section 3,we will adopt this a $ne-invariant local shape descriptor and use them to compute a set of sim-ilarity measures for every coupled feature points on a pair of curves.

D.Shen et al./Pattern Recognition 33(2000)1909}19181911

Fig.1.An illustration of the area-based semi-local shape de-

scriptor.

Fig.2.(a)An illustration of the Tree descriptor;(b)A di !erence

measure between two corresponding vectors.

2.3.Tree-descriptor

It is easy to observe that for every feature point (x I ,y I

)

on the curve r ,the vector joining this feature point and its neighboring feature point should be parallel to the corresponding vector on the curve r if the two curves were parallel.In Fig.2,for example,if the two matching curves were parallel,the vector linking two successive feature points < I and < I \H

on one curve should also be

parallel to the vector linking the corresponding pairs of feature points < J and < J \H

on the other curve,where

!M )j )1or 1)j )M and M is a small constant compared to N G .(To satisfy the requirements,1)k !j )N and 1)l !j )N ,here we limit the integer variables k and l in the domains,M #1)k )N !M and M #1)l )N !M .)If we jointly

consider the same number (M )of feature points before and after the feature point

and de "ne the resulting set

of Tree-liked vectors 1ree (

,then

every corresponding pair of vectors,respectively,in 1ree (< I )and 1ree (< J

)should also be parallel.Notice,

there are 2H M vectors (or lines)in the set 1ree (

),which

is named Tree descriptor in this paper.An a $ne-invari-ant measure will be de "ned for the two Tree descriptors,1ree (< I )and 1ree (< J ),in Section 3.

3.Detection of parallel curves

3.1.De x nition of the a z ne-in v ariant local similarity

matrix

3.1.1.A similarity measure based on the Semi-local shape descriptor

Suppose that two curves r and r are parallel and the feature points < I and < J

,respectively,on the "rst curve

r and the second curve r are the corresponding points.Then their feature vectors,F I and F J

,should be the

same.More importantly,this property holds even under a $ne-transformation.Mathematically,the matching er-ror S I J between the feature vectors F I and F J is as

follows:

S I J "(F J !F I )2G (F J !F I

),where G is an M ;M diagonal matrix de "ned by a Gaus-sian function,i.e.

G "[g KK ]+"+and g KK "

e \ K +\

N .

In fact,G is a weighting matrix used for controlling the contributions from di !erent feature elements.For simpli-"cation,we use a normalized similarity measure S I J

represent the similarity of feature point pair.A de "nition of S I J can be obtained from the matching error S I J as

follows:

S I J "1!

S I J Max I J S

I J

.(1)

From the above de "nition,it is easy to observe that the value of S G J is also invariant to any a $ne transformation.

3.1.2.A similarity measure based on the Tree-descriptor From Section 2.3,we observe qualitatively that for two parallel curves,the corresponding vectors,respectively,in the sets 1ree (< I )and 1ree (< J

)should also be parallel.

That is,the vector < I < I \H

should be parallel to the

vector < J < J \H

.To formalize this observation and to

design a similarity measure that is a $ne invariant,an area-based technique is also suggested here.If the vector

1912 D.Shen et al./Pattern Recognition 33(2000)1909}1918

Fig.3.An example showing that in practice two perceptually parallel curves are not always exactly parallel,but their corresponding Tree descriptors are similar (see right-corner sub "gure,where one curve has been moved to match another curve).

< I < I \H is exactly parallel to the vector < J < J \H ,the following measure 1IJ

(j )should be 0.

1I J (j )"0.5#< I < I \H #)#< J < J \H #)"sin IJH

",where IJH "angle(< I < I \H ,< J < J \H )and #< I < I \H

#is the

length of vector < I < I \H .1IJ

(j )is in e !ect the magnitude

of the cross-product of the two vectors.In Fig.2(b),we align the vectors < J < J \H and < I < I \H

and made the point

< J localized on the point < I

.This way,the descriptor 1IJ

(j )is equal to the area of the triangle with the three vertices < I ,< I \H and (< J \H

) .(Notice that the de "nition of

1I J

(j )is relatively a $ne-invariant.)But in practice,for example,for hand-drawn parallel curves or curves extracted by image processing routines,two curves are seldom exactly parallel.Fig.3gives examples for such inexact parallelism.We can determine the degree of local parallelism 1I J

be-tween the two curve segments from their corresponding Tree descriptor,1ree (< I )and 1ree (< J

),as follows:

1I J "+

H \+H $ 1I J

(j )"+

H \+H $

0.5#< I < I \H #)#< J < J \H #)"sin IJH

where IJH "angle(< I < I \H ,< J < J \H

Similarly,we can normalize 1I J

as follow,and render

1I J

exactly a $ne invariant.1I J "1!1I J Max I J 1

I J

(2)

3.1.3.A z ne-in v ariant local similarity matrix

These two measures of local similarity,derived,respec-tively,from our Semi-local shape descriptor and Tree descriptor,can be combined and used to de "ne the a z ne-in v ariant local similarity measure as follows:E I J "(1! )S I J # 1I J

,(3)

where is a regularization parameter used for controlling the contribution from the two terms.In our experiments,we use "0.75.Notice the value of E I J

is between 0

and 1.

We can therefore compute the above similarity measures for every pair of feature points,respectively,on the two curves to form an a z ne-in v ariant local similarity matrix .Each element of such a matrix gives a measure of local similarity for a pair of points,respectively,on the two curves.We show in the following that using the a z ne-in v ariant local similarity matrix ,parallelism detec-tion between two curves can be achieved by detecting

D.Shen et al./Pattern Recognition 33(2000)1909}19181913

Fig.4.Parallelism detection on two thick curves in (a1).Sub "gures (a1}a4)shows the a $ne-transformed curves and their parallelism detection results by our method,where thin lines link the corresponding points.Sub "gure (b1)represents the shape similarity measures based on Semi-local shape descriptor,while sub "gure (b2)represents the parallel measures based on the Tree-descriptor.The combined a $ne-invariant local similarity matrix is shown in (c1).The binarized a $ne invariant local similarity matrix is given in (c2).Sub "gure (c3)gives the result of line segmentation,while in (c4)the grey line is the "tting line for this segmented region.

a line with slope #1within the matrix.This greatly simpli "es the parallelism detection process.

Let us assume that one segment (Seg

)on the "rst

curve r is parallel to another segment (Seg

)on the

second curve r ,and also the k th feature point on the segment Seg

of the "rst curve r corresponds to the l th

feature point on the segment Seg

of the second curve r .

Under this ideal condition,the a $ne-invariant local similarity measure should be E I J "1.This way,if we

visualize the local similarity matrix,E "[E I J

],as an

image with intensities between 0and 1(level 1means white ),then,in the ideal case,we would observe in this image a continuous white line (i.e.line of 1s)passing through the position (k ,l )with slope equal to #1(see Fig.4(c1)for example).

In practice,since noise and deformation on the curves may occur,the a $ne-invariant local similarity measure,E I J

,may not be exactly 1.To cater for noise,as well as 1914 D.Shen et al./Pattern Recognition 33(2000)1909}1918

For some applications,we may be unable to guarantee that the sampling orders,respectively,for the two studied curves are the same.In these cases,we have to operate the above algorithm on the same curves twice.During the x rst operation,the algo-rithm is performed on the two curves with the sampling orders provided originally.If there exist any pair of parallel segments on these two curves,they can be directly detected.During the second operation,we reverse one curve 's sampling order and then perform the algorithm

again.

Fig.5.Parallelism detection on two thick curves.Tests are performed under random a $ne-transformations.

variability in the sample point selection and to make allowance for deformation,we instead look for high intensity lines with slope #1in the image produced by the a $ne-invariant local similarity matrix (also see Fig.4.(c1}c4)for example).

The reason why we suggest combining the two sim-ilarity measures for parallelism detection can be ex-plained by the example described below.For instance,if the shapes of two curves are identical then the similarity measure based on the semi-local shape descriptor alone is su $cient to detect such occurrence.However,in gen-eral,two curves having identical shape cannot be con-sidered parallel, e.g.when one curve has undergone a rotational transform with respect to the other.So the second similarity measure based on Tree descriptor is needed in order to constrain that the two curves to have the similar shape as well as orientation for parallelism detection.

3.2.Parallelism detection based on the a z ne-in v ariant local similarity matrix

An important conclusion of the above discussions is that lines of 1s with slope #1in the a z ne-in v ariant local similarity matrix indicates the location and exis-tence of parallel segments,respecti v ely,on the two cur v es .It follows that parallelism detection can be formulated as a line detection problem within the similarity matrix,more importantly,the orientation of the line becomes a known a priori under this formulation.

Many algorithms exist for line detection from image intensities.Here,we "rst binarize the a $ne-invariant local similarity matrix at a suitable threshold value.In our experiments,we set our threshold at S G J

"https://www.wendangku.net/doc/158654714.html,-ing this threshold,we can get a binarized local similarity matrix,where E I J "0if E I J

(0.55.(Fig.4(c2)shows a

binarized local similarity image from Fig.4(c1).)

Given the binarized local similarity matrix,it is easy to detect all line segments with slope #1within it through suitable spatial "ltering such as morphological opening and closing with a line structuring element (Fig.4(c3)).For every connected regions,a line "tting procedure is employed to obtain the "tted line.See Fig.4(c4)for example.

Interestingly,there may exist a set of lines within the matrix,which gives the set of potential parallel curve segments in the two curves.In fact,we can easily obtain the transformation relationship between every pair of segments,since we already know their correspondence [10,11].Such transformation information can be used to determine whether one curve segment has been rotated through a large orientation with respect to another curve segment.We can "lter out the pair of curve segments which are separated by a signi "cant angle of rotation between them if necessary.

Based on the above development,we can de "ne our parallelism detection algorithm as follows:

(1)Binarize the a $ne-invariant local similarity matrix.(2)Detect line segments within it with slope #1using

line-"tting procedure.

(3)Select "tted lines satisfying the constraint condition

that the pairs of curve segments should be related with only a small rotation angle,and with at least a certain length.

(4)Display the lines joining the corresponding points,

respectively,on the two curves.

4.Experimental results

In this section,we will provide a series of experimental results on parallelism detection.The proposed algorithm is tested by (a)curves obtained from natural or hand-drawn images (Figs.4}7),and (b)curves from hand-written digits (Fig.8).

Fig.4illustrates the process of parallelism detection.The two curves being studied are the two thick curves in (a1).Sub "gure (b1)represents the Semi-local similarity measures S G J

calculated by Semi-local shape descriptor,

while sub "gure (b2)represents the Tree similarity

measures 1I J

by the Tree descriptor.Observing these D.Shen et al./Pattern Recognition 33(2000)1909}19181915

Fig.8.Parallelism detection experiments on handwriting digits under a $

ne-transformations.

Fig.6.Another example on parallelism detection,where two thick curves are the matching curves.All the tests are performed under random a $ne-transformations on a pair of

curves.Fig.7.Two pairs of segments on the two thick curves are,respectively,parallel.The thin lines are the resulted parallelism detected by our method.

two similarity images,it is easy to see that the Semi-local similarity measure S G J

and the Tree similarity measure

1I J

in fact compare di !erent shape information localized on the two curves.The a $ne-invariant local similarity

matrix is shown in (c1).The binarized similarity matrix is given in (c2).The result of line detection is given in sub "gure (c3),while the "tted line for detected line segments is shown as a grey line in (c4).Sub "gures (a1}a4)shows the a $ne-transformed curves (thick curves)and the results of parallelism detection by our method,where thin lines link the corresponding points.Other two parallelism detection experiments are given in Figs.5and 6.

There may exist more than one signi "cant pairs of parallel segments on two curves.Fig.7shows an example of the detection of two pairs of parallel segments.

As an application,we also show experimentally that our algorithm can be applied to the skeletons of

1916 D.Shen et al./Pattern Recognition 33(2000)1909}1918

handwriting digits,which may be useful for online or o!-line handwriting digits checking.Since the result of parallelism detection and the total matching error(a summation of the combined local similarity measures)on the detected pair of segments can be used for determining the similarity between the input handwriting digit and the models in the database.Fig.8shows some prelimi-nary results on hand-written digits.

5.Conclusion

In this paper,we present two new shape descriptors, Semi-local shape descriptor and Tree descriptor,which can be used for parallelism detection between two3D planar curves.The Semi-local shape descriptor captures both local and semi-local features for every feature point on the curves,and the Tree descriptor serves to give measure on the degree of local parallelism for the seg-ments on a curve with respect to another curve.Based on these two descriptors,we develop an a$ne-invariant local similarity matrix and simplify the problem of paral-lelism detection into a line detection problem within the a$ne-invariant local similarity matrix,computed for the two curves.

Since these two shape descriptors provide su$cient local and semi-local shape information at every feature point along a curve,the process of detecting parallelism is thus robust against both noise and deformations.More-over,the technique allows all signi"cant pairs of parallel segments within two curves to be detected.

In our experiments,we applied the proposed technique to detecting randomly a$ne-transformed curves.Some of the testing curves are obtained from natural images, while others are manually drawn.We also applied the proposed technique to the skeletons of handwriting digits,which may be interesting if parallelism detection were used as an approach for recognizing online/o!-line handwriting digits.References

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[12]H.H.S.Ip,W.H.Wong,Detecting perceptually parallel

curves*criteria and force-driven optimization,Comput.

Vision Image Understanding68(2)(1997)190}208. [13]L.van Gool,T.Moons, D.Ungureanu, E.Pauwels,

Symmetry from shape and shape from symmetry,Int.J.

Robotics Res.14(5)(1995)407}424.

[14]W.H.Wong,D.Shen,H.H.S.Ip,A$ne invariant shape

matching for content-based retrieval,ICARCV'96, Singapore,December1996.

About the Author*DINGGANG SHEN received his B.S.,M.S.and Ph.D.degrees in Electronics Engineering from Shanghai JiaoTong University(SJTU)in1990,1992and1995,respectively.He worked as Research Assistant in the Department of Computer Science at the Hong Kong University of Science&Technology from December1994to June1995.From September1995to February1996,he was a Lecturer of Communication Engineering at Shanghai JiaoTong University.He was a Research Fellow in the Department of Computer Science at City University of Hong Kong,from February1996to August1997.From June1997to February1999,he worked"rst as Post-Doctoral Fellow and then as Research Fellow in the School of Electrical and Electronic Engineering at Nanyang Technological University,Singapore.Since January1999,he worked as Postdoctoral Research Fellow in School of Medicine at Johns Hopkins University,doing medical imaging.His research interests are in the areas of computer vision,pattern recognition,image processing, neural network and image indexing and retrieval.

About the Author*HORACE H.S.IP received his B.Sc.(First Class Honours)degree in Applied Physics and Ph.D.degree in Image Processing from University College London,United Kingdom,in1980and1983,respectively.Presently,he is the Professor and Head of the Computer Science Department and also heads the Image Computing Research Group,at City University of Hong Kong.His research interests include image processing and analysis,pattern recognition,hypermedia computing systems and computer graphics. Prof.Ip is a member of the Editorial Boards for Pattern Recognition(Elsevier),the International Journal of Multimedia Tools and

D.Shen et al./Pattern Recognition33(2000)1909}19181917

1918 D.Shen et al./Pattern Recognition33(2000)1909}1918

Applications(Kluwer Academic),and the Chinese Journal of CAD and Computer Graphics(The Chinese Academy of Science)and a guest editor of the international journal of Real-Time Imaging(Academic Press).

Prof.Ip serves on the IAPR Governing Board and co-chairs its Technical Committee on Multimedia Systems.He was the Chairman of the IEEE(HK)Computer chapter,and the Founding President of the Hong Kong Society for Multimedia and Image Computing.He has published over80papers in international journals and conference proceedings.

About the Author*EAM KHWANG TEOH received his B.E.and M.E.degrees in Electrical Engineering from the University of Auckland,New Zealand in1980and1982,respectively,and the Ph.D.degree in Electrical&Computer Engineering from the University of Newcastle,New South Wales in1986.Presently,he is a Vice-Dean and an Associate Professor in the School of Electrical and Electronic Engineering,Nanyang Technological University,Singapore.He is a co-inventor of an Australian Patent on An Adaptive Thickness Controller for a Rolling Mill.His current research interests are in the"eld of Computer Vision and Pattern Recognition, Intelligent Systems,Robotics and Industrial Automation.He has published more than150journal and conference papers in these areas.

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初中开学第一课主题班会初中开学第一课主题班会同学们，新学期新打算，你们做了怎样的计划和目标呢? 请班委会代表发言，学生代表做准备。 3、班委代表发言作为班委会的一员，我要严格要求自己，处处做表率。升入初中以来，我总认为时间长着呢，学习态度不端正，成绩不理想。在这初中生活的最后一个学期，我一定努力学习，以优异的成绩升入高中深造。此外生活在这个班级中，我要和同学们团结起来，和睦相处在这个大集体里，珍惜我们之间的友谊。对自己的工作大胆负责，给同学们创造好的学习环境。班主任：谢谢班委会代表精彩的发言，下面请学生代表发言。 4、学生代表发言来到闫什镇中学，相聚在九年级二班，是我们的缘分。原来，我从不预习，预习也就是只是个形式，做给老师看罢了，对于课堂四十分钟，心情好便听一点，心情不好也就开小差。学习也是依个人的喜好而定，喜欢的老师所教科目成绩优异，然而不喜欢的老师所教科目成绩却十分差。现在是初中生活的最后一个学期，我感到了压力，有压力才有动力，我一定努力拼搏，为进入高中做好准备。另外尊敬师长，团结同学，积极参加各种活动。班主任：

新视野大学英语读写教程第一册课文翻译及课后答案

Unit 1 1学习外语是我一生中最艰苦也是最有意义的经历之一。虽然时常遭遇挫折，但却非常有价值。 2我学外语的经历始于初中的第一堂英语课。老师很慈祥耐心，时常表扬学生。由于这种积极的教学方法，我踊跃回答各种问题，从不怕答错。两年中，我的成绩一直名列前茅。 3到了高中后，我渴望继续学习英语。然而，高中时的经历与以前大不相同。以前，老师对所有的学生都很耐心，而新老师则总是惩罚答错的学生。每当有谁回答错了，她就会用长教鞭指着我们，上下挥舞大喊：“错！错！错！”没有多久，我便不再渴望回答问题了。我不仅失去了回答问题的乐趣，而且根本就不想再用英语说半个字。 4好在这种情况没持续多久。到了大学，我了解到所有学生必须上英语课。与高中老师不。大学英语老师非常耐心和蔼，而且从来不带教鞭！不过情况却远不尽如人意。由于班大，每堂课能轮到我回答的问题寥寥无几。上了几周课后，我还发现许多同学的英语说得比我要好得多。我开始产生一种畏惧感。虽然原因与高中时不同，但我却又一次不敢开口了。看来我的英语水平要永远停步不前了。 5直到几年后我有机会参加远程英语课程，情况才有所改善。这种课程的媒介是一台电脑、一条电话线和一个调制解调器。我很快配齐了必要的设备并跟一个朋友学会了电脑操作技术，于是我每周用5到7天在网上的虚拟课堂里学习英语。 6网上学习并不比普通的课堂学习容易。它需要花许多的时间，需要学习者专心自律，以跟上课程进度。我尽力达到课程的最低要求，并按时完成作业。 7我随时随地都在学习。不管去哪里，我都随身携带一本袖珍字典和笔记本，笔记本上记着我遇到的生词。我学习中出过许多错，有时是令人尴尬的错误。有时我会因挫折而哭泣，有时甚至想放弃。但我从未因别的同学英语说得比我快而感到畏惧，因为在电脑屏幕上作出回答之前，我可以根据自己的需要花时间去琢磨自己的想法。突然有一天我发现自己什么都懂了，更重要的是，我说起英语来灵活自如。尽管我还是常常出错，还有很多东西要学，但我已尝到了刻苦学习的甜头。 8学习外语对我来说是非常艰辛的经历，但它又无比珍贵。它不仅使我懂得了艰苦努力的意义，而且让我了解了不同的文化，让我以一种全新的思维去看待事物。学习一门外语最令人兴奋的收获是我能与更多的人交流。与人交谈是我最喜欢的一项活动，新的语言使我能与陌生人交往，参与他们的谈话，并建立新的难以忘怀的友谊。由于我已能说英语，别人讲英语时我不再茫然不解了。我能够参与其中，并结交朋友。我能与人交流，并能够弥合我所说的语言和所处的文化与他们的语言和文化之间的鸿沟。 III. 1. rewarding 2. communicate 3. access 4. embarrassing 5. positive 6. commitment 7. virtual 8. benefits 9. minimum 10. opportunities IV. 1. up 2. into 3. from 4. with 5. to 6. up 7. of 8. in 9. for 10.with V. 1.G 2.B 3.E 4.I 5.H 6.K 7.M 8.O 9.F 10.C Sentence Structure VI. 1. Universities in the east are better equipped, while those in the west are relatively poor. 2. Allan Clark kept talking the price up, while Wilkinson kept knocking it down. 3. The husband spent all his money drinking, while his wife saved all hers for the family. 4. Some guests spoke pleasantly and behaved politely, while others wee insulting and impolite. 5. Outwardly Sara was friendly towards all those concerned, while inwardly she was angry. VII. 1. Not only did Mr. Smith learn the Chinese language, but he also bridged the gap between his culture and ours. 2. Not only did we learn the technology through the online course, but we also learned to communicate with friends in English. 3. Not only did we lose all our money, but we also came close to losing our lives.

新大学日语简明教程课文翻译

新大学日语简明教程课文翻译第21课一、我的留学生活我从去年12月开始学习日语。已经3个月了。每天大约学30个新单词。每天学15个左右的新汉字，但总记不住。假名已经基本记住了。简单的会话还可以，但较难的还说不了。还不能用日语发表自己的意见。既不能很好地回答老师的提问，也看不懂日语的文章。短小、简单的信写得了，但长的信写不了。来日本不久就迎来了新年。新年时，日本的少女们穿着美丽的和服，看上去就像新娘。非常冷的时候，还是有女孩子穿着裙子和袜子走在大街上。我在日本的第一个新年过得很愉快，因此很开心。现在学习忙，没什么时间玩，但周末常常运动，或骑车去公园玩。有时也邀朋友一起去。虽然我有国际驾照，但没钱，买不起车。没办法，需要的时候就向朋友借车。有几个朋友愿意借车给我。二、一个房间变成三个从前一直认为睡在褥子上的是日本人，美国人都睡床铺，可是听说近来纽约等大都市的年轻人不睡床铺，而是睡在褥子上，是不是突然讨厌起床铺了？日本人自古以来就睡在褥子上，那自有它的原因。人们都说日本人的房子小，从前，很少有人在自己的房间，一家人住在一个小房间里是常有的是，今天仍然有人过着这样的生活。在仅有的一个房间哩，如果要摆下全家人的床铺，就不能在那里吃饭了。这一点，褥子很方便。早晨，不需要褥子的时候，可以收起来。在没有了褥子的房间放上桌子，当作饭厅吃早饭。来客人的话，就在那里喝茶；孩子放学回到家里，那房间就成了书房。而后，傍晚又成为饭厅。然后收起桌子，铺上褥子，又成为了全家人睡觉的地方。如果是床铺的话，除了睡觉的房间，还需要吃饭的房间和书房等，但如果使用褥子，一个房间就可以有各种用途。据说从前，在纽约等大都市的大学学习的学生也租得起很大的房间。但现在房租太贵，租不起了。只能住更便宜、更小的房间。因此，似乎开始使用睡觉时作床，白天折小能成为椅子的、方便的褥子。

初中德育主题班会教案.pdf

初中德育主题班会教案学校德育是指教育者按照一定的社会或阶级要求，有目的、有计划、有系统地对受教育者施加思想、政治和道德等方面的影响，小编收集了初中德育主题班会教案，欢迎阅读。初中德育主题班会教案【一】活动背景：在当今的青少年学生中，不少人对应有的礼仪不重视，礼仪观念淡薄，导致思想品德滑坡。一些人在学校里，不会尊重他人，不会礼让，不讲礼貌；在社会上不懂怎样称呼他人，甚至随心所欲，满口粗言烂语；在家里不懂孝敬长辈，唯我独尊，为所欲为等形象屡见不鲜，这些现象不得不引起我们的深思。青少年学习”礼仪”，要以学会尊重他人为起点，礼仪本身就是尊重人的外在表现形式，”礼仪”从话里来，话从心中来，只有从内心尊重人，才会有得体的礼仪言行，尊重他人是人与人接触的必要和首要态度。活动目的： 1、通过看录像、听录音、阅读材料、讨论等系列活动，使学生懂得我们中华民族是世界闻名的”礼仪之邦”，讲文明礼貌是中华民族的优良传统，是做人的美德，更是一个现代文明人必须具备的美德。 2、通过主题班会活动，使学生继承优良传统美德，增强爱国情感，从小养成良好的行为习惯，初步树立社会责任感。2、把礼仪常规贯穿到歌谣、小品、朗诵等各种表演形式之中，让学生受到情趣的熏陶和思想品德的教育，懂得礼仪对于每个学生成长的重要性。活动准备： 1、开班会前，我们班开展一系列教育活动作为班会的前期铺垫：搜集中华文明礼仪的故事等资料；调查争做文明学生的做法。 2、关于学生礼仪的音像、文字材料。 3、环境布置（黑板、场地等）。 4、组织学生准备有关节目。

活动过程：一、活动导入主持人：自古以来就是礼仪之邦，文明礼貌是中华民族的优良传统，作为高中生，我们更不能忘记传统，应该力争做一个讲文明、懂礼貌的好学生，让文明之花常开心中，把文明之美到处传播！现在我宣布：《文明礼仪伴我行》主题班会现在开始。二、活动开始（一）、家庭文明礼仪。主持人：是一个有着几千年文明历史的古国，文化源远流长。作为礼仪之邦，历史上有很多故事至今仍深深的教育着我们，下面请观看历史故事：《孔融让梨》、《黄香诚心敬父母》（放录像）（放完录像）主持人：看到这两个小故事，同学们觉得在生活中我们应该怎么对待我们的父母和兄弟姐妹？学生自由发言。主持人：现在我们都是独生子女，没有兄弟姐妹，那么我们在一起生活的同学们呢？看了下面的表演的小品，我想大家一定会有不同的看法。下面请欣赏由高烨等表演的小品：《快乐的同学们》（表演结束）主持人：通过这个小品，大家认为该如何与同学们相处？学生自由发言。主持人：如果家里来了客人我们应该怎么做呢？下面请欣赏小品《家里来客了》（二）、校园文明礼仪主持人：是一个有着几千年文明历史的古国，文化源远流长“礼学”是文化的重要组成部分。在，自古以来，讲究做人要懂得礼貌谦让，因此被称为“文章

新视野大学英语第一册Unit 1课文翻译

新视野大学英语第一册Unit 1课文翻译学习外语是我一生中最艰苦也是最有意义的经历之一。虽然时常遭遇挫折，但却非常有价值。我学外语的经历始于初中的第一堂英语课。老师很慈祥耐心，时常表扬学生。由于这种积极的教学方法，我踊跃回答各种问题，从不怕答错。两年中，我的成绩一直名列前茅。到了高中后，我渴望继续学习英语。然而，高中时的经历与以前大不相同。以前，老师对所有的学生都很耐心，而新老师则总是惩罚答错的学生。每当有谁回答错了，她就会用长教鞭指着我们，上下挥舞大喊：“错！错！错！” 没有多久，我便不再渴望回答问题了。我不仅失去了回答问题的乐趣，而且根本就不想再用英语说半个字。好在这种情况没持续多久。到了大学，我了解到所有学生必须上英语课。与高中老师不同，大学英语老师非常耐心和蔼，而且从来不带教鞭！不过情况却远不尽如人意。由于班大，每堂课能轮到我回答的问题寥寥无几。上了几周课后，我还发现许多同学的英语说得比我要好得多。我开始产生一种畏惧感。虽然原因与高中时不同，但我却又一次不敢开口了。看来我的英语水平要永远停步不前了。直到几年后我有机会参加远程英语课程，情况才有所改善。这种课程的媒介是一台电脑、一条电话线和一个调制解调器。我很快配齐了必要的设备并跟一个朋友学会了电脑操作技术，于是我每周用5到7天在网上的虚拟课堂里学习英语。网上学习并不比普通的课堂学习容易。它需要花许多的时间，需要学习者专心自律，以跟上课程进度。我尽力达到课程的最低要求，并按时完成作业。我随时随地都在学习。不管去哪里，我都随身携带一本袖珍字典和笔记本，笔记本上记着我遇到的生词。我学习中出过许多错，有时是令人尴尬的错误。有时我会因挫折而哭泣，有时甚至想放弃。但我从未因别的同学英语说得比我快而感到畏惧，因为在电脑屏幕上作出回答之前，我可以根据自己的需要花时间去琢磨自己的想法。突然有一天我发现自己什么都懂了，更重要的是，我说起英语来灵活自如。尽管我还是常常出错，还有很多东西要学，但我已尝到了刻苦学习的甜头。学习外语对我来说是非常艰辛的经历，但它又无比珍贵。它不仅使我懂得了艰苦努力的意义，而且让我了解了不同的文化，让我以一种全新的思维去看待事物。学习一门外语最令人兴奋的收获是我能与更多的人交流。与人交谈是我最喜欢的一项活动，新的语言使我能与陌生人交往，参与他们的谈话，并建立新的难以忘怀的友谊。由于我已能说英语，别人讲英语时我不再茫然不解了。我能够参与其中，并结交朋友。

新大学日语阅读与写作1 第3课译文

习惯与礼仪我是个漫画家，对旁人细微的动作、不起眼的举止等抱有好奇。所以，我在国外只要做错一点什么，立刻会比旁人更为敏锐地感觉到那个国家的人们对此作出的反应。譬如我多次看到过，欧美人和中国人见到我们日本人吸溜吸溜地出声喝汤而面露厌恶之色。过去，日本人坐在塌塌米上，在一张低矮的食案上用餐，餐具离嘴较远。所以，养成了把碗端至嘴边吸食的习惯。喝羹匙里的东西也象吸似的，声声作响。这并非哪一方文化高或低，只是各国的习惯、礼仪不同而已。日本人坐在椅子上围桌用餐是1960年之后的事情。当时，还没有礼仪规矩，甚至有人盘着腿吃饭。外国人看见此景大概会一脸厌恶吧。韩国女性就座时，单腿翘起。我认为这种姿势很美，但习惯于双膝跪坐的日本女性大概不以为然，而韩国女性恐怕也不认为跪坐为好。日本等多数亚洲国家，常有人习惯在路上蹲着。欧美人会联想起狗排便的姿势而一脸厌恶。日本人常常把手放在小孩的头上说“好可爱啊！”，而大部分外国人会不愿意。如果向回教国家的人们劝食猪肉和酒，或用左手握手、递东西，会不受欢迎的。当然，饭菜也用右手抓着吃。只有从公用大盘往自己的小盘里分食用的公勺是用左手拿。一旦搞错，用黏糊糊的右手去拿，

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