JP2011047830A

JP2011047830A - Position measuring system, arithmetic unit and program for measuring position

Info

Publication number: JP2011047830A
Application number: JP2009197396A
Authority: JP
Inventors: Yasuji Seko; 保次瀬古
Original assignee: Fuji Xerox Co Ltd
Current assignee: Fujifilm Business Innovation Corp
Priority date: 2009-08-27
Filing date: 2009-08-27
Publication date: 2011-03-10

Abstract

<P>PROBLEM TO BE SOLVED: To provide a position measuring system capable of measuring the position without confusing basic markers for measuring the position of an object imaged by an imaging device with an identification marker for distinction, and to provide an arithmetic unit and a program for measuring the position. <P>SOLUTION: A position measuring system includes; an object 1 having four basic markers a1, b1, c1, d1 forming a quadrangle as a geometrical shape on the plane in a known positional relationship and an identification marker a2 disposed on a plane; an imaging device 3 having a two-dimensional imaging element 2; and an arithmetic unit 4 that calculates a compound ratio utilizing four points on a straight line obtained from an image information of the basic markers and identification marker imaged by the imaging device 3 to identify four basic markers a1, b1, c1, d1 based on the calculated compound ratio, performing the computation to determine at least either one of a three-dimensional position or an angle of the object 1 in accordance with the position information of four identified basic markers a1, b1, c1, d1. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

本発明は、位置計測システム、位置計測用演算装置およびプログラムに関するものである。 The present invention relates to a position measurement system, a position measurement arithmetic device, and a program.

従来から物体の３次元位置を計測する手段として種々の技術が提案されている。例えば、特許文献１には、３次元空間で物体の位置及び方向を決定するための技術が開示されている。この技術は、互いに距離及び幾何の既知な基本標識が探され、基本標識に関してその位置及び方向が知られている任意の点の位置または任意の線の方向が決定される。基本標識にマーカー（基本標識）を配置し、コンピュータ装置を使って、マーカーの位置及びマーカーが固定された装置の方向を計算する。マーカーの位置を決定するための方法は、少なくとも一つのカメラでマーカーを写す工程と、マーカーのイメージを生成する工程と、マーカーの画素座標を探す工程と、画素座標からマーカーの位置を計算するべく基準データを使用する工程とから成る。また、特許文献２には、対象物の位置や方向を簡易かつ高精度に測定することができる技術が開示されている。この技術は、例えば矩形状のカードの頂点に配置した複数のＬＥＤ光源（基本標識）からの光により光リング像を形成し、この光リング像を撮像素子により検出し、その検出情報および各光源の位置関係に基づいて各光源の位置を計測するものである。さらに、特許文献３には、視点方向に依存しないで任意の方向からＩＤタグを読み込み、かつ識別することができる物体ＩＤコード認識装置に関する技術が開示されている。 Conventionally, various techniques have been proposed as means for measuring the three-dimensional position of an object. For example, Patent Document 1 discloses a technique for determining the position and direction of an object in a three-dimensional space. This technique searches for basic markers that are known in distance and geometry from each other and determines the position of any point or the direction of any line whose position and orientation are known with respect to the basic marker. A marker (basic mark) is placed on the basic mark, and the position of the marker and the direction of the apparatus on which the marker is fixed are calculated using a computer device. A method for determining the position of a marker includes: capturing a marker with at least one camera; generating a marker image; searching for a pixel coordinate of the marker; and calculating a marker position from the pixel coordinate. Using the reference data. Patent Document 2 discloses a technique that can easily and accurately measure the position and direction of an object. In this technology, for example, a light ring image is formed by light from a plurality of LED light sources (basic signs) arranged at the apex of a rectangular card, the light ring image is detected by an image sensor, and the detection information and each light source are detected. The position of each light source is measured based on the positional relationship. Furthermore, Patent Document 3 discloses a technique related to an object ID code recognition device that can read and identify an ID tag from an arbitrary direction without depending on the viewpoint direction.

特開２００５−５３７５８３号公報JP 2005-537583 A 特開２００８−５８２０４号公報JP 2008-58204 A 特開２００４−１９２３４２号公報JP 2004-192342 A

本発明の目的は、撮像装置で撮像した物体の位置計測用の基本標識を識別用の識別標識と混同することなく位置計測を行うことができる位置計測システム、位置計測用演算装置およびプログラムを提供することにある。 An object of the present invention is to provide a position measurement system, a position measurement calculation device, and a program capable of performing position measurement without confusing a basic mark for position measurement of an object imaged by an imaging device with an identification mark for identification. There is to do.

本発明は、上記目的を達成するために、以下の位置計測システム、位置計測用演算装置およびプログラムを提供する。
（１）平面上に幾何学的形状を形成する位置関係の分かっている４つ以上の基本標識および前記平面上に配置される１つ以上の識別標識を有する物体と、２次元撮像素子を有する撮像装置と、前記撮像装置により撮像した前記基本標識および前記識別標識の画像情報から得られた直線上の４点を利用して複比を計算し、前記計算した複比に基づいて前記４つ以上の基本標識を識別し、前記識別した４つ以上の基本標識の位置情報に基づいて前記物体の３次元位置および角度の少なくとも一方を求める演算を行う演算装置とを備えた位置計測システム。
（２）前記直線上の４点が、前記４つ以上の基本標識をそれぞれ頂点に配置した四角形以上の多角形における第１の対角線の両端に位置する２つの前記基本標識と、前記第１の対角線上に位置する前記識別標識と、前記第１の対角線とそれとは別の第２の対角線との交点である上記（１）記載の位置計測システム。
（３）前記直線上の４点が、前記４つ以上の基本標識をそれぞれ頂点に配置した四角形以上の多角形における隣接する第１および第２の前記基本標識と、前記多角形の外側に位置する前記識別標識と前記多角形における第３の前記基本標識とを結ぶ第１の直線および第４の前記基本標識とを結ぶ第２の直線と第１および第２の前記基本標識を結ぶ直線との２つの交点である上記（１）記載の位置計測システム。
（４）前記直線上の４点が、前記４つ以上の基本標識をそれぞれ頂点に配置した四角形以上の多角形におけるある対角線の両端に位置する２つの前記基本標識と、前記多角形の内側に位置する幾何学的形状の輪郭部と前記対角線との２つの交点にそれぞれ位置する２つの前記識別標識である上記（１）記載の位置計測システム。
（５）前記直線上の４点が、４つ以上の前記識別標識をそれぞれ頂点に配置した四角形以上の多角形におけるある対角線の両端に位置する２つの前記識別標識と、前記多角形の内側に位置する幾何学的形状の輪郭部と前記対角線との２つの交点にそれぞれ位置する２つの前記基本標識である上記（１）記載の位置計測システム。
（６）前記直線上の４点が、前記４つ以上の基本標識をそれぞれ頂点に配置した四角形以上の多角形の内側に位置する四角形以上の多角形の頂点に位置する隣接する２つの前記識別標識と、前記隣接する２つの前記識別標識を通る直線と前記基本標識を頂点に有する多角形の２辺との２つの交点である上記（１）記載の位置計測システム。
（７）前記直線上の４点が、４つ以上の前記識別標識をそれぞれ頂点に配置した四角形以上の多角形の内側に位置する四角形以上の多角形の頂点に位置する隣接する２つの前記基本標識と、前記隣接する２つの前記基本標識を通る直線と前記識別標識を頂点に有する多角形の２辺との２つの交点である上記（１）記載の位置計測システム。
（８）前記基本標識を頂点に有する多角形および前記識別標識を頂点に有する多角形がそれぞれ四角形である上記（６）または（７）記載の位置計測システム。
（９）前記基本標識または前記識別標識が円形形状である上記（１）〜（８）のいずれかに記載の位置計測システム。
（１０）前記直線上の４点が、前記４つ以上の基本標識をそれぞれ頂点に配置した四角形以上の多角形における隣接する第１および第２の前記基本標識と、前記多角形の外側に位置する４つ以上の前記識別標識をそれぞれ頂点に配置した四角形以上の多角形における隣接する第１および第２の２つの前記識別標識を通る第１および第２の直線と第１および第２の前記基本標識を結ぶ直線との２つの交点である上記（１）記載の位置計測システム。
（１１）前記直線上の４点が、第１および第２の前記基本標識と、第３の前記基本標識と第１の前記識別標識とを通る第１の直線および第４の前記基本標識と第２の前記識別標識とを通る第２の直線と第１および第２の前記基本標識を結ぶ直線との２つの交点である上記（１）記載の位置計測システム。
（１２）平面上に幾何学的形状を形成する位置関係の分かっている４つ以上の基本標識および前記平面上に配置される１つ以上の識別標識を有する物体を２次元撮像素子を有する撮像装置により撮像した前記基本標識および前記識別標識の画像情報から得られた直線上の４点を利用して複比を計算する手段と、前記計算した複比に基づいて前記４つ以上の基本標識を識別する手段と、前記識別した４つ以上の基本標識の位置情報に基づいて前記物体の３次元位置および角度の少なくとも一方を演算する手段とを備えた位置計測用演算装置。
（１３）コンピュータに、平面上に幾何学的形状を形成する位置関係の分かっている４つ以上の基本標識および前記平面上に配置される１つ以上の識別標識を有する物体を２次元撮像素子を有する撮像装置により撮像した前記基本標識および前記識別標識の画像情報から得られた直線上の４点を利用して複比を計算する手順、前記計算した複比に基づいて前記４つ以上の基本標識を識別する手順、前記識別した４つ以上の基本標識の位置情報に基づいて前記物体の３次元位置および角度の少なくとも一方を演算する手順を実行させるプログラム。 In order to achieve the above object, the present invention provides the following position measurement system, position measurement arithmetic device and program.
(1) An object having four or more basic signs having a known positional relationship forming a geometric shape on a plane and one or more identification signs arranged on the plane, and a two-dimensional imaging device A cross ratio is calculated using four points on a straight line obtained from image information of the imaging device and the basic sign and the identification sign taken by the imaging device, and the four ratios are calculated based on the calculated cross ratio. A position measurement system comprising: an arithmetic unit that identifies the above basic signs and performs an operation for obtaining at least one of a three-dimensional position and an angle of the object based on position information of the identified four or more basic signs.
(2) The two basic signs located at both ends of the first diagonal line in the polygons of quadrilateral or more in which the four points on the straight line each have the four or more basic signs arranged at the vertices, and the first The position measurement system according to (1), which is an intersection of the identification mark located on a diagonal line, the first diagonal line, and a second diagonal line different from the first diagonal line.
(3) Four points on the straight line are positioned outside the polygon and the first and second basic signs adjacent to each other in a quadrilateral or more polygon in which the four or more basic signs are arranged at the vertices, respectively. A first straight line connecting the identification mark and the third basic sign in the polygon and a second straight line connecting the fourth basic sign and a straight line connecting the first and second basic signs The position measurement system according to (1), which is an intersection of the two.
(4) The four points on the straight line include two basic signs positioned at both ends of a diagonal line in a polygon of four or more squares each having the four or more basic signs arranged at the vertices, and inside the polygon. The position measurement system according to (1), wherein the two identification marks are respectively located at two intersections of a contour portion of a geometric shape and a diagonal line.
(5) The four points on the straight line include two identification marks positioned at both ends of a diagonal line in a polygon of four or more squares each having four or more identification marks arranged at the vertices, and inside the polygon. The position measurement system according to (1), wherein the two basic signs are respectively located at two intersections of a contour portion of a geometric shape and a diagonal line.
(6) The two adjacent identifications at which the four points on the straight line are located at the vertices of the quadrilateral or higher polygon located inside the quadrilateral or higher polygon each having the four or more basic signs arranged at the vertices, respectively. The position measurement system according to (1) above, which is two intersections of a sign, a straight line passing through the two adjacent identification signs, and two sides of a polygon having the basic sign at the apex.
(7) The two adjacent basic points located at the vertices of a quadrilateral or higher polygon that are located on the inside of a quadrilateral or higher polygon each having four points on the straight line, each having four or more identification marks arranged at the vertices The position measurement system according to (1), which is two intersections of a sign, a straight line passing through the two adjacent basic signs, and two sides of a polygon having the identification sign at the apex.
(8) The position measurement system according to (6) or (7), wherein the polygon having the basic sign at the apex and the polygon having the identification sign at the apex are each a quadrangle.
(9) The position measurement system according to any one of (1) to (8), wherein the basic mark or the identification mark has a circular shape.
(10) The four points on the straight line are positioned outside the polygon and the first and second basic signs adjacent to each other in a quadrilateral or more polygon in which the four or more basic signs are arranged at the vertices, respectively. The first and second straight lines passing through the two adjacent first and second identification signs and the first and second of the identification signs in a polygon of four or more squares each having four or more identification signs arranged at the vertices. The position measurement system according to the above (1), which is two intersections with a straight line connecting basic signs.
(11) Four points on the straight line include the first and second basic signs, the first straight line passing through the third basic sign and the first identification sign, and the fourth basic sign. The position measurement system according to the above (1), which is two intersections of a second straight line passing through the second identification mark and a straight line connecting the first and second basic signs.
(12) Imaging with an object having a two-dimensional imaging device an object having four or more basic signs having a known positional relationship forming a geometric shape on a plane and one or more identification signs arranged on the plane Means for calculating a cross ratio using four points on a straight line obtained from image information of the basic sign and the identification sign picked up by a device; and the four or more basic signs based on the calculated cross ratio And a means for calculating at least one of the three-dimensional position and the angle of the object based on the positional information of the four or more identified basic signs.
(13) A two-dimensional image pickup device that has an object having four or more basic signs having a known positional relationship forming a geometric shape on a plane and one or more identification signs arranged on the plane. A procedure for calculating a cross ratio using four points on a straight line obtained from image information of the basic sign and the identification sign picked up by an image pickup apparatus having the above, and the four or more based on the calculated cross ratio A program for executing a procedure for identifying a basic sign and a procedure for calculating at least one of a three-dimensional position and an angle of the object based on position information of the four or more identified basic signs.

請求項１に記載の位置計測システムによれば、撮像装置で撮像した物体の位置計測用の基本標識を識別用の識別標識と混同することなく位置計測を行うことができる。
請求項２に記載の位置計測システムによれば、４つ以上の基本標識と１つの識別標識を利用して複比を計算することができる。
請求項３に記載の位置計測システムによれば、４つ以上の基本標識と１つの識別標識を利用して複比を計算することができる。
請求項４に記載の位置計測システムによれば、本構成を有しないものに比べ背景画像から基本標識および識別標識を容易に識別し複比を計算することができる。
請求項５に記載の位置計測システムによれば、本構成を有しないものに比べ背景画像から基本標識および識別標識を容易に識別し複比を計算することができる。
請求項６に記載の位置計測システムによれば、基本標識および識別標識の付与が分かり易く複比の計算を容易にすることができる。
請求項７に記載の位置計測システムによれば、基本標識および識別標識の付与が分かり易く複比の計算を容易にすることができる。
請求項８に記載の位置計測システムによれば、基本標識の配置が単純で物品の３次元位置の計算を容易にすることができる。
請求項９に記載の位置計測システムによれば、本構成を有しないものに比べ基本標識または識別標識を精度良く検出することができる。
請求項１０に記載の位置計測システムによれば、基本標識および識別標識の付与が分かり易く複比の計算を容易にすることができる。
請求項１１に記載の位置計測システムによれば、基本標識および識別標識の付与が分かり易く複比の計算を容易にすることができる。
請求項１２に記載の位置計測用演算装置によれば、撮像装置で撮像した物体の位置計測用の基本標識を識別用の識別標識と混同することなく位置計測を行うことができる。
請求項１３に記載のプログラムによれば、撮像装置で撮像した物体の位置計測用の基本標識を識別用の識別標識と混同することなく位置計測を行うことができる。 According to the position measurement system of the first aspect, it is possible to perform position measurement without confusing the basic mark for position measurement of the object imaged by the imaging device with the identification mark for identification.
According to the position measurement system of the second aspect, the cross ratio can be calculated using four or more basic signs and one identification sign.
According to the position measurement system of the third aspect, the cross ratio can be calculated using four or more basic signs and one identification mark.
According to the position measurement system of the fourth aspect, it is possible to easily identify the basic mark and the identification mark from the background image and calculate the cross ratio, compared with the system that does not have this configuration.
According to the position measurement system of the fifth aspect, it is possible to easily identify the basic mark and the identification mark from the background image and calculate the cross ratio as compared to the position measurement system that does not have this configuration.
According to the position measurement system of the sixth aspect, it is easy to understand the provision of the basic mark and the identification mark, and the cross ratio can be easily calculated.
According to the position measurement system of the seventh aspect, it is easy to understand the provision of the basic mark and the identification mark, and the calculation of the cross ratio can be facilitated.
According to the position measurement system of the eighth aspect, the arrangement of the basic signs is simple, and the calculation of the three-dimensional position of the article can be facilitated.
According to the position measurement system of the ninth aspect, it is possible to detect the basic marker or the identification marker with higher accuracy than those without this configuration.
According to the position measurement system of the tenth aspect, it is easy to understand the provision of the basic mark and the identification mark, and the calculation of the cross ratio can be facilitated.
According to the position measuring system of the eleventh aspect, it is easy to understand the provision of the basic mark and the identification mark, and the cross ratio can be easily calculated.
According to the calculation device for position measurement according to the twelfth aspect, it is possible to perform position measurement without confusing the basic mark for position measurement of the object imaged by the imaging device with the identification mark for identification.
According to the program of the thirteenth aspect, it is possible to perform the position measurement without confuse the basic mark for measuring the position of the object imaged by the imaging device with the identification mark for identification.

本発明に係る位置計測システムの一実施例を示す図である。It is a figure which shows one Example of the position measurement system which concerns on this invention. 物品における基本標識および識別標識の配置の一例を示す図である。It is a figure which shows an example of arrangement | positioning of the basic mark and identification mark in articles | goods. 図１の演算装置の一例を示すブロック図である。It is a block diagram which shows an example of the arithmetic unit of FIG. コンピュータにより実行される手順の一例を示すフロー図である。It is a flowchart which shows an example of the procedure performed by a computer. ４つの基本標識を有する物体の３次元位置の演算方法の一例を説明するための図である。It is a figure for demonstrating an example of the calculation method of the three-dimensional position of the object which has four basic signs. 物品における基本標識および識別標識の配置の他の例を示す図である。It is a figure which shows the other example of arrangement | positioning of the basic label and identification label | marker in articles | goods. （ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。(A), (b) is a figure which shows the further another example of arrangement | positioning of the basic label and identification label | marker in articles | goods. （ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。(A), (b) is a figure which shows the further another example of arrangement | positioning of the basic label and identification label | marker in articles | goods. （ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。(A), (b) is a figure which shows the further another example of arrangement | positioning of the basic label and identification label | marker in articles | goods. （ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。(A), (b) is a figure which shows the further another example of arrangement | positioning of the basic label and identification label | marker in articles | goods. 物品における基本標識および識別標識の配置のさらに他の例を示す図である。It is a figure which shows the further another example of arrangement | positioning of the basic label and identification label | marker in articles | goods. 物品における基本標識および識別標識の配置のさらに他の例を示す図である。It is a figure which shows the further another example of arrangement | positioning of the basic label and identification label | marker in articles | goods.

図１は、本発明に係る位置計測システムの一実施例を示す図である。本システムは、図示のように、平面上に幾何学的形状として四角形を形成する位置関係の分かっている４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および平面上に配置される識別標識ａ２を有する物体１と、２次元撮像素子２を有する撮像装置３と、撮像装置３により撮像した基本標識および識別標識の画像情報から得られた直線上の４点を利用して複比を計算し、計算した複比に基づいて４つの基本標識ａ１，ｂ１，ｃ１，ｄ１を識別し、識別した４つの基本標識ａ１，ｂ１，ｃ１，ｄ１の位置情報に基づいて物体１の３次元位置および角度の少なくとも一方を求める演算を行う演算装置４とを備える。ここで、基本標識ａ１，ｂ１，ｃ１，ｄ１は、物体１の３次元位置を計測するために設けられる計測用マーカーである。また、識別標識ａ２は、物品１を他の物品と識別するために設けられる識別（ＩＤ）用マーカーである。複比の計算については後述する。 FIG. 1 is a diagram showing an embodiment of a position measurement system according to the present invention. As shown in the figure, the system has four basic signs a1, b1, c1, d1 whose positions are known to form a square as a geometric shape on a plane and an identification mark a2 arranged on the plane. The cross ratio is calculated using the four points on the straight line obtained from the image information of the object 1, the imaging device 3 having the two-dimensional imaging device 2, and the basic sign and the identification sign taken by the imaging device 3. The four basic signs a1, b1, c1, d1 are identified based on the cross ratio, and at least the three-dimensional position and angle of the object 1 are determined based on the positional information of the identified four basic signs a1, b1, c1, d1. And an arithmetic device 4 that performs an operation for obtaining one. Here, the basic signs a1, b1, c1, and d1 are measurement markers provided for measuring the three-dimensional position of the object 1. The identification mark a2 is an identification (ID) marker provided to identify the article 1 from other articles. The calculation of the cross ratio will be described later.

物品１としてはカードや基板等の板状のものを用いることができるが、これに限定されない。基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２は、カメラで撮像して画像情報が得られるものであれば特に限定されない。例えば基本標識および識別標識を示す印を物品１の平面に印刷あるいは貼付することができる。また、基本標識および識別標識としてＬＥＤ等の光源を用いることができ、さらに光源の代わりに再帰反射板を用い、その再帰反射板を照明するための照明装置を備えるようにしてもよい。撮像装置３は、例えばＣＣＤやＣＭＯＳセンサ等の２次元撮像素子２を搭載したデジタルカメラが用いられるが、これに限定されない。演算装置４は、撮像装置３の図示しない通信手段と有線あるいは無線で接続され、撮像装置３と通信できるように構成される。演算装置４は、例えばパーソナルコンピュータ（ＰＣ）等のコンピュータが用いられるが、これに限定されない。なお、図１の例では、基本標識は４つとしたが５つ以上でもよく、また識別標識は１つとしたが２つ以上でもよい。以下の例でも同様である。基本標識が５つ以上の場合、幾何学的形状は基本標識の数に応じて四角形以上の多角形とすることができる。 The article 1 can be a plate-like object such as a card or a substrate, but is not limited to this. The basic signs a1, b1, c1, d1 and the identification sign a2 are not particularly limited as long as they can be imaged by imaging with a camera. For example, a mark indicating a basic mark and an identification mark can be printed or affixed on the plane of the article 1. Further, a light source such as an LED can be used as the basic mark and the identification mark, and a retroreflecting plate may be used instead of the light source, and an illuminating device for illuminating the retroreflecting plate may be provided. As the imaging device 3, for example, a digital camera equipped with a two-dimensional imaging device 2 such as a CCD or a CMOS sensor is used, but the imaging device 3 is not limited to this. The arithmetic device 4 is connected to a communication unit (not shown) of the imaging device 3 by wire or wirelessly and configured to be able to communicate with the imaging device 3. For example, a computer such as a personal computer (PC) is used as the arithmetic device 4, but is not limited thereto. In the example of FIG. 1, the number of basic signs is four, but may be five or more, and the number of identification signs is one, but may be two or more. The same applies to the following examples. When there are five or more basic signs, the geometric shape can be a polygon more than a square depending on the number of basic signs.

上述の直線上の４点は、本例では図２に示すように、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形における第１の対角線５の両端に位置する２つの基本標識ａ１，ｃ１と、第１の対角線５上に位置する識別標識ａ２と、第１の対角線５とそれとは別の第２の対角線６との交点ｖである。この直線上の４点ａ１，ａ２，ｖ，ｃ１を用いて次のようにして複比の計算を行う。
複比(a1,a2,v,c1)=(a1a2/a2c1)/(a1v/vc1)、または
複比(c1,v,a2,a1)=(c1v/va1)/(c1a2/a2a1) As shown in FIG. 2, in this example, the four points on the straight line are two points located at both ends of the first diagonal line 5 in the quadrangle in which the four basic signs a1, b1, c1, and d1 are arranged at the vertices, respectively. This is an intersection v of the basic signs a 1 and c 1, the identification sign a 2 located on the first diagonal line 5, and the first diagonal line 5 and another second diagonal line 6. The cross ratio is calculated as follows using the four points a1, a2, v, and c1 on the straight line.
Cross ratio (a1, a2, v, c1) = (a1a2 / a2c1) / (a1v / vc1), or cross ratio (c1, v, a2, a1) = (c1v / va1) / (c1a2 / a2a1)

複比は、射影変換において不変量である。射影変換は、空間に２つの平面があるとき、１つの平面上にある図形を定点からでた光線によって射影し、別の平面に移す変換であり、撮像装置により物品を撮像する場合に適用できる。基本標識と識別標識が配置された平面を有する物品の位置や傾きが変化しても複比は不変なので、複比を物品の識別（ＩＤ）情報として用いて物品を識別することができる。 The cross ratio is an invariant in the projective transformation. Projective transformation is a transformation in which when there are two planes in space, a figure on one plane is projected by a light beam from a fixed point and transferred to another plane, and can be applied when imaging an article with an imaging device. . Since the cross ratio does not change even if the position or inclination of the article having a plane on which the basic sign and the identification sign are arranged changes, the article can be identified using the cross ratio as the article identification (ID) information.

図３は、図１の演算装置の一例を示すブロック図である。演算装置４は、撮像装置３で撮像した基本標識および識別標識の画像情報を入力する入力部４１と、入力した基本標識および識別標識の画像情報から得られた直線上の４点を利用して複比を計算し、計算した複比に基づいて４つの基本標識ａ１，ｂ１，ｃ１，ｄ１を識別し、識別した４つの基本標識ａ１，ｂ１，ｃ１，ｄ１の位置情報に基づいて物体１の３次元位置および角度の少なくとも一方を求める演算を行う演算部（ＣＰＵ）４２と、演算した物品１の３次元位置および角度の少なくとも一方を例えばモニタ等の表示装置に出力する出力部４３とを備える。 FIG. 3 is a block diagram illustrating an example of the arithmetic device of FIG. The arithmetic device 4 uses the input unit 41 for inputting the image information of the basic sign and the identification sign imaged by the imaging device 3, and four points on the straight line obtained from the input image information of the basic sign and the identification sign. The cross ratio is calculated, the four basic signs a1, b1, c1, d1 are identified based on the calculated cross ratio, and the object 1 is identified based on the positional information of the identified four basic signs a1, b1, c1, d1. A calculation unit (CPU) 42 that performs calculation for obtaining at least one of a three-dimensional position and an angle, and an output unit 43 that outputs at least one of the calculated three-dimensional position and angle of the article 1 to a display device such as a monitor, for example. .

演算部４２には記憶部４４が接続され、両者間で情報の授受が行われる。記憶部４４には、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２の位置情報、並びに直線上の４点ａ１，ａ２，ｖ，ｃ１の複比を格納したテーブルが用意されている。演算部４２は、記憶部４４から、計算した複比と対応する４つの基本標識ａ１，ｂ１，ｃ１，ｄ１の位置情報を取得し、この位置情報に基づいて物体の３次元位置および角度の少なくとも一方を求める演算を行う。なお、記憶部４４は演算部４２で実行されるプログラムやそこで用いられる各種情報を格納するものであり、内部メモリとして構成することができるが、これに限定されず、外部に接続した記憶装置でもよい。 A storage unit 44 is connected to the calculation unit 42, and information is exchanged between them. The storage unit 44 has a table storing the positional information of the four basic signs a1, b1, c1, d1 and the identification mark a2 and the cross ratio of the four points a1, a2, v, c1 on the straight line for each article. It is prepared. The calculation unit 42 acquires position information of the four basic signs a1, b1, c1, and d1 corresponding to the calculated cross ratio from the storage unit 44, and based on the position information, at least the three-dimensional position and the angle of the object are obtained. An operation for obtaining one is performed. The storage unit 44 stores a program executed by the calculation unit 42 and various types of information used therein, and can be configured as an internal memory. However, the storage unit 44 is not limited thereto, and may be a storage device connected to the outside. Good.

以上の手順は、コンピュータに次のプログラムを実行させることで実施することができる。図４はコンピュータにより実行される手順の一例を示すフロー図である。すなわち、このプログラムは、コンピュータに、平面上に幾何学的形状を形成する位置関係の分かっている４つ以上の基本標識および前記平面上に配置される１つ以上の識別標識を有する物体を２次元撮像素子を有する撮像装置により撮像した前記基本標識および前記識別標識の画像情報を入力する手順（ステップ５１）、画像情報から得られた直線上の４点を利用して複比を計算する手順（ステップ５２）、前記計算した複比に基づいて前記４つ以上の基本標識を識別する手順（ステップ５３）、前記識別した４つ以上の基本標識の位置情報に基づいて前記物体の３次元位置および角度の少なくとも一方を演算する手順（ステップ５４）を実行させるものである。本例では、プログラムを演算装置の記憶部に格納した実施形態として説明したが、このプログラムをＣＤＲＯＭ等の記憶媒体に格納して又は通信手段によって提供することも可能である。以下、物体の３次元位置の演算方法の一例について述べる。 The above procedure can be implemented by causing a computer to execute the following program. FIG. 4 is a flowchart showing an example of a procedure executed by the computer. That is, this program gives two objects to a computer having four or more basic signs having a known positional relationship forming a geometric shape on a plane and one or more identification signs arranged on the plane. A procedure for inputting image information of the basic marker and the identification marker imaged by an imaging device having a three-dimensional imaging device (step 51), a procedure of calculating a cross ratio using four points on a straight line obtained from the image information (Step 52), a procedure for identifying the four or more basic signs based on the calculated cross ratio (Step 53), and a three-dimensional position of the object based on the positional information of the identified four or more basic signs And a procedure (step 54) for calculating at least one of the angles. In this example, the program is described as an embodiment in which the program is stored in the storage unit of the arithmetic device. However, the program may be stored in a storage medium such as a CDROM or provided by communication means. Hereinafter, an example of a method for calculating the three-dimensional position of an object will be described.

図５は、４つの基本標識を有する物体の３次元位置の演算方法の一例を説明するための図である。以下、基本標識をＬＥＤ等で構成された光源として説明する。本例では、４つの光源を例えば正方形の角に配置し、そのうちの３つの光源の組み合わせを２つ考える。そして、各々の３点を用いて、以下の計算から２つの解を導出する。その２つの解の内一つは光源位置が全く同じ値を示すので、それを正解とする。これにより、光源セット（物体）の位置と角度を決定することができる。 FIG. 5 is a diagram for explaining an example of a method for calculating a three-dimensional position of an object having four basic signs. Hereinafter, the basic sign will be described as a light source composed of an LED or the like. In this example, four light sources are arranged at, for example, square corners, and two combinations of the three light sources are considered. Then, using each of the three points, two solutions are derived from the following calculation. Since one of the two solutions shows exactly the same light source position, it is assumed to be the correct answer. Thereby, the position and angle of the light source set (object) can be determined.

まず、図５において、光源（基本標識）ａ１，ｂ１，ｃ１の画像面（カメラの２次元撮像素子面）１０上の画像位置ｅ１，ｅ２，ｅ３とカメラの光学中心２０との関係から、カメラ座標系における光源位置の方向ベクトルＤｉ（ｉ＝１，２，３）を算出する。Ｄｉは規格化した単位ベクトルとする。 First, in FIG. 5, from the relationship between the image positions e1, e2, e3 on the image plane (camera two-dimensional image sensor surface) 10 of the light sources (basic signs) a1, b1, c1 and the optical center 20 of the camera, the camera A direction vector Di (i = 1, 2, 3) of the light source position in the coordinate system is calculated. Di is a standardized unit vector.

光源ａ１，ｂ１，ｃ１の空間の位置ベクトルをｐ１，ｐ２，ｐ３とすると、これらはＤｉの延長線上に存在するので、その係数をｔ１，ｔ２，ｔ３として、
p1=t1・D1
p2=t2・D2 式１
p3=t3・D3
で表すことができる。 Assuming that the spatial position vectors of the light sources a1, b1, and c1 are p1, p2, and p3, these exist on the extension line of Di, and their coefficients are t1, t2, and t3.
p1 = t1 ・ D1
p2 = t2 · D2 Equation 1
p3 = t3 ・ D3
Can be expressed as

三角形の形状は最初からわかっており、その長さを各々
p1p2=L1
p2p3=L2 式２
p3p1=L3
とすると次式が得られる。式中「^」は累乗を表す。
(t1x1-t2x2)^2+(t1y1-t2y2)^2+(t1z1-t2z2)^2=L1^2
(t2x2-t3x3)^2+(t2y2-t3y3)^2+(t2z2-t3z3)^2=L2^2 式３
(t3x3-t1x1)^2+(t3y3-t1y1)^2+(t3z3-t1z1)^2=L3^2 The shape of the triangle is known from the beginning and its length is
p1p2 = L1
p2p3 = L2 Equation 2
p3p1 = L3
Then, the following equation is obtained. In the formula, “^” represents a power.
(t1x1-t2x2) ^ 2 + (t1y1-t2y2) ^ 2 + (t1z1-t2z2) ^ 2 = L1 ^ 2
(t2x2-t3x3) ^ 2 + (t2y2-t3y3) ^ 2 + (t2z2-t3z3) ^ 2 = L2 ^ 2 Formula 3
(t3x3-t1x1) ^ 2 + (t3y3-t1y1) ^ 2 + (t3z3-t1z1) ^ 2 = L3 ^ 2

整理すると
t1^2-2t1t2(x1x2+y1y2+z1z2)+t2^2-L1^2=0
t2^2-2t2t3(x2x3+y2y3+z2z3)+t3^2-L2^2=0 式４
t3^2-2t3t1(x3x1+y3y1+z3z1)+t1^2-L3^2=0
が得られ、次式となる。式中「sqrt」は平方根を表す。
t1=A1・t2±sqrt((A1^2-1)・t2^2+L1^2)
t2=A2・t3±sqrt((A2^2-1)・t3^2+L2^2) 式５
t3=A3・t1±sqrt((A3^2-1)・t1^2+L3^2)
ここで、A1,A2,A3は次式のとおりである。
A1=x1x2+y1y2+z1z2
A2=x2x3+y2y3+z2z3 式６
A3=x3x1+y3y1+z3z1 When you organize
t1 ^ 2-2t1t2 (x1x2 + y1y2 + z1z2) + t2 ^ 2-L1 ^ 2 = 0
t2 ^ 2-2t2t3 (x2x3 + y2y3 + z2z3) + t3 ^ 2-L2 ^ 2 = 0 Formula 4
t3 ^ 2-2t3t1 (x3x1 + y3y1 + z3z1) + t1 ^ 2-L3 ^ 2 = 0
Is obtained, and the following equation is obtained. In the formula, “sqrt” represents a square root.
t1 = A1 ・ t2 ± sqrt ((A1 ^ 2-1) ・ t2 ^ 2 + L1 ^ 2)
t2 = A2 ・ t3 ± sqrt ((A2 ^ 2-1) ・ t3 ^ 2 + L2 ^ 2) Equation 5
t3 = A3 ・ t1 ± sqrt ((A3 ^ 2-1) ・ t1 ^ 2 + L3 ^ 2)
Here, A1, A2, and A3 are as follows.
A1 = x1x2 + y1y2 + z1z2
A2 = x2x3 + y2y3 + z2z3 Equation 6
A3 = x3x1 + y3y1 + z3z1

実数解を持つために、式５の平方根の中が正になる。
t1≦ sqrt(L3^2/(1-A3^2))
t2≦ sqrt(L1^2/(1-A1^2)) 式７
t3≦ sqrt(L2^2/(1-A2^2)) To have a real solution, the square root of Equation 5 is positive.
t1 ≦ sqrt (L3 ^ 2 / (1-A3 ^ 2))
t2 ≦ sqrt (L1 ^ 2 / (1-A1 ^ 2)) Equation 7
t3 ≦ sqrt (L2 ^ 2 / (1-A2 ^ 2))

この条件を満たす実数ｔ１、ｔ２、ｔ３を順次、式５に代入し、式５が成立するすべてのｔ１，ｔ２，ｔ３を算出する。次に上記の式１からｐ１，ｐ２，ｐ３を、すなわち、光源の３次元位置を算出する。光源が３つの場合には２つの解ができるが、本例の場合は光源が４つあるので、他の３つの光源、例えばａ１，ｂ１，ｄ１について上記と同様の計算を行い別の２つの解を導出する。その２つの解の内一つは光源位置が全く同じ値を示すので、それを正解とする。４つを超える基本標識がある場合も同様である。このようにして光源セット（物体）の３次元位置を決定することができる。物体の角度は、その３次元位置から物体の向く方向として求めることができる。光源（基本標識）の３次元位置の算出方法は上記に限定されず、別の方法で行ってもよい。 Real numbers t1, t2, and t3 satisfying this condition are sequentially substituted into Expression 5, and all t1, t2, and t3 that satisfy Expression 5 are calculated. Next, p1, p2, and p3, that is, the three-dimensional position of the light source are calculated from the above equation 1. If there are three light sources, two solutions can be made. In this example, there are four light sources, so the same calculation is performed for the other three light sources, for example, a1, b1, d1, and another two light sources. Derive a solution. Since one of the two solutions shows exactly the same light source position, it is assumed to be the correct answer. The same applies when there are more than four basic signs. In this way, the three-dimensional position of the light source set (object) can be determined. The angle of the object can be obtained as the direction in which the object faces from the three-dimensional position. The method for calculating the three-dimensional position of the light source (basic marker) is not limited to the above, and another method may be used.

図６は、物品における基本標識および識別標識の配置の他の例を示す図である。本例では、上述の直線上の４点は、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形６１における隣接する第１および第２の基本標識ａ１，ｂ１と、四角形６１の外側に位置する識別標識ａ２と四角形６１における第３の基本標識ｄ１とを結ぶ第１の直線６２および第４の基本標識ｃ１とを結ぶ第２の直線６３と第１および第２の基本標識ａ１，ｂ１を結ぶ直線６４との２つの交点ｖ，ｗである。この直線上の４点ａ１，ｖ，ｗ，ｂ１を用いて次のようにして複比の計算を行う。
複比(a1,v,w,b1)=(a1v/vb1)/(a1w/wb1)、または
複比(b1,w,v,a1)=(b1w/wa1)/(b1v/va1)
本例の場合は、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２の位置情報、並びに直線上の４点ａ１，ｖ，ｗ，ｂ１の複比が格納されている。 FIG. 6 is a diagram showing another example of the arrangement of basic signs and identification signs in an article. In this example, the four points on the straight line described above are the first and second basic signs a1, b1 adjacent to each other in the square 61 in which the four basic signs a1, b1, c1, d1 are arranged at the vertices, and the square 61. The first straight line 62 connecting the identification mark a2 located outside the first straight line 62 and the fourth basic mark c1 connecting the third basic mark d1 in the square 61 and the first and second basic signs. Two intersection points v and w with the straight line 64 connecting a1 and b1. Using the four points a1, v, w, b1 on this straight line, the cross ratio is calculated as follows.
Cross ratio (a1, v, w, b1) = (a1v / vb1) / (a1w / wb1), or cross ratio (b1, w, v, a1) = (b1w / wa1) / (b1v / va1)
In the case of this example, the storage unit 44 of the arithmetic device 4 stores the position information of the four basic signs a1, b1, c1, d1 and the identification mark a2 and the four points a1, v, w, The cross ratio of b1 is stored.

図７（ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。図７（ａ）の例では、上述の直線上の４点は、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形７１における対角線７２の両端に位置する２つの基本標識ａ１，ｃ１と、四角形７１の内側に位置する四角形７３の輪郭部と対角線７２との２つの交点にそれぞれ位置する２つの識別標識ａ２，ｃ２、または、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形７１における対角線７３の両端に位置する２つの基本標識ｂ１，ｄ１と、四角形７１の内側に位置する四角形７３の輪郭部と対角線７４との２つの交点にそれぞれ位置する２つの識別標識ｂ２，ｄ２である。この直線上の４点ａ１，ａ２，ｃ２，ｃ１、またはｂ１，ｂ２，ｄ２，ｄ１を用いて次のようにして複比の計算を行う。
複比(a1,a2,c2,c1)=(a1a2/a2c1)/(a1c2/c2c1)、または
複比(c1,c2,a2,a1)=(c1c2/c2a1)/(c1a2/a2a1)、または
複比(b1,b2,d2,d1)=(b1b2/b2d1)/(b1d2/d2d1)、または
複比(d1,d2,b2,b1)=(d1d2/d2b1)/(d1b2/b2b1)
本例の場合は、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ａ１，ａ２，ｃ２，ｃ１、またはｂ１，ｂ２，ｄ２，ｄ１の複比が格納されている。 FIGS. 7A and 7B are diagrams showing still another example of the arrangement of basic signs and identification signs in an article. In the example of FIG. 7A, the four points on the straight line are two basic signs a1 located at both ends of the diagonal 72 in the quadrilateral 71 having the four basic signs a1, b1, c1, and d1 arranged at the vertices, respectively. , C1 and two identification signs a2, c2 or four basic signs a1, b1, c1, d1 respectively located at two intersections of the contour part of the square 73 located inside the square 71 and the diagonal 72 Two basic signs b1 and d1 positioned at both ends of the diagonal line 73 in the quadrangle 71 arranged at the vertex, respectively, and two intersections between the contour part of the square 73 positioned inside the quadrilateral 71 and the diagonal line 74, respectively. Identification marks b2 and d2. Using the four points a1, a2, c2, c1 or b1, b2, d2, d1 on this straight line, the cross ratio is calculated as follows.
Cross ratio (a1, a2, c2, c1) = (a1a2 / a2c1) / (a1c2 / c2c1), or cross ratio (c1, c2, a2, a1) = (c1c2 / c2a1) / (c1a2 / a2a1), or Cross ratio (b1, b2, d2, d1) = (b1b2 / b2d1) / (b1d2 / d2d1), or cross ratio (d1, d2, b2, b1) = (d1d2 / d2b1) / (d1b2 / b2b1)
In the case of this example, the storage unit 44 of the arithmetic unit 4 stores the position information of the four basic signs a1, b1, c1, d1 and the identification signs a2, b2, c2, d2 and four points on a straight line for each article. A cross ratio of a1, a2, c2, c1 or b1, b2, d2, d1 is stored.

また、図７（ｂ）の例では、上述の直線上の４点は、４つの識別標識ａ２，ｂ２，ｃ２，ｄ２をそれぞれ頂点に配置した四角形７５における対角線７６の両端に位置する２つの基本標識ａ２，ｃ２と、四角形７５の内側に位置する基本標識に係る四角形７７の輪郭部と対角線７６との２つの交点にそれぞれ位置する２つの基本標識ａ１，ｃ１、または、４つの識別標識ａ２，ｂ２，ｃ２，ｄ２をそれぞれ頂点に配置した四角形７５における対角線７６の両端に位置する２つの識別標識ｂ２，ｄ２と、四角形７５の内側に位置する四角形７７の輪郭部と対角線７８との２つの交点にそれぞれ位置する２つの基本標識ｂ１，ｄ１である。この直線上の４点ａ２，ａ１，ｃ１，ｃ２、またはｂ２，ｂ１，ｄ１，ｄ２を用いて次のようにして複比の計算を行う。
複比(a2,a1,c1,c2)=(a2a1/a1c2)/(a2c1/c1c2)、または
複比(c2,c1,a1,a2)=(c2c1/c1a2)/(c2a1/a1a2)、または
複比(b2,b1,d1,d2)=(b2b1/b1d2)/(b2d1/d1d2)、または
複比(d2,d1,b1,b2)=(d2d1/d1b2)/(d2b1/b1b2)
本例の場合は、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ａ２，ａ１，ｃ１，ｃ２、またはｂ２，ｂ１，ｄ１，ｄ２の複比が格納されている。 In the example of FIG. 7B, the four points on the straight line are two basic points located at both ends of the diagonal line 76 in the quadrangle 75 in which the four identification marks a2, b2, c2, and d2 are arranged at the vertices, respectively. Two basic signs a1 and c1 respectively located at two intersections of the signs a2 and c2 and the outline 77 and the diagonal line 76 of the square 77 relating to the basic sign located inside the square 75, or four identification signs a2, Two intersections of two identification marks b2 and d2 positioned at both ends of the diagonal line 76 in the quadrangle 75 having b2, c2 and d2 at the vertices, and a contour of the quadrangle 77 positioned inside the quadrangle 75 and the diagonal line 78 Are two basic signs b1 and d1, respectively. Using the four points a2, a1, c1, c2 or b2, b1, d1, d2 on this straight line, the cross ratio is calculated as follows.
Cross ratio (a2, a1, c1, c2) = (a2a1 / a1c2) / (a2c1 / c1c2), or cross ratio (c2, c1, a1, a2) = (c2c1 / c1a2) / (c2a1 / a1a2), or Cross ratio (b2, b1, d1, d2) = (b2b1 / b1d2) / (b2d1 / d1d2), or cross ratio (d2, d1, b1, b2) = (d2d1 / d1b2) / (d2b1 / b1b2)
In the case of this example, the storage unit 44 of the arithmetic unit 4 stores the position information of the four basic signs a1, b1, c1, d1 and the identification signs a2, b2, c2, d2 and four points on a straight line for each article. A cross ratio of a2, a1, c1, c2 or b2, b1, d1, d2 is stored.

図８（ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。図８（ａ）が図７（ａ）と異なる点は、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形８１の内側に位置する幾何学的形状が長円形８３であることであり、その他の点は図７（ａ）と同様である。また、図８（ｂ）が図７（ｂ）と異なる点は、４つの識別標識ａ２，ｂ２，ｃ２，ｄ２をそれぞれ頂点に配置した四角形８５の内側に位置する幾何学的形状が基本標識に係る長円形８７であることであり、その他の点は図７（ｂ）と同様である。本例の図８（ａ）の場合も、図７（ａ）の場合と同様に、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ａ１，ａ２，ｃ２，ｃ１、またはｂ１，ｂ２，ｄ２，ｄ１の複比が格納されている。また、本例の図８（ｂ）の場合も、図７（ｂ）の場合と同様に、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ａ２，ａ１，ｃ１，ｃ２、またはｂ２，ｂ１，ｄ１，ｄ２の複比が格納されている。 FIGS. 8A and 8B are diagrams showing still another example of the arrangement of basic signs and identification signs in an article. FIG. 8A is different from FIG. 7A in that the geometric shape located inside the quadrangle 81 in which the four basic signs a1, b1, c1, and d1 are arranged at the vertices is an oval 83. The other points are the same as in FIG. Further, FIG. 8B is different from FIG. 7B in that the geometric shape located inside the quadrangle 85 in which the four identification markers a2, b2, c2, and d2 are arranged at the vertices is the basic marker. This is the oval 87, and the other points are the same as in FIG. 7B. Also in the case of FIG. 8A of this example, as in the case of FIG. 7A, four basic signs a1, b1, c1, d1 and identification signs are stored in the storage unit 44 of the arithmetic unit 4 for each article. The position information of a2, b2, c2, d2 and the cross ratio of four points a1, a2, c2, c1 or b1, b2, d2, d1 on the straight line are stored. Also in the case of FIG. 8B of this example, as in the case of FIG. 7B, four basic signs a1, b1, c1, d1 and The position information of the identification marks a2, b2, c2, d2 and the cross ratio of the four points a2, a1, c1, c2 or b2, b1, d1, d2 on the straight line are stored.

図９（ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。図９（ａ）の例では、上述の直線上の４点は、例えば４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形９１の内側に位置する四角形９２の頂点に位置する隣接する２つの識別標識ａ２，ｂ２と、この隣接する２つの識別標識ａ２，ｂ２を通る直線９３と四角形９１の２辺との２つの交点ｙ、ｗ、または、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形９１の内側に位置する四角形９２の頂点に位置する隣接する２つの識別標識ｂ２，ｃ２と、この隣接する２つの識別標識ａ２，ｂ２を通る直線９４と四角形９１の２辺との２つの交点ｖ、ｘである。この場合、さらに他の直線上の４点を選択することができるが、この場合も上記と同様なので説明を省略する。この直線上の４点ｙ，ａ２，ｂ２，ｗ、またはｖ，ｂ２，ｃ２，ｘを用いて次のようにして複比の計算を行う。
複比(y,a2,b2,w)=(ya2/a2w)/(yb2/b2w)、または
複比(w,b2,a2,y)=(wb2/b2y)/(wa2/a2y)、または
複比(v,b2,c2,x)=(vb2/b2x)/(vc2/c2x)、または
複比(x,c2,b2,v)=(xc2/c2v)/(xb2/b2v)
本例の場合は、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ｙ，ａ２，ｂ２，ｗ、またはｖ，ｂ２，ｃ２，ｘの複比が格納されている。 FIGS. 9A and 9B are diagrams showing still another example of the arrangement of basic signs and identification signs in an article. In the example of FIG. 9A, the above four points on the straight line are located at the vertices of the quadrangle 92 located inside the quadrangle 91 in which, for example, four basic signs a1, b1, c1, and d1 are arranged at the vertices. Two intersections y and w between two adjacent identification signs a2 and b2 and a straight line 93 passing through the two adjacent identification signs a2 and b2 and two sides of the square 91, or four basic signs a1, b1, Two adjacent identification marks b2 and c2 positioned at the apex of the quadrangle 92 located inside the quadrilateral 91 where c1 and d1 are arranged at the apexes respectively, and a straight line 94 and a quadrangle passing through the two adjacent identification signs a2 and b2 Two intersection points v and x with two sides of 91. In this case, four points on another straight line can be selected. In this case as well, the description is omitted because it is similar to the above. Using the four points y, a2, b2, w or v, b2, c2, x on this straight line, the cross ratio is calculated as follows.
Cross ratio (y, a2, b2, w) = (ya2 / a2w) / (yb2 / b2w), or cross ratio (w, b2, a2, y) = (wb2 / b2y) / (wa2 / a2y), or Cross ratio (v, b2, c2, x) = (vb2 / b2x) / (vc2 / c2x), or cross ratio (x, c2, b2, v) = (xc2 / c2v) / (xb2 / b2v)
In the case of this example, the storage unit 44 of the arithmetic unit 4 stores the position information of the four basic signs a1, b1, c1, d1 and the identification signs a2, b2, c2, d2 and four points on a straight line for each article. The cross ratio of y, a2, b2, w or v, b2, c2, x is stored.

また、図９（ｂ）の例では、上述の直線上の４点は、例えば４つの識別標識ａ２，ｂ２，ｃ２，ｄ２をそれぞれ頂点に配置した四角形９５の内側に位置する四角形９６の頂点に位置する隣接する２つの基本標識ａ１，ｂ１と、この隣接する２つの基本標識ａ１，ｂ１を通る直線９７と四角形９５の２辺との２つの交点ｙ’、ｗ’、または、４つの識別標識ａ２，ｂ２，ｃ２，ｄ２をそれぞれ頂点に配置した四角形９５の内側に位置する四角形９６の頂点に位置する隣接する２つの基本標識ｂ１，ｃ１と、この隣接する２つの基本標識ｂ１，ｃ１を通る直線９８と四角形９５の２辺との２つの交点ｖ’、ｘ’である。この場合、さらに他の直線上の４点を選択することができるが、ここでは説明を省略する。この直線上の４点ｙ’，ａ１，ｂ１，ｗ’、またはｖ’，ｂ１，ｃ１，ｘ’を用いて次のようにして複比の計算を行う。
複比(y',a1,b1,w')=(y'a1/a1w')/(y'b1/b1w')、または
複比(w',b1,a1,y')=(w'b1/b1y')/(w'a1/a1y')、または
複比(v',b1,c1,x')=(v'b1/b1x')/(v'c1/c1x')、または
複比(x',c1,b1,v')=(x'c1/c1v')/(x'b1/b1v')
本例の場合は、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ｙ’，ａ１，ｂ１，ｗ’、またはｖ’，ｂ１，ｃ１，ｘ’の複比が格納されている。 In the example of FIG. 9B, the above four points on the straight line are, for example, the vertices of a rectangle 96 positioned inside a rectangle 95 in which four identification markers a2, b2, c2, and d2 are arranged at the vertices, respectively. Two intersecting points y ′, w ′ between two adjacent basic signs a1 and b1 and a straight line 97 passing through the two adjacent basic signs a1 and b1 and two sides of the square 95, or four identification signs Passes through two adjacent basic signs b1 and c1 located at the apex of the square 96 located inside the square 95 in which a2, b2, c2 and d2 are arranged at the apexes, and the two adjacent basic signs b1 and c1. Two intersection points v ′ and x ′ between the straight line 98 and the two sides of the quadrangle 95 are shown. In this case, four points on another straight line can be selected, but the description is omitted here. Using the four points y ′, a1, b1, w ′ or v ′, b1, c1, x ′ on this straight line, the cross ratio is calculated as follows.
Cross ratio (y ', a1, b1, w') = (y'a1 / a1w ') / (y'b1 / b1w'), or cross ratio (w ', b1, a1, y') = (w ' b1 / b1y ') / (w'a1 / a1y'), or cross ratio (v ', b1, c1, x') = (v'b1 / b1x ') / (v'c1 / c1x'), or Ratio (x ', c1, b1, v') = (x'c1 / c1v ') / (x'b1 / b1v')
In the case of this example, the storage unit 44 of the arithmetic unit 4 stores the position information of the four basic signs a1, b1, c1, d1 and the identification signs a2, b2, c2, d2 and four points on a straight line for each article. The cross ratio of y ′, a1, b1, w ′ or v ′, b1, c1, x ′ is stored.

図１０（ａ）、（ｂ）は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。図１０（ａ）が図９（ａ）と異なる点は、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ円形形状としたことであり、その他の点は図９（ａ）と同様である。また、図１０（ｂ）が図９（ｂ）と異なる点は、４つの識別標識ａ２，ｂ２，ｃ２，ｄ２をそれぞれ円形形状としたことであり、その他の点は図９（ｂ）と同様である。本例の図１０（ａ）の場合も、図９（ａ）の場合と同様に、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ｙ，ａ２，ｂ２，ｗ、またはｖ，ｂ２，ｃ２，ｘの複比が格納されている。また、本例の図１０（ｂ）の場合も、図９（ｂ）の場合と同様に、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２，ｂ２，ｃ２，ｄ２の位置情報、並びに直線上の４点ｙ’，ａ１，ｂ１，ｗ’、またはｖ’，ｂ１，ｃ１，ｘ’の複比が格納されている。 FIGS. 10A and 10B are diagrams showing still another example of the arrangement of basic signs and identification signs in an article. FIG. 10 (a) is different from FIG. 9 (a) in that the four basic signs a1, b1, c1, and d1 are circular, and the other points are the same as in FIG. 9 (a). . Further, FIG. 10B is different from FIG. 9B in that the four identification signs a2, b2, c2, and d2 are each circular, and the other points are the same as in FIG. 9B. It is. Also in the case of FIG. 10A of this example, as in the case of FIG. 9A, four basic signs a1, b1, c1, d1 and identification signs are stored in the storage unit 44 of the arithmetic unit 4 for each article. The position information of a2, b2, c2, d2 and the cross ratio of four points y, a2, b2, w or v, b2, c2, x on the straight line are stored. Also in the case of FIG. 10B of this example, as in the case of FIG. 9B, the four basic markers a1, b1, c1, d1 and The position information of the identification marks a2, b2, c2, d2 and the cross ratio of the four points y ′, a1, b1, w ′ or v ′, b1, c1, x ′ on the straight line are stored.

図１１は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。本例では、上述の直線上の４点は、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１をそれぞれ頂点に配置した四角形１１１における隣接する第１および第２の基本標識ｃ１，ｄ１と、四角形１１１の外側に位置する４つの識別標識をそれぞれ頂点に配置した四角形１１２における隣接する第１および第２の２つの識別標識ｂ２，ｃ２およびａ２，ｄ２を通る第１および第２の直線１１３，１１４と第１および第２の基本標識ｃ１，ｄ１を結ぶ直線１１５との２つの交点ｘ，ｙである。この直線上の４点ｃ１，ｘ，ｙ，ｄ１を用いて次のようにして複比の計算を行う。
複比(c1,x,y,d1)=(c1x/xd1)/(c1y/yd1)、または
複比(d1,y,x,c1)=(d1y/yc1)/(d1x/xc1)
本例の場合は、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２の位置情報、並びに直線上の４点ｃ１，ｘ，ｙ，ｄ１の複比が格納されている。 FIG. 11 is a diagram showing still another example of the arrangement of basic signs and identification signs in an article. In the present example, the four points on the straight line described above are the first and second basic signs c1, d1 adjacent to each other in the quadrangle 111 having the four basic signs a1, b1, c1, d1 arranged at the vertices, and the quadrangle 111. First and second straight lines 113 and 114 passing through two adjacent first and second identification signs b2, c2 and a2, d2 in a quadrangle 112 having four identification signs located outside the area, respectively. Two intersection points x and y with the straight line 115 connecting the first and second basic signs c1 and d1. The cross ratio is calculated as follows using the four points c1, x, y, and d1 on the straight line.
Cross ratio (c1, x, y, d1) = (c1x / xd1) / (c1y / yd1), or cross ratio (d1, y, x, c1) = (d1y / yc1) / (d1x / xc1)
In the case of this example, the storage unit 44 of the computing device 4 stores the position information of the four basic signs a1, b1, c1, d1 and the identification mark a2 and the four points c1, x, y, The cross ratio of d1 is stored.

図１２は、物品における基本標識および識別標識の配置のさらに他の例を示す図である。本例では、上述の直線上の４点は、第１および第２の基本標識ａ１，ｂ１と、第３の基本標識ｄ１と第１の識別標識ａ２とを通る第１の直線１２１および第４の基本標識ｃ１と第２の識別標識ｂ２とを通る第２の直線１２２と第１および第２の基本標識を結ぶ直線１２３との２つの交点ｖ，ｗである。この直線上の４点ａ１，ｖ，ｗ，ｂ１を用いて次のようにして複比の計算を行う。
複比(a1,v,w,b1)=(a1v/vb1)/(a1w/wb1)、または
複比(b1,w,v,a1)=(b1w/wa1)/(b1v/va1)
本例の場合は、演算装置４の記憶部４４に、物品ごとに、４つの基本標識ａ１，ｂ１，ｃ１，ｄ１および識別標識ａ２の位置情報、並びに直線上の４点ａ１，ｖ，ｗ，ｂ１の複比が格納されている。 FIG. 12 is a diagram showing still another example of the arrangement of basic signs and identification signs in an article. In this example, the four points on the straight line are the first straight line 121 and the fourth straight line passing through the first and second basic signs a1 and b1, the third basic sign d1 and the first identification sign a2. Are two intersections v and w of a second straight line 122 passing through the basic mark c1 and the second identification mark b2 and a straight line 123 connecting the first and second basic signs. Using the four points a1, v, w, b1 on this straight line, the cross ratio is calculated as follows.
Cross ratio (a1, v, w, b1) = (a1v / vb1) / (a1w / wb1), or cross ratio (b1, w, v, a1) = (b1w / wa1) / (b1v / va1)
In the case of this example, the storage unit 44 of the arithmetic device 4 stores the position information of the four basic signs a1, b1, c1, d1 and the identification mark a2 and the four points a1, v, w, The cross ratio of b1 is stored.

以上において説明した物品における基本標識および識別標識の配置は例示であり、これに限定されず、これ以外の配置も可能である。基本標識および識別標識の画像情報から得られた直線上の４点を利用して複比を計算し、これを予めテーブル化した複比と比較することで、対応する物品の基本標識を得ることができる。これは射影変換において不変量である複比によって物品を識別することができるからである。複比はＩＤ情報をもつので、ある物品において基本標識と識別標識との区別が付きにくい場合、あるいは多くの物品がある中で特定の物品の位置計測をする場合に、複比を用いて物品を特定することは有効である。 The arrangement of the basic sign and the identification sign in the article described above is an example, and the arrangement is not limited to this, and other arrangements are possible. By calculating the cross ratio using four points on the straight line obtained from the image information of the basic sign and the identification sign, and comparing this with the cross ratio previously tabulated, the basic sign of the corresponding article is obtained. Can do. This is because an article can be identified by a cross ratio that is an invariant in projective transformation. Since the cross ratio has ID information, when it is difficult to distinguish between the basic sign and the identification mark in a certain article, or when the position of a specific article is measured while there are many articles, the article using the cross ratio is used. It is effective to specify.

１物体
２２次元撮像素子
３撮像装置
４演算装置
５第１の対角線
６第２の対角線 DESCRIPTION OF SYMBOLS 1 Object 2 Two-dimensional image sensor 3 Imaging device 4 Arithmetic device 5 1st diagonal 6 2nd diagonal

Claims

An object having four or more basic signs having a known positional relationship forming a geometric shape on a plane and one or more identification signs arranged on the plane, and an imaging apparatus having a two-dimensional imaging device The cross ratio is calculated using four points on a straight line obtained from the image information of the basic sign and the identification sign captured by the imaging device, and the four or more basics are calculated based on the calculated cross ratio. A position measurement system comprising: an arithmetic unit that identifies a sign and performs an operation for obtaining at least one of a three-dimensional position and an angle of the object based on position information of the identified four or more basic signs.

The four points on the straight line are two basic signs positioned at both ends of a first diagonal line in a polygon of four or more squares each having the four or more basic signs arranged at the vertices, and the first diagonal line. The position measurement system according to claim 1, wherein the position measurement system is an intersection of the identification mark that is positioned, the first diagonal line, and a second diagonal line different from the first diagonal line.

The four points on the straight line are the first and second basic signs adjacent to each other in a polygon of a quadrilateral or more with the four or more basic signs arranged at the vertices, and the identification located outside the polygon. A first straight line connecting the sign and the third basic sign in the polygon, a second straight line connecting the fourth basic sign, and a straight line connecting the first and second basic signs. The position measurement system according to claim 1, which is an intersection.

The four points on the straight line are two basic signs positioned at both ends of a diagonal line in a polygon of four or more squares each having the four or more basic signs arranged at the vertices, and a geometry located inside the polygon. The position measurement system according to claim 1, wherein the two identification marks are respectively located at two intersections between a contour portion of a geometric shape and the diagonal line.

The four points on the straight line are the two identification marks positioned at both ends of a diagonal line in a polygon of four or more squares each having four or more of the identification marks arranged at the vertices, and the geometry positioned inside the polygon. The position measurement system according to claim 1, wherein the two basic signs are respectively located at two intersections between a contour portion of a geometric shape and the diagonal line.

The two adjacent identification marks located at the vertices of the quadrilateral or more polygons, the four points on the straight line are located inside the quadrilateral or more polygons each having the four or more basic signs arranged at the vertices; The position measurement system according to claim 1, which is two intersections of a straight line passing through the two adjacent identification signs and two sides of a polygon having the basic sign as a vertex.

The two adjacent basic signs located at the vertices of the quadrilateral or more polygons that are located inside the quadrilateral or more polygons each having four points on the straight line, each having four or more identification signs arranged at the vertices; The position measurement system according to claim 1, wherein the position measurement system is two intersections between a straight line passing through the two adjacent basic signs and two sides of a polygon having the identification sign at the apex.

The position measurement system according to claim 6 or 7, wherein the polygon having the basic sign at the apex and the polygon having the identification sign at the apex are each a quadrangle.

The position measurement system according to claim 6, wherein the basic mark or the identification mark has a circular shape.

The four points on the straight line are the first and second basic signs adjacent to each other in a polygon of four or more squares each having the four or more basic signs arranged at the vertices, and four located outside the polygon. The first and second straight lines passing through the two adjacent first and second identification signs and the first and second basic signs in a quadrilateral or more polygon having the identification signs arranged at the vertices, respectively. The position measurement system according to claim 1, wherein the position measurement system is two intersections with a connecting straight line.

The four points on the straight line pass through the first and second basic signs, the third basic sign and the first identification sign, the first straight line and the fourth basic sign and the second 2. The position measurement system according to claim 1, wherein the position measurement system is an intersection of a second straight line passing through the identification mark and a straight line connecting the first and second basic signs.

An object having four or more basic signs having a known positional relationship forming a geometric shape on a plane and one or more identification signs arranged on the plane is imaged by an imaging apparatus having a two-dimensional imaging element. Means for calculating a cross ratio using four points on a straight line obtained from image information of the basic sign and the identification sign, and identifying the four or more basic signs based on the calculated cross ratio An apparatus for position measurement, comprising: means; and means for calculating at least one of a three-dimensional position and an angle of the object based on position information of the four or more identified basic signs.

Imaging with a two-dimensional imaging device an object having four or more basic signs having a known positional relationship forming a geometric shape on a plane and one or more identification signs arranged on the plane A procedure for calculating a cross ratio using four points on a straight line obtained from image information of the basic sign and the identification sign picked up by a device, and the four or more basic signs based on the calculated cross ratio A program for executing an identifying procedure and a procedure for calculating at least one of a three-dimensional position and an angle of the object based on positional information of the identified four or more basic signs.