JP2569401B2 - How to measure and display the degree of deformation of similar shapes - Google Patents
How to measure and display the degree of deformation of similar shapesInfo
- Publication number
- JP2569401B2 JP2569401B2 JP61028289A JP2828986A JP2569401B2 JP 2569401 B2 JP2569401 B2 JP 2569401B2 JP 61028289 A JP61028289 A JP 61028289A JP 2828986 A JP2828986 A JP 2828986A JP 2569401 B2 JP2569401 B2 JP 2569401B2
- Authority
- JP
- Japan
- Prior art keywords
- shape
- deformation
- degree
- deformed
- reference shape
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Lifetime
Links
Landscapes
- Length Measuring Devices With Unspecified Measuring Means (AREA)
- Image Analysis (AREA)
Description
【発明の詳細な説明】 ［産業上の利用分野］ 本発明は、類似形状の変形度を定量的に計測表示する
方法に関するものである。Description: TECHNICAL FIELD The present invention relates to a method for quantitatively measuring and displaying the degree of deformation of a similar shape.
［従来の技術］ 一般に、類似性をもつ複数の物体形状について、それ
らの類似性がどの程度のものであるか、あるいはどのよ
うな態様で変形しているかを定量的に計測表示すること
は、非常に困難であり、従来から、類似形状の変形の程
度を満足に計測表示する方法は提案されていない。[Prior Art] Generally, for a plurality of object shapes having similarity, quantitatively measuring and displaying how much similarity is or how the object is deformed is It is very difficult, and a method of measuring and displaying the degree of deformation of a similar shape satisfactorily has not been proposed.
しかしながら、例えばパターン認識技術等によって認
識した物体形状が、基準となる物体形状に対してどの程
度類似しているかを調べたり、あるいは混在する複数の
類似形状の物体をその形状に応じて仕分けする場合など
に、形状相互の類似性を判断するために、形状変化の傾
向をも含めた基準形状に対する変形の程度を定量的に計
測表示できるようにしておけば、極めて有効に利用でき
るものと考えられる。However, for example, when examining how similar an object shape recognized by a pattern recognition technique or the like is to a reference object shape, or when sorting a plurality of mixed objects having similar shapes according to the shape. In order to judge the similarity between shapes, for example, if it is possible to quantitatively measure and display the degree of deformation with respect to the reference shape including the tendency of shape change, it can be considered to be extremely effective .
［発明が解決しようとする問題点］ 本発明の目的は、基準形状と変形形状の類似性に関
し、例えば、完全に同一形状であるとか、相似性を有す
るとか、特定方向に変形しているなどの、変形の傾向を
も含めて、基準形状に対する変形程度を極めて簡易な手
段で定量的に計測表示できる方法を提供することにあ
る。[Problems to be Solved by the Invention] An object of the present invention relates to the similarity between a reference shape and a deformed shape. For example, the shape is completely identical, has similarity, or is deformed in a specific direction. Another object of the present invention is to provide a method capable of quantitatively measuring and displaying the degree of deformation with respect to a reference shape, including the tendency of deformation, by extremely simple means.
［問題点を解決するための手段］ 上記目的を達成するため、本発明の計測表示方法は、
基準形状が有する多数の特徴点（ｎ個）に対応する特徴
点を備えた上記基準形状と対比すべき変形形状につい
て、基準形状の重心を原点とした直交座標系における上
記基準形状の各特徴点の座標（x,y）と、上記基準形状
と対比すべき変形形状の重心を原点とした直交座標系に
おける上記基準形状の特徴点に対点の座標（x,y）と、
上記基準形状と対比すべき変形形状の重心を原点とした
直交座標系における上記基準形状の特徴点に対応する各
特徴点の座標（ｘ′,y′）から、 ｘ′＝αｉ・ｘ ｙ′＝βｉ・ｙ （ｉ＝1,2,・・,n） によって与えられる各特徴点についての変換係数（αi,
βｉ）を求め、上記変形形状の変形度をこれらの変換係
数により基準形状との対比において二次元的に計測表示
ることを特徴とするものである。[Means for Solving the Problems] In order to achieve the above object, the measurement display method of the present invention comprises:
For the deformed shape to be compared with the reference shape having feature points corresponding to a number of feature points (n) of the reference shape, each feature point of the reference shape in an orthogonal coordinate system with the origin being the center of gravity of the reference shape And coordinates (x, y) of a feature point of the reference shape in the orthogonal coordinate system with the center of gravity of the deformed shape to be compared with the reference shape as an origin,
From the coordinates (x ′, y ′) of each feature point corresponding to the feature point of the reference shape in the orthogonal coordinate system with the origin being the center of gravity of the deformed shape to be compared with the reference shape, x ′ = α i · xy '= Β i · y (i = 1,2, ···, n), and the transform coefficient (α i ,
β i ) is obtained, and the degree of deformation of the deformed shape is measured and displayed two-dimensionally in comparison with the reference shape using these conversion coefficients.
［作 用］ 基準形状と変形形状の類似性、即ち変形度が、変換係
数（αi,βｉ）によって二次元的に計測表示され、各特
徴点についての変換係数の分散状態から、変形形状が基
準形状に対してどのように変形しているのか、その変形
の傾向を知ることができる。特に、上記変換係数による
類似形状の変形度の計測表示は、各特徴点についての二
つの変換係数（αi,βｉ）を利用するので、その値によ
り変形図形が基準図形に対して無方向的に変形している
とか、基準図形に対して拡大または縮小されているこ
と、x,yの方向との関連における拡大、縮小とか、ま
た、拡大または縮小等の変形の程度を表わすことにな
る。[Operation] The similarity between the reference shape and the deformed shape, that is, the degree of deformation is measured and displayed two-dimensionally by the conversion coefficients (α i , β i ). Is deformed with respect to the reference shape, and the tendency of the deformation can be known. In particular, the measurement and display of the degree of deformation of a similar shape by the above conversion coefficient uses two conversion coefficients (α i , β i ) for each feature point. Deformation, expansion or contraction with respect to the reference figure, enlargement / reduction in relation to the x and y directions, and the degree of transformation such as enlargement or reduction .
［発明の効果］ このような本発明の方法によれば、基準形状と変形形
状の類似性を、特徴点についての上記変換係数（αi,β
ｉ）を求めるという極めて簡易な手段で、しかも少ない
データ量での速い処理により定量化することができ、そ
のうえ、例えば両形状が完全に同一であるとか、相似性
を有するとか、特定方向に変形しているなどの、変形の
傾向をも含めて、基準形状に対する変形度を容易に認識
し易い状態で計測表示することができる。[Effect of the Invention] According to the method of the present invention, the similarity between the reference shape and the deformed shape is determined by using the conversion coefficients (α i , β
i ) can be quantified by a very simple means of obtaining a small amount of data and by rapid processing, and furthermore, for example, both shapes are completely identical, similar, or deformed in a specific direction. It is possible to measure and display the degree of deformation with respect to the reference shape, including the tendency of deformation, such that the degree of deformation is easily recognized.
［実施例］ 以下に図面を参照して本発明の方法をさらに詳細に説
明する。EXAMPLES Hereinafter, the method of the present invention will be described in more detail with reference to the drawings.
いま、第１図に示すように、多数の特徴点P1,P2,P3,
・・間を直線または曲線によって結んだ適宜形状の基準
となる図形が存在し、その図形の重心Ｇにｘ−ｙ直交座
標系の原点があるものとする。上記特徴点は、図形や物
体形状を表わす線上の各頂点、折曲点、一定間隔でとっ
た円弧上の点、その他、何らかの意味をもつ点群によっ
て構成されるものである。また、上記基準図形と対比す
べき第２図のような変形図形が存在し、同様にその図形
の重心Ｇにｘ′−ｙ′直交座標系の原点があるものとす
る。この変形図形は、第１図の各特徴点に対応する対応
特徴点Ｐ′1,P′2,P′3,・・を有するものである。Now, as shown in FIG. 1, a number of feature points P 1 , P 2 , P 3 ,
It is assumed that there is a figure which is a reference of an appropriate shape which is connected by a straight line or a curve, and that the center of gravity G of the figure has the origin of the xy orthogonal coordinate system. The feature points are constituted by vertices on a line representing a figure or an object shape, bending points, points on a circular arc taken at regular intervals, and other point groups having some meaning. It is also assumed that there is a deformed figure as shown in FIG. 2 to be compared with the reference figure, and that the origin of the x'-y 'rectangular coordinate system is located at the center of gravity G of the figure. This deformed figure has corresponding feature points P ′ 1 , P ′ 2 , P ′ 3 ,... Corresponding to the respective feature points in FIG.
上述した基準図形及び変形図形の各特徴点の座標を、
それぞれｘ−ｙ直交座標系及びｘ′−ｙ′座標系によっ
て表わし、さらに、各特徴点についてｘ−ｙ座標系から
ｘ′−ｙ′座標系への座標変換を、 ｘ′＝αｉ・ｘ ｙ′＝βｉ・ｙ によって行うと、変換係数（αi,βｉ）を求めることが
できる。The coordinates of each feature point of the reference graphic and the deformed graphic are
Each 'represented by the coordinate system, further, x'-y from x-y coordinate system for each feature point' x-y orthogonal coordinate system and x'-y coordinate transformation to the coordinate system, x '= α i · x By performing y ′ = β i · y, the conversion coefficient (α i , β i ) can be obtained.
本発明は、この変換係数（αi,βｉ）に基づいて、変
形図形の基準形状に対する変形度を二次元的に計測表示
しようとするものであり、各特徴点の変換係数（αi,β
ｉ）については、それらの平均値や２次モーメントを求
めるなどの手段により、平均的な変形度を求めることが
できる。The present invention intends to measure and display the degree of deformation of the deformed figure with respect to the reference shape two-dimensionally based on the conversion coefficients (α i , β i ). The conversion coefficients (α i , β i , β
Regarding i ), an average degree of deformation can be obtained by means such as obtaining an average value or a second moment.
このような方法によって得られた各特徴点についての
変換係数（αi,βｉ）は、その値自体が基準図形に対す
る変形図形の変形の傾向を示すことになる。即ち、それ
らの値をα−β直角座標系に表示した第３図からわかる
ように、各特徴点についての変換係数がすべて（α＝1,
β＝１）である場合には、変形図形が基準図形と同一で
あり、それらの変換係数が、第３図に例示しているよう
に、（α＝1,β＝１）の近辺にランダムに分散している
場合には、変形図形が基準図形に対して無方向的に変形
していることになる。The values of the conversion coefficients (α i , β i ) for each feature point obtained by such a method indicate the tendency of the deformed figure to be deformed with respect to the reference figure. That is, as can be seen from FIG. 3 in which these values are displayed in the α-β rectangular coordinate system, all the conversion coefficients for each feature point are (α = 1,
In the case of β = 1), the deformed figure is the same as the reference figure, and their conversion coefficients are random around (α = 1, β = 1) as illustrated in FIG. In this case, the deformed figure is deformed non-directionally with respect to the reference figure.
また、同図に示す多数の点群が直線L1の方向にずれて
いることは、変形図形が基準図形に対して拡大または縮
小されていることを意味し、さらに多数の点群が直線L2
の方向にずれていることは、変形図形が、x,yの一方に
拡大し、他方に縮小していることを意味している。Moreover, a large number of point cloud shown in the figure is shifted in the direction of the straight line L 1 means that the deformation shape is enlarged or reduced relative to the reference figure, a larger number of the point group is straight line L Two
Means that the deformed figure is enlarged in one of x and y and reduced in the other.
さらにまた、上記点群が直線L3またはL4の方向にずれ
ていることは、変形図形がｘ方向またはｙ方向にのみ拡
大または縮小されていることを意味している。Furthermore, the above-mentioned point group is shifted in the direction of the straight line L 3 or L 4 are, which means that the deformation figure is enlarged or reduced only in the x or y direction.
しかも、これらのずれの量が拡大または縮小等の変形
の程度を表わすことになる。In addition, the amounts of these deviations indicate the degree of deformation such as enlargement or reduction.
【図面の簡単な説明】 第１図は本発明に係る変形度計測表示方法における基準
形状についての説明図、第２図は同変形形状についての
説明図、第３図は平面形状における変換係数についての
説明図である。 αi,βｉ……変換係数BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory diagram of a reference shape in a deformation degree measuring and displaying method according to the present invention, FIG. 2 is an explanatory diagram of the deformed shape, and FIG. FIG. α i , β i …… Conversion coefficient
───────────────────────────────────────────────────── フロントページの続き (72)発明者 戸田 重郎 鎌倉市梶原４丁目７番１号 株式会社野 村総合研究所内 (56)参考文献 特開 昭55−131711（ＪＰ，Ａ) 特開 昭52−45954（ＪＰ，Ａ) ──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Shigeo Toda 4-7-1 Kajiwara, Kamakura-shi Nomura Research Institute, Inc. (56) References JP-A-55-131711 (JP, A) JP-A-52 −45954 (JP, A)
Claims (1)
対応する特徴点を備えた上記基準形状と対比すべき変形
形状について、基準形状の重心を原点とした直交座標系
における上記基準形状の各特徴点の座標（x,y）と、上
記基準形状と対比すべき変形形状の重心を原点とした直
交座標系における上記基準形状の特徴点に対応する各特
徴点の座標（ｘ′,y′）から、 ｘ′＝αｉ・ｘ ｙ′＝βｉ・ｙ （ｉ＝1,2,・・,n） によって与えられる各特徴点についての変換係数（αi,
βｉ）を求め、上記変形形状の変形度をこれらの変形係
数により基準形状との対比において二次元的に計測表示
することを特徴とする類似形状の変形度の計測表示方
法。1. A deformed shape to be compared with the reference shape having feature points corresponding to a large number (n) of feature points of the reference shape, the reference shape in an orthogonal coordinate system having a center of gravity of the reference shape as an origin. The coordinates (x, y) of each feature point of the shape and the coordinates (x ′ ′) of each feature point corresponding to the feature point of the reference shape in an orthogonal coordinate system whose origin is the center of gravity of the deformed shape to be compared with the reference shape , y ′), the conversion coefficient (α i , y i) for each feature point given by x ′ = α i · x y ′ = β i · y (i = 1, 2,..., n)
β i ), and a method for measuring and displaying the degree of deformation of a similar shape, wherein the degree of deformation of the deformed shape is two-dimensionally measured and displayed in comparison with a reference shape using these deformation coefficients.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP61028289A JP2569401B2 (en) | 1986-02-12 | 1986-02-12 | How to measure and display the degree of deformation of similar shapes |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP61028289A JP2569401B2 (en) | 1986-02-12 | 1986-02-12 | How to measure and display the degree of deformation of similar shapes |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS62185113A JPS62185113A (en) | 1987-08-13 |
| JP2569401B2 true JP2569401B2 (en) | 1997-01-08 |
Family
ID=12244451
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP61028289A Expired - Lifetime JP2569401B2 (en) | 1986-02-12 | 1986-02-12 | How to measure and display the degree of deformation of similar shapes |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2569401B2 (en) |
Families Citing this family (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102506807B (en) * | 2011-10-24 | 2014-03-26 | 北京航天计量测试技术研究所 | Method for measuring deformation amount of mechanical structure |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS55131711A (en) * | 1979-04-02 | 1980-10-13 | Hitachi Ltd | Solid object deformation measuring method |
-
1986
- 1986-02-12 JP JP61028289A patent/JP2569401B2/en not_active Expired - Lifetime
Also Published As
| Publication number | Publication date |
|---|---|
| JPS62185113A (en) | 1987-08-13 |
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Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EXPY | Cancellation because of completion of term |