JP4109094B2 - Method for measuring the rotational and flight characteristics of a sphere - Google Patents

Description

【００７３】
実空間上の点Ｐとその像Ｑとの関係を直接表すためには、両者の関係を同じ座標系で表さなければならない。そこで、上記で定義した実空間から光軸をＺ軸とし、画像軸Ｕ及びＶ軸に平行であるＸ及びＹ軸をもつ座標系への変換行列Ｍを用いて、数式２が得られる。
【００７４】
【数２】

【００７５】
ＯＰとＯＱは互いに同一直線上にあり、その長さの比がＬ：Ｆであることから、数式３が得られる。
【００７６】
【数３】

【００７７】
数式２を数式３へ代入することによって、３式のうちの１式からＬを求め、そのＬを他の２式に代入することにより、以下の数式４が得られる。
【００７８】
【数４】

【００７９】
この数式４における変数をまとめ、Ｕ，Ｖ，Ｘ，Ｙ，Ｚについて整理すれば、数式５が得られる。
【００８０】
【数５】

【００８１】
１１個の係数を求めるためには、カメラ２台では６組の（Ｘ，Ｙ，Ｚ）と（Ｕ，Ｖ）が得られれば数式５に代入することによって算出できるが、測定誤差の影響を抑えるために、６組以上の既知の実空間座標を測定することが望ましい。また、カメラ１台では１２コ以上の（Ｘ，Ｙ，Ｚ）と（Ｕ，Ｖ）が必要である。カメラ３台では４コ以上となる。
【００８２】
以上の方法によって、既知の実空間座標と二次元的な画像上の座標の関係を把握することができる。この関係を利用して、図７に示すように、コンピュータ上の仮想的な球体のマークの座標をカメラのフィルム面上の二次元的な座標を求めることができる。即ち、仮想ゴルフボール３０の三次元空間座標上のマーク３０の位置を、二次元的な画像上に変換することができる。
【００８３】
次に、仮想的な三次元球体上のマークを二次元座標へ投影した場合、フィルム画像上にマークが存在するかしないか（マークが表に存在するか裏に存在するか）を判定する方法について説明する。
【００８４】
図２に示すフローチャートで示したマークが表あるいは裏のどちらに存在するのかを判定する方法を以下に示す。上記数式５で定義した１１個の係数を求めることができ、それらの係数を利用してカメラレンズの三次元座標を計算する。
【００８５】
図８に示すように、レンズ中心Ｏ（Ｘ_０，Ｙ_０，Ｚ_０）とし、仮想球体重心Ｐ（Ｇ_Ｘ，Ｇ_Ｙ，Ｇ_Ｚ）とすると、ベクトルＯＰは、数式６のようになる。
【００８６】
【数６】

【００８７】
ベクトルＯＰと球の径Ｒを用いて、レンズ中心から球体への接線長さｌは、数式７で表される。
【００８８】
【数７】

【００８９】
仮想的な球体の斜線部分を二次元に投影した場合、実際に撮影できるマーク（表側）と定義し、それ以外のマークを裏側と定義する。レンズ中心と仮想的な球体上のマークの長さをＬとすると、Ｌは仮想的な球体の重心位置と既知である各マークの位置関係により決まる。
【００９０】
Ｌ＜ｌ：球体上のマークは実際に測定できる画像の方向（表側）であり、ＧＡ計算に利用するマーク。
Ｌ≧ｌ：球体上のマークは実際に測定できない画像の方向（裏側）であり、ＧＡ計算に利用しないマーク。
【００９１】
以上の方法により、仮想的な球体上の全てのマークでＧＡの計算に用いることができるマークであるか否かを判定することができる。しかし、レンズの中心位置Ｏ（Ｘ_０，Ｙ_０，Ｚ_０）を求める必要がある。そこで、上記数式４と数式５を用いてレンズの中心位置を決定する。これらの式を比較すると、以下のような関係式（数式８）が成り立つ。
【００９２】
【数８】

【００９３】
数式８は変数が１２個存在するが、１１式しかないので、このままでは、Ｘ_０，Ｙ_０，Ｚ_０を計算できない。そこで、変換行列Ｍの行列式を計算し、数式９の関係式を追加することによって、１２式から１２個の変数を求めることができ、Ｘ_０，Ｙ_０，Ｚ_０を求めることができる。
【００９４】
【数９】

【００９５】
次に、実物のゴルフボール２０が回転する状態を撮影できる位置にＣＣＤカメラ１１を配置しており、ゴルフボール２０との距離やカメラレンズの倍率等を適宜調整している。
【００９６】
上記配置状態で、ＣＣＤカメラ１１の前をゴルフボール２０が通過する際に、マイクロフラッシュを所要の時間間隔で２回発光させ、一枚の二次元映像にゴルフボール２０が二個写った静止映像を画像メモリ１１ｂに得ている。ここで得られた二次元映像を図９に示す。このように撮影した映像データを二値化処理用のプログラムで白と黒に二値化してから、ディスプレイ画面１８上で、各マーク２１毎に二次元の座標値を読み取ると共に、読みとった値をハードディスク１５ａに記録している。
【００９７】
姿勢認識プログラムにより、上記方法で予め導出した三次元座標と二次元座標の間の関係を用いて、仮想ゴルフボール３０の三次元空間座標上のマーク位置を、二次元的な画像上に変換することで求めた二次元の仮想マーク座標値と、上記撮影により得られた映像上に存在する実物のゴルフボール２０の二次元の映像マーク座標値とが一致するように、各々移動操作、回転操作を行っている。
これにより、仮想ゴルフボール３０の基準姿勢及び基準位置に対する姿勢及び位置を特定している。この移動操作、回転操作を行う量を、最適化手法の一種である遺伝的アルゴリズムを用いて演算している。
姿勢変位操作において操作範囲を限定しており、遺伝的アルゴリズムを用いて座標変換や移動変換する角度や位置の探索範囲を球体が物理的に回転可能な範囲に限定している。具体的には、０°〜３６０°の全ての範囲を探索していたものを回転可能な範囲に限定している。さらに、ボールが飛行する全空間ではなく位置を限定している。具体的な、限定範囲は上述の通りである。
【００９８】
以下に、本実施形態の遺伝的アルゴリズム（ＧＡ）を用いた最適化の条件を示す。
任意に設定した三次元直行座標の各軸周りの回転角度（α、β、γ）、三次元空間での仮想ゴルフボール３０の重心座標（Ｘ_０、Ｙ_０、Ｚ_０）の計６項目を設計変数としている。この６項目の数値を六変数としている。ＧＡによる最適化では、設計変数をコード化しておく必要があるが、α、β、γ、Ｘ_０、Ｙ_０、Ｚ_０の各変数（実数値）を１０ビットの２進法に変換したものをコードとして使用している。
【００９９】
また、本実施形態のＧＡによる最適化の基本設定値を以下に示す。
個体数：５０
染色体長：６０ビット
設計変数の数：６変数（１変数あたり１０ビット）
終了条件（適合度の最大値が−０．００２以上であれば終了）
マークの数：４２
【０１００】
コンピュータにより上記操作を行って得られた二次元投影図と、撮影した二次元投影図をパターンマッチングする。この時のパターンの類似度を下記の数式１０で定義し、これを目的関数として、その最大値を遺伝的アルゴリズムによって探索する。
【０１０１】
【数１０】

【０１０２】
上記数式１０において、Ｘｉは撮影した投影図のマークの二次元座標（原点は球体（ボール）の中心座標）、Ｙｉは遺伝的アルゴリズムで得た値によって回転させた後のボールの三次元空間での重心位置から、既知の実空間座標と二次元的な画像上の座標の関係を利用して求めた投影図のマークの二次元座標（原点は球体の中心座標）である。
また、distance(ａ,ｂ)は２つの点ａ、ｂの距離を示し、ｍｉｎ_ｊはｊ（ｊ＝１からｎ、ｎはマークの個数）に関して最小値を表し、Σはｉ（ｉ＝１からｎ、ｎはマークの個数）に関して和をとることを意味する。ただし、Ｎはマーク数である。それぞれの画像について、マーク間距離の最小値を全てのマークについて計算し、その総和を適合度とする。
【０１０３】
上記目的関数の演算は揃えられた各個体全てに対して行われ、これら演算より各個体毎の適合度が求められる。
遺伝的アルゴリズムの最適化計算の終了条件は、事前の測定結果から、球体の回転角度あるいは位置が正しく計算できる適合度の値を予め導出しておき、その適合度の値を用いている。上記のように、適合度が−０．００２以上であれば、最適化計算を終了する。適合度が−０．００２以上となる個体が有している六変数の値が、仮想ゴルフボールの姿勢変位の最適解であると判断し、この個体によりゴルフボール２０の三次元姿勢及び位置を特定している。なお、遺伝的アルゴリズムの世代交代シミュレーションを終了させる方法は、上記以外の方法でも良い。
【０１０４】
三次元座標上の点の回転は３×３の回転行列を点の座標にかければ良い。この回転行列は上記α、β、γの値が決まれば決定する。よって、この回転行列を求めることにより、各画像での基準となる位置からのゴルフボールの回転量を決定することができる。最適化計算では、α、β、γを変量させることによりゴルフボールを回転させ、撮影映像とのずれが最小になるようにα、β、γを決定している。
また、上記手法で各々の映像における回転行列を求めることができるが、２つの映像間でどれだけ回転しているかと求めるためには、１つの映像の回転行列に、もう１つの映像の回転行列の逆行列をかければ良い。ここで求められた回転行列をもとに、回転軸ベクトルと回転角度を算出する。
【０１０５】
具体的には、適合度の終了条件を満たす個体が有する三次元座標空間のＸ軸、Ｙ軸、Ｚ軸回りの回転角度（α、β、γ）の数値より、三行三列の回転行列を求め、この回転行列が、ゴルフボール２０の姿勢を定める行列となっている。即ち、Ｘ軸、Ｙ軸、Ｚ軸の各軸回りに回転させる回転行列Ｒｘ、Ｒｙ、Ｒｚは、下記のように表記される。
【０１０６】
【数１１】

【０１０７】
一方、上記仮想ゴルフボールの基準姿勢及び基準位置から、姿勢認識プログラムで特定されるゴルフボール２０の姿勢及び位置を特定する行列である回転行列Ｒは、各軸回りの回転行列Ｒｘ、Ｒｙ、Ｒｚより下記のように表記される。
【０１０８】
【数１２】

【０１０９】
また、他のゴルフボール２０の映像に対しても上記と同様の演算および適合度の評価を行い、ゴルフボール２０の姿勢及び位置を特定する回転角度（α’、β’、γ’）より回転行列を求めている。
【０１１０】
以上より、上記数式１２で特定されるある時間のゴルフボール２０の姿勢を特定する回転行列をＲ１、他の時間のゴルフボール２０の姿勢を特定する回転行列をＲ２として、ある時間のゴルフボール２０の姿勢を他の時間のゴルフボール２０の姿勢へと一致させる回転行列をＲ１２とすると、回転行列Ｒ１２は下式で求められる。
【０１１１】
【数１３】

【０１１２】
上式で求められる回転行列Ｒ１２に伴う、図１０に示す座標変換される際の回転軸（座標軸）の方向（ｕ１、ｕ２、ｕ３）と回転角度Ψは、下記の数式１４、１５で求められる。
【０１１３】
【数１４】

【０１１４】
【数１５】

【０１１５】
上記求めた回転角度Ψと二つの映像間の撮影された時間間隔から、ある時間から他の時間にわたるゴルフボール２０の回転量と回転軸方法を求めている。
なお、二つ以上の映像間の回転量等を求めるには、各連続する前後の映像から上記同様にして各映像間の回転量等を求めて球体の回転量等を連続的に求めるようにしている。
【０１１６】
また、上記手法で各々の映像におけるゴルフボール重心位置の３成分の移動速度を求めることによって、打出角や振れ角等の飛行経路を含む飛行特性を算出できる。具体的には、ある時刻でのボールの重心位置Ｇｘ（ｔ）、Ｇｙ（ｔ）、Ｇｚ（ｔ）とすると、３成分の移動速度Ｖｘ、Ｖｙ、Ｖｚとボール速度Ｖは、下記の数式１６により求められる。
【０１１７】
【数１６】

【０１１８】
また、打出角及び振れ角は、下記の数式１７により求められる。ただし、ボールの進行方向をＸ軸、左右方向をＹ軸、高さ方向をＺ軸とする。
【０１１９】
【数１７】

【０１２０】
以下、本発明の実施例について詳述する。
（実験１）
赤道・経度０°，１８０°方向が正面に向くようにゴルフボール４０をティーアップし、図３と同様にゴルフボール４０にマーク４１を付して、図１１に示すように、ヘッドスピード（ＨＳ）を測定する２つのＨＳ測定センサ４２（４２Ａ、４２Ｂ）によりドライバーのＨＳを測定すると共に、第１カメラ４３Ａ及び第２カメラ４３Ｂで外力を受けずに回転飛行するゴルフボール４０を３ｍｓ間隔で撮影した。第１カメラ４３Ａは第２センサ４２Ｂをトリガ信号としてインパクトから３．２ｍｓ後にストロボが発光し撮影した。第２カメラ４３Ｂは第２センサ４２Ｂをトリガ信号としてインパクトから６．２ｍｓ後にストロボが発光し撮影した。屋内の条件を異ならせた。
【０１２１】
ゴルフボールのバックスピン（１０００ｒｐｍ〜４０００ｒｐｍ）、サイドスピン（−３０００ｒｐｍ〜３０００ｒｐｍ）、軸スピン（−５００ｒｐｍ〜５００ｒｐｍ）について、飛行方向をＹ軸、左右方向をＸ軸、これら２軸に垂直な方向をＺ軸と定義した場合、Ｘ軸周り、Ｙ軸周り、Ｚ軸周りの各回転角度を第１カメラ、第２カメラで測定した。結果を表１に示す。
ヘッドスピード４０ｍ／ｓでドライバー打撃時においてスピン量は上記バックスピン量、サイドスピン量、軸スピン量になることが試験的に判明しており、そのデータを参照した。例えば、１０００ｒｐｍでボール打撃から（３．２−１．７５）＝１．４５ｍｓ後のゴルフボールの回転角度（Ｘ軸回り）では、
１０００ｒｐｍ×２π／６０（rad/s）×３６０／２π（deg/s）×１．４５×１０^−３(s)＝８．７ｄｅｇとなる。他も同様に計算した。
【０１２２】
【表１】

【０１２３】
表１に示すように、第１カメラで撮影されるゴルフボールの回転角度範囲、第２カメラで撮影される回転角度範囲を限定できることが確認できた。即ち、ゴルフボールが物理的に回転可能な範囲は、ゴルフボールの任意の基準位置に対してＹ軸回りに−９０〜９０［ｄｅｇ］、Ｘ軸回りに５〜１２０［ｄｅｇ］、Ｚ軸回りに−１５〜１５[ｄｅｇ]の範囲となることが確認できた。
【０１２４】
（実験２）
ドライバーによる実打テストを１０球行い、実施例１と比較例１の２種類の測定方法で計算時間の比較を検証した。なお、計算時間に関する部分以外はどちらの方法を用いても同じ結果となるような条件で測定を行った。結果を表２に示す。
使用したパソコンはＰｅｎｔｉｕｍ（Ｒ） IV １．５ＧＨｚ メモリ２Ｇ相当のＰＣを使用した。
【０１２５】
【表２】

【０１２６】
（実施例１）
上記実施形態と同様の方法により、本発明の測定方法でバックスピン及びサイドスピンの回転量、振れ角、打出角、ボール速度を算出した。即ち、遺伝的アルゴリズムの探索範囲の限定とその範囲内にのみマークを付加して測定を行った。
【０１２７】
（比較例１）
遺伝的アルゴリズムを用いた最適化手法で計算したが、遺伝的アルゴリズムの探索範囲の限定とマークを付加位置の限定を行わなかった。
【０１２８】
表２に示すように、１０種類の様々な打球パターンのいずれにおいても実施例１は、比較例１に比べて計算時間が大幅に短縮され、瞬時に測定結果が得られることが確認できた。
【０１２９】
【発明の効果】
以上の説明より明らかなように、本発明によれば、球体の回転量を予測可能な状態で該球体の複数の二次元映像を得ると共に、基準姿勢及び基準位置に対して操作範囲を限定して姿勢変位操作している。このため、姿勢変位操作における回転角度や位置等の探索範囲を限定することができ、回転角度、振れ角、打出角等の演算量を飛躍的に低減することができる。よって、大幅に計算時間を短縮することができ、短時間で瞬時に球体の回転特性や飛行特性を測定することができる。
【０１３０】
また、球体の三次元姿勢及び位置を特定しているため、ある時間の三次元姿勢及び位置と、他の時間の三次元姿勢及び位置との関係から球体の回転数と回転軸方向等の回転特性、飛行経路や飛行速度等の飛行特性を容易かつ高精度で測定することができる。よって、外力を受けず回転している球体であるゴルフボールのスピン量や、打球の打出角や振れ角の測定に最適であり、特に振れ角の測定の精度を向上することができる。
【０１３１】
また、対象となる球体を適宜撮影すれば、球体の映像を基にコンピュータ内のプログラムに従って演算され、自動的に球体の回転特性や飛行特性を測定できるので、測定にかかる手間を大幅に削減することができる。
【０１３２】
さらに、遺伝的アルゴリズムの最適化計算の終了条件を、所定の適合度の値を用いて規定している。このように、最適化計算を適合度で規定し計算を終了することで、計算時間の短縮を図ることができる。
【図面の簡単な説明】
【図１】 （Ａ）は、本発明の球体の回転特性と飛行特性の測定装置の構成を示す図、（Ｂ）は概略斜視図である。
【図２】 本発明の球体の回転特性と飛行特性の測定方法のフローチャートである。
【図３】 球体にマークを付した位置を説明する図である。
【図４】 球体の極座標を説明する図である。
【図５】 マークを付した仮想球体の概略図である。
【図６】 三次元空間上の座標と二次元的な画像上の座標の位置関係を示す図である。
【図７】 仮想球体の三次元空間座標上のマーク位置を、二次元的な画像上に変換する方法を示す図である。
【図８】 レンズ中心と球体との関係を示す図である。
【図９】 球体の二次元映像を示す図である。
【図１０】 回転軸方向および回転角度を説明する図である。
【図１１】 実験１のゴルフボールの撮影状況を説明する図である。
【図１２】 （Ａ）（Ｂ）は従来の測定方法による二次元ボール画像である。
【図１３】 （Ａ）は別の従来の測定装置の概略図、（Ｂ）は（Ａ）の装置によるボール画像である。
【図１４】 （Ａ）は他の別の従来の測定装置の斜視図、（Ｂ）は測定領域を通過したゴルフボールを示す三次元領域の斜視図である。
【符号の説明】
１０ 測定装置
１５ コンピュータ
２０ ゴルフボール
２１ マーク
３０ 仮想ゴルフボール[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for measuring the rotation characteristics and flight characteristics of a sphere, and more specifically, specifies the three-dimensional posture and position of a sphere such as a golf ball, and determines the rotation speed, rotation axis direction, flight path, flight speed, and the like of the sphere. It measures accurately in a short time.
[0002]
[Prior art]
Conventionally, various measuring methods and apparatuses have been proposed for measuring the amount of rotation of various spheres such as golf balls.
For example, light is projected onto a sphere with a reflective tape on the surface or a sphere with a black painted area that does not reflect light on the surface, and the amount of rotation of the sphere is measured from the change in the amount of reflected light obtained by the rotation of the sphere. There is a way to do it. However, in this method, only the amount of light is measured and the contour of the sphere, the posture displacement, and the like are not measured, so the direction of the rotation axis of the sphere cannot be specified. Therefore, a plurality of rotating spheres with a mark on the surface are photographed at predetermined time intervals, and the rotation amount and rotation axis angle of the sphere are often obtained from the displacement state of the marks in each photographed image. .
[0003]
Specific examples of an apparatus and method for determining the amount of rotation of a sphere from a photographed image with such a mark include a sphere rotation amount measuring device disclosed in Japanese Patent No. 2810320 and a golf ball motion measuring method disclosed in Japanese Patent Application Laid-Open No. 10-186474. Patent No. 2950450 includes a device for measuring the flight characteristics of a moving sports object.
[0004]
As shown in FIGS. 12 (A) and 12 (B), the measuring device proposed by the present applicant in Japanese Patent No. 2810320 takes a picture of a sphere T having a center point C with marks P and Q twice. Two two-dimensional images G1 and G2 are obtained, the spherical radius in each image is defined as a unit radius, and the spherical marks P, Q, P ′, Q ′ and the center points C, C ′ are defined for each image. Three-dimensional coordinates are calculated from two-dimensional coordinates on the image. Using the calculated three-dimensional coordinates as a three-dimensional vector, the vector movement amount is obtained between the two images G1 and G2, and the rotation amount and the rotation axis direction are calculated and measured.
[0005]
In addition, as shown in FIG. 13A, the measuring method disclosed in Japanese Patent Laid-Open No. 10-186474 determines the shooting time with a sensor 2 that detects the movement of a club at the time of hitting, and the first and second cameras 1A, 1B. The ball image G3 showing the two balls B1 and B1 ′ shown in FIG. 13B is obtained by taking a picture of the ball B1 with a long time. The two-dimensional ball image G3 is processed in the same manner as described above, and the rotation amount of the ball is calculated and measured.
[0006]
Furthermore, the measuring apparatus 4 of Japanese Patent No. 2950450 in FIG. 14A is an image in which two balls B2 and B2 ′ with a mark Ba attached to one image are captured by two synchronized cameras 5A and 5B. The three-dimensional coordinates are derived based on the principle approximated to triangulation in association with the relationship of the visual field between the cameras 5A and 5B. Thus, a three-dimensional region diagram of the ball B2 and the like shown in FIG. 14B is obtained, and various characteristics of the ball are measured. A method for deriving three-dimensional coordinates in this way is known as a DLT (Direct Liner Transformation) method.
[0007]
Furthermore, Japanese Patent No. 3185850 proposes a monitor device that measures and displays the flight characteristics of sports objects. Specifically, one image is shot using at least one camera using shutter means or the like, and at least one camera has a known coordinate set in advance in a target space. It is necessary to calibrate using a predetermined number of points or more. Using the relationship between the known three-dimensional spatial coordinates and the two-dimensional coordinates projected on the film surface of the camera, six variables (three mass center of gravity coordinates of the sphere and three rotations from the reference coordinates) are represented by Taylor's theorem. The linearization can be solved by iterative calculation of 8 degrees, and the three-dimensional coordinates of the points (marks) fixed on the ball are obtained based on the length in the real space without using the radius of the ball image as a reference. be able to. Therefore, it is no longer necessary to accurately capture the contour of the ball image, and problems such as insufficient brightness due to the high-speed shutter means for obtaining a still image of the ball moving at high speed are alleviated. It has been made.
[0008]
[Patent Document 1]
Japanese Patent No. 2810320
[Patent Document 2]
Japanese Patent Laid-Open No. 10-186474
[Patent Document 3]
Japanese Patent No. 2950450 [0011]
[Patent Document 4]
Japanese Patent No. 3185850 [0012]
[Problems to be solved by the invention]
However, in the measurement apparatus of FIGS. 12A and 12B and the measurement method of FIGS. 13A and 13B, the radius of the ball image is used for the calculation related to the measurement. The accuracy of the calculated three-dimensional vector is affected, and it is necessary to obtain a spherical radius with high accuracy from the captured image, in addition to taking an image as a measurement base with high accuracy. However, in order to obtain a still image of a ball image flying at high speed, for example, a high-speed camera equipped with a high-speed shutter is used. Hard to get.
[0013]
Therefore, in the captured image, a relatively clear image can be obtained near the center of the ball, which is the position facing the camera, but it is difficult to capture the outline of the ball, which is a sphere. Even if you devise, it is difficult to improve. As a result, the ball outline of the photographed image becomes unclear, the dimensional accuracy of the radius read from the ball image is deteriorated, and the measurement accuracy with respect to the amount of rotation of the ball has to be naturally reduced.
[0014]
On the other hand, in the measurements shown in FIGS. 14A and 14B, the three-dimensional coordinates for the mark on the ball surface are obtained with reference to the length of the real space without using the radius of the ball image. There is an advantage that there is no need to take a picture and the problem of insufficient light intensity does not occur. However, in order to obtain the three-dimensional coordinates of the marks on the ball surface with high accuracy, it is necessary to photograph the ball relatively large in the image so that each mark can be read accurately. In order to take a large image of the ball in this way, it is necessary to shorten the time interval for photographing the two ball images, and the amount of rotation between the two ball images is naturally reduced.
[0015]
On the other hand, in order to increase the measurement accuracy of the amount of rotation of the ball, the displacement of the mark position is increased by increasing the movement distance of the mark, that is, the amount of rotation of the ball between the two photographed ball images is increased. There is a need for a condition that conflicts with enlarging the ball image.
[0016]
Therefore, if the ball image is enlarged, even if the three-dimensional coordinates of the mark can be measured with high accuracy, there is a problem that the accuracy of the measurement of the amount of rotation of the ball is reduced because the positional change between the images is small . On the other hand, if shooting is performed so as to increase the amount of rotation of the ball, two ball images must be captured at a time interval, and the measurement accuracy for the amount of rotation of the ball increases, but the ball image becomes smaller. The measurement accuracy of the three-dimensional coordinates of the mark is lowered, and in any case, there is a problem that both the three-dimensional coordinates of the mark and the rotation amount of the ball cannot be measured with high accuracy.
[0017]
To solve the above problem, prepare two sets of devices required for measurement, take a picture of one ball with the first set of devices, and take another ball image with the second set of devices at a time interval. It may be assumed that both the three-dimensional coordinates of the mark and the ball rotation amount are measured with high accuracy. However, in the measurement, it is necessary to calibrate a total of four high-speed cameras between the two sets, and the configuration of the device becomes very complicated and the cost is greatly increased. It is actually difficult to use two sets.
[0018]
Furthermore, when calculating and measuring the amount of rotation of the ball from the amount of movement of the mark on the photographed ball surface, the specific mark in the first ball image corresponds to any mark in the second ball image. It is necessary to find out. However, when the direction of the rotation axis of the ball can be predicted and there is little change in the rotation of the ball between images, the above identification is relatively easy, but the reason is that the direction of the rotation axis changes greatly from measurement to measurement. When the direction of the rotation axis cannot be predicted or when the amount of rotation of the ball is large, the above-mentioned determination becomes very difficult, and there is a possibility that measurement of the amount of rotation of the ball or the like may be impossible by automatic recognition by a computer or the like. Further, even if a human makes the above-mentioned squeezing, there is a possibility that it takes time or mistaking the snooping.
[0019]
In addition, if the mark in the first ball image turns to the back side due to the rotation of the ball in the second ball image and does not appear on the ball surface on the image, the measurement itself is not possible. Since it becomes possible, there are limitations on the measurement direction of the camera, the rotation direction of the ball to be measured, and the like.
[0020]
Furthermore, in Japanese Patent No. 3185850, the mark that was visible on the first ball image is not reflected on the second ball image due to the rotation of the ball. That is, when the mark on the first ball image turns around on the back side of the ball, there is a problem that measurement is impossible. Therefore, there is a problem in that the shooting direction with the camera and the rotation direction of the ball to be measured are limited and lack of portability.
[0021]
The present invention has been made in view of the above-described various problems, and the computer shortens the rotational characteristics such as the rotational speed and the rotational axis direction of the flying rotating sphere and the flight characteristics such as the flight path and the flight speed. The task is to measure accurately in time.
[0022]
[Means for Solving the Problems]
In order to solve the above problem, the present invention captures a plurality of two-dimensional images of the sphere by photographing a rotating sphere with a plurality of marks on the surface a plurality of times at predetermined time intervals, Similarly, a virtual sphere with a mark on the surface is created on the three-dimensional space coordinates of the computer, and the arbitrary posture and arbitrary position of the virtual sphere are set as the reference posture and reference position of the virtual sphere,
Using at least one imaging means, the relationship between the three-dimensional coordinates and the two-dimensional coordinates is derived in advance,
Using the above relationship, the mark position on the three-dimensional space coordinate of the virtual sphere is converted to a two-dimensional image to obtain a two-dimensional virtual mark coordinate value, and the sphere existing on the video is Find the 2D image mark coordinate value,
And the virtual mark coordinate values, as the video marked coordinates and matches, the virtual sphere, with respect to the reference posture and the reference position, predict the photographing time interval of the moving speed and the image of the rotating spheres When the rotation direction of the rotating sphere is defined as the Y axis, the left and right direction is defined as the X axis, and the direction perpendicular to these two axes is defined as the Z axis, to the rotatable range, -90~90 [deg] to the Y axis with respect to the reference posture, 5-120 to X-axis [deg], the range of -15~15 [deg] to the Z axis Limited to the above-mentioned virtual sphere posture displacement operation, and by the amount of the posture displacement operation, for each two-dimensional image of the sphere, specify the three-dimensional posture and position of the sphere,
A sphere characterized in that the rotation characteristics and flight characteristics of the sphere are calculated from the three-dimensional attitude and position at a certain time and the three-dimensional attitude and position at another time specified for each of the two-dimensional images. Provides a method for measuring the rotation characteristics and flight characteristics of the aircraft.
[0023]
In the present invention, since the three-dimensional posture and position of the sphere are specified by the method as described above, the rotation of the sphere is determined from the relationship between the three-dimensional posture and position at a certain time and the three-dimensional posture and position at another time. Rotational characteristics such as number and rotational axis direction, flight characteristics such as flight path and flight speed can be easily measured with high accuracy in a short time. Therefore, it is most suitable for the measurement of the spin amount of a golf ball that is rotating without receiving external force, the launch angle and the deflection angle of a hit ball, and particularly to improve the measurement accuracy of the left and right deflection angles at the time of hitting a ball. Can do.
[0024]
Specifically, a plurality of two-dimensional images of the sphere are obtained, and the rotation amount range and the flight range that can be predicted from the moving speed of the rotating sphere and the shooting time interval of the image with respect to the reference posture and the reference position are limited. In addition, the posture displacement operation is performed within an angular range in which the rotating sphere can be physically rotated . For this reason, the search range such as the rotation angle and the flight path in the posture displacement operation can be limited, and the calculation amount such as the rotation angle, the swing angle, and the launch angle can be drastically reduced. Therefore, the calculation time can be greatly shortened, and the rotation characteristics and flight characteristics of the sphere can be measured instantaneously in a short time. The predictable range of rotation amount and flight range refer to a search range that limits the magnitude of external force and shooting time when external force is applied to the sphere, and specifically, the golf club that hit the golf ball. The search range is limited in consideration of the count, head speed, and the flash time of the strobe attached to the camera.
[0025]
The amount of posture displacement operation with respect to the reference posture and the reference position is obtained by calculation according to an optimization method called a genetic algorithm, and the search range of the angle and position for coordinate conversion and movement conversion using the genetic algorithm is determined as described above. It is preferable that the sphere is limited to a range in which the sphere can be physically rotated or moved. As a result, the amount of calculation can be reduced without reducing the calculation accuracy, and more accurate measurement can be performed in a shorter time. The range in which the sphere can be physically rotated or moved refers to a search range in which the magnitude of the external force and the shooting time when the external force is applied to the sphere as described above are limited. That is, taking as an example the case where the sphere is a golf ball, when the spin amount of the golf ball is measured, it is a range that can be rotated from the reference posture and a range that can be translated from the reference position. .
[0026]
Further, it is preferable that a plurality of marks are provided on the surface of the sphere only in a range where the sphere can be physically rotated. In addition, more efficient measurement can be performed. It should be noted that the mark may be attached outside the range in which the sphere can be physically rotated to such an extent that the calculation time does not become long.
The surface of the sphere is preferably marked with 10 or more and 100 or less, and more preferably 30 or more and 50 or less. If the number is less than 10, the number of marks that can be read from the observation direction becomes too small, and the posture may not be specified. This is because it becomes longer and the efficiency deteriorates.
[0027]
It is preferable that the limited range of the rotation amount and the movement amount with respect to the reference posture and the reference position is determined according to the moving speed of the sphere and the shooting time interval of the video. As a result, the measurement time for the rotation characteristics and the flight characteristics can be further shortened.
It is suitable for measuring the flight characteristics of a sphere that moves at a moving speed of 40 m / s to 90 m / s, and further 50 m / s to 80 m / s.
In addition, when two or more shots are taken with two cameras, the first camera takes a picture of 0.5 ms to 4.0 ms after the sphere moves from the reference position, and the second camera takes the sphere at the reference position. It is preferable to take a video of 1.5 ms to 8.0 ms after the movement. The time interval for shooting multiple times is preferably 1.0 ms to 4.0 ms.
[0029]
In order to search for the rotation angle using the genetic algorithm, it has been conventionally considered that it is unknown how much the sphere rotates from the initial state of the sphere, so that the sphere in the virtual space is 0 to 360 [deg] around the XYZ axis. The rotation angle was searched in all the ranges. However, if the purpose of use is clear to some extent, for example, when measuring the amount of rotation of a golf ball, the calculation of the amount of rotation using a genetic algorithm is greatly reduced by limiting the rotation angle search range. can do.
[0030]
The reason why −90 to 90 [deg] around the Y axis with respect to an arbitrary reference position of the sphere is that when the head speed is 40 m / s and W # 1 is used, the spin is 1000 rpm to 4000 rpm. . The reason why the angle is set to 5 to 120 [deg] around the X axis is that when the head speed is 40 m / s and W # 1 is used, the spin becomes −3000 rpm to 3000 rpm. Further, the reason why the speed is set to -15 to 15 [deg] around the Z axis is that when the head speed is 40 m / s and W # 1 is used, the spin becomes -500 rpm to 500 rpm. This condition is particularly useful for analyzing the rotational characteristics and flight characteristics of a golf ball measured by a measuring apparatus for spherical characteristics and flight characteristics described later. In order to include the range of both the first camera and the second camera, it is necessary to consider the above conditions.
[0031]
When the flight direction of the sphere is defined as the Y-axis, the left-right direction is defined as the X-axis, and the direction perpendicular to these two axes is defined as the Z-axis, the range in which the sphere is physically movable is relative to the reference position of the sphere. In the case of an image taken with the first camera, the Y-axis direction is in the range of 50 mm to 100 mm, the X-axis direction is in the range of -100 mm to 100 mm, the Z-axis direction is in the range of 0 mm to 100 mm, and in the case of the image taken with the second camera Are preferably in the range of 150 mm to 300 mm, the X axis direction in the range of −300 mm to 300 mm, and the Z axis direction in the range of 0 mm to 300 mm.
[0032]
For example, when the head speed at the time of hitting a golf ball is 40 m / s, the ball speed is estimated to be 40 to 60 m / s in consideration of the ball speed being about 1 to 1.5 times the head speed. If the shutter of the first camera is made to emit light after 1.45 ms after the ball impact, the distance can be obtained from (ball speed) × (shutter time) (about 58 to 87 mm). Similarly, if the shutter of the second camera emits light after 4.45 ms after the ball impact, the distance is about 178 to 267 mm when the tee is used as a reference. The range in the Y-axis direction is determined so as to include these two ranges. Next, the X axis determines the above range by limiting the left and right ball deflection angles to −45 to 45 deg, and the Z axis also determines the above range by limiting the ball launch angle to 0 to 45 deg. That is, the above range is particularly suitable for the shooting interval when the golf ball is hit at the head speed.
[0033]
It is preferable that the termination condition of the optimization calculation of the genetic algorithm is defined using a predetermined fitness value. Thus, the calculation time can be shortened by defining the optimization calculation with the fitness and ending the calculation.
Specifically, from the previous measurement result, a fitness value that can correctly calculate the rotation angle or position of the sphere is derived in advance, and the optimization calculation is completed using the fitness value. Time has been shortened. For example, in the measurement of the rotation amount of a golf ball, the conformity that is less than 2 deg with respect to the solution (with a back spin within ± 50 rpm) and within 0.1 deg with respect to the launch angle / vibration angle is −0.00299 or more ( 0 is the most optimal). Therefore, if the degree of conformity is −0.002 or more, by adding a convergence condition for ending the optimization calculation, the calculation can be completed with only one trial, and the calculation time can be greatly shortened.
[0034]
Specifically, a case where a golf ball is used as a sphere will be described. By teeing up the marked golf ball in the same direction, the image taken by the first camera of the two cameras is backspin if the measured golf ball is hit by the driver, The range in which side spin and axial spin are physically generated can be limited. In general, the amount of rotation of a golf ball struck by a driver is 1000 rpm to 4000 rpm for a back spin, −3000 rpm to 3000 rpm for a side spin, and −500 to 500 rpm for an axial spin. If the shooting time, a certain initial ball speed and the number of clubs used are known, the rotation angle and movement range can be limited. Therefore, the rotation angle range of the golf ball photographed with the first camera and the rotation angle photographed with the second camera can be limited.
[0035]
In addition, if the number of clubs that hit the golf ball position search range is known, the position range can be limited to some extent from the initial ball speed. As described above, the calculation time can be greatly shortened by considerably limiting the search range.
[0036]
The posture displacement operation is a virtual sphere movement operation and a rotation operation, and it is preferable that the amount of the posture displacement operation with respect to the reference posture and the reference position is obtained by calculation according to an optimization method called a genetic algorithm.
[0037]
Since the virtual sphere formed on the computer arbitrarily sets the reference posture and the reference position, the reference posture and the reference position are different in size, position, and posture from the photographed two-dimensional video sphere. ing. Therefore, in order to display the orientation and position of the sphere with the reference orientation of the virtual sphere in the virtual space and the relative coordinate value with respect to the reference position in the three-dimensional space obtained from the three-dimensional and two-dimensional relational expressions, two virtual spheres are displayed. An operation for displacing the posture is required so as to coincide with the posture and position of the sphere of the three-dimensional image.
[0038]
This posture displacement is performed by moving and rotating the virtual sphere on the computer, such as parallel movement. By appropriately determining the amount of the displacement operation in the parallel movement, the virtual sphere is moved to the actual sphere posture and position. Accordingly, the posture and position of the sphere can be specified with high accuracy by the relative posture value with respect to the reference posture and the reference position in the three-dimensional space obtained from the three-dimensional and two-dimensional relational expressions. . In the present invention, it is preferable that the determination of the displacement manipulated variable is regarded as an optimization problem, and calculation is performed using a computer algorithm called a genetic algorithm, which is one of the solutions to the optimization problem.
[0039]
The calculation method using the above genetic algorithm has characteristics that are different from other optimization methods such as simulated annealing, gradient method, and other linear programming methods. In other words, it has features such as coding (coding) a character string, a vector, and the like, and setting a fitness for evaluating a calculation result based on an objective function.
[0040]
The genetic algorithm is a probabilistic solution that simultaneously searches for an optimal solution from a large number of individuals by an operation, and the calculated solution can be optimized. Therefore, it is useful to match the virtual sphere on the computer with the attitude and position of the sphere in the two-dimensional image while referring to a plurality of marks on the sphere.
[0041]
In the calculation according to the genetic algorithm, as the three independent variables related to the centroid position of the sphere, the amount of the rotation operation is set as three independent variables related to the three-dimensional rotation operation of the virtual sphere, The above operations are performed based on the numerical values of these six variables. The six variables determined in this way correspond to the relative coordinate values with respect to the reference position in the three-dimensional space for which the reference posture and the three-dimensional and two-dimensional relational expressions are obtained. Therefore, if the numerical values of these six variables are obtained, The posture and position can be specified.
[0042]
Note that the three variables related to the moving operation include the position of the center of gravity of the sphere (three (x, y, z)). Further, the three independent variables related to the three-dimensional rotation operation include rotation angles around the horizontal axis, the vertical axis, and the vertical axis, which are orthogonal coordinate axes in the virtual three-dimensional space.
[0043]
An image of a rotating sphere without receiving an external force is photographed using at least one photographing means, and the relationship between the three-dimensional coordinates and the two-dimensional coordinates is derived and grasped in advance. For this reason, the positional relationship between the marks on the two-dimensional image can be obtained from the positional relationship between the marks on the virtual sphere created on the computer. Therefore, by using the above relationship, the mark position on the three-dimensional space coordinate of the virtual sphere can be converted to a two-dimensional image to obtain a two-dimensional virtual mark coordinate value. Therefore, two-dimensional virtual marks and three-dimensional virtual marks, which were not possible in the past, can now be handled, and even two-dimensional virtual spheres can have three-dimensional information and grasp depth information. Can do. In the conventional method, the depth direction is not taken into consideration and the projection is merely performed, and all the two-dimensional images are on a plane. Conventionally, the projection direction is one direction, but in the present invention, the projection direction differs depending on the position of the virtual sphere.
Therefore, even when the edge of the sphere is not clearly seen, or even when the sphere image is photographed at the edge of the screen or is photographed small, it can be measured with high accuracy.
[0044]
In addition, by associating the posture and position of the virtual sphere and the actual sphere with the virtual mark coordinate value and the video mark coordinate value as described above, the posture and position of the actual sphere can be used as a reference in the virtual three-dimensional space. It can be expressed by a relative coordinate value with respect to the posture and the reference position. Along with this, it becomes possible to use relative coordinate values for the reference posture and reference position of the virtual space for the analysis of the rotation characteristics and flight characteristics of the sphere, making it easy to analyze the rotation characteristics and flight characteristics of the sphere on the computer. Automatic calculation can be performed. The reference position means the origin of the three-dimensional coordinate system defined when the relationship between the three-dimensional space and the two-dimensional image is obtained. Specifically, it refers to the center of gravity of the ball placed at the tee.
[0045]
In the present invention, the posture and position of the sphere are specified from a plurality of marks of the sphere of each captured two-dimensional image without using the sphere outline data. For this reason, as long as even the mark attached to the sphere can be clearly confirmed in each image, even if the outline of the sphere is unclear, it is possible to measure the attitude and position of the sphere with high accuracy. In order to have the computer automatically recognize the spherical mark from the captured two-dimensional image, it is conceivable to perform binarization processing for displaying only the white and black on the captured image.
[0046]
In addition, the rotation characteristic of the sphere is obtained by calculating a rotation matrix related to the rotation operation when the three-dimensional posture and position at a certain time coincide with the three-dimensional posture and position at another time. The amount of rotation of the sphere is calculated by multiplying the rotation matrix of a sphere at a certain time whose time interval can be specified by the inverse matrix of the rotation matrix of the sphere at another time. If the numerical value of the rotation matrix from the sphere posture at a certain time obtained by calculating in this way to the sphere posture at another time is determined, the amount of rotation can also be determined, and the rotation axis vector, that is, the rotation axis The direction can also be easily determined.
[0047]
Further, the flight characteristics of the sphere are obtained by calculating the movement amount and the movement direction of the centroid coordinates of the sphere when the three-dimensional attitude and position at a certain time are matched with the three-dimensional attitude and position at another time.
[0048]
When deriving the relationship between the three-dimensional coordinates and the two-dimensional coordinates in advance, at least twelve or more three-dimensional coordinates are used when one camera is used, and at least six or more are used when two cameras are used. It is preferable to use the three-dimensional coordinates.
Thereby, the relationship between the three-dimensional space and the two-dimensional space can be obtained. That is, the relationship between the real space and the image on the camera can be clarified. This is because if the number of coordinates is smaller than the number of three-dimensional coordinates, the number of known numbers for the variables is small, so that simultaneous equations showing a three-dimensional and two-dimensional relationship cannot be solved.
[0049]
As a method for obtaining a two-dimensional virtual mark coordinate value by converting a mark position on a three-dimensional space coordinate of a virtual sphere into a two-dimensional image, a reference posture and a reference position sphere constructed on a computer are used. For example, the mark may be projected onto a two-dimensional image using the relationship between the known real space three-dimensional coordinates and the coordinates on the two-dimensional image.
[0050]
As design variables in the posture displacement operation, a total of six rotation angles of the sphere around each of the horizontal axis, the vertical axis, and the vertical axis, which are orthogonal coordinate axes in the virtual three-dimensional space, and the three-dimensional center of gravity position of the sphere are used. Preferably it is.
Thereby, since the depth information of the sphere can be calculated, the rotation characteristic and the flight characteristic can be calculated simultaneously.
[0051]
Examples of the sphere to be measured include various ball games such as golf balls and tennis balls. This is useful for analysis of rotation characteristics, flight characteristics, etc. when these balls are used.
[0052]
In addition, since it is fundamentally difficult to clearly photograph the contour of the ball image, it is preferable to measure the rotation characteristics without using the contour data of the ball image. In particular, when the ball is photographed at the end of the photographed image, the right or left portion of the ball is shaded by the effect of the strobe, so it is preferable to measure the rotational characteristics without using the contour portion as much as possible.
[0053]
In addition, the following devices may be mentioned as the optimal device for measuring the rotational characteristics and flight characteristics of the sphere of the present invention.
An imaging means capable of imaging the sphere from each direction, a recording means for recording a two-dimensional image of the sphere obtained by the imaging, a virtual sphere similar to the sphere is created in a three-dimensional coordinate space, and the virtual sphere Based on the two-dimensional image of the sphere, the three-dimensional posture and position of the sphere is specified, and calculating means for calculating the rotation characteristics and flight characteristics of the sphere,
The arithmetic means has a coordinate conversion program capable of deriving a relationship between three-dimensional coordinates and two-dimensional coordinates in advance using at least one photographing means,
And, the two-dimensional video mark coordinate value of the sphere on the two-dimensional video matches the two-dimensional virtual mark coordinate value obtained by converting the mark position on the three-dimensional coordinate of the virtual sphere, There is provided a posture recognition program for performing a posture displacement operation on the virtual sphere and specifying the three-dimensional posture and position of the sphere by the amount of the posture displacement operation with respect to the reference posture and the reference position of the virtual sphere. Thereby, the attitude | position of a sphere, a rotation characteristic, and a flight characteristic can be calculated | required accurately. In particular, it is possible to take an image in which the amount of rotation of the sphere can be predicted to some extent.
[0054]
The calculation means preferably has an optimization program for calculating the reference posture and the amount of posture displacement operation with respect to the reference position according to a genetic algorithm. Thereby, the calculation by the above-described measurement method can be easily performed, and the calculation accuracy can be improved.
[0055]
It is preferable that the photographing unit is configured to be able to photograph a rotating or moving sphere without receiving an external force or the like a plurality of times at predetermined time intervals.
Specifically, in order to capture a two-dimensional image of a real sphere, an image capturing means for capturing images such as a still camera and a CCD camera and a recording means for recording images such as a film and an image memory are required. It is. In addition, a micro flash is also used to obtain an instantaneous still state ball image using a short-time luminance difference. Even if a sphere that moves at a high speed of 10 m / s or more is an object to be measured, a still image without blur can be obtained by using a high-speed shutter or a micro flash.
[0056]
It is preferable to use two cameras as the photographing means. It is preferable that the interval be easily variable without calibration. By making the interval between the two cameras and the shooting time interval relatively long, the angle change can be increased and the measurement accuracy of the rotational speed can be increased. In addition, it is easy to recognize which mark position on the first ball image corresponds to which mark position on the second ball image, and automation can be facilitated. Note that one or a plurality of two-dimensional image capturing means can be applied.
[0057]
In order to obtain multiple images, it is necessary to capture the image of the sphere at least twice. However, a single camera can be used to capture multiple spheres on a single image, such as by flashing the microflash multiple times. Alternatively, one sphere may be projected on each of a plurality of images with one camera. Further, a two-dimensional image may be taken for each camera at a required time interval using a plurality of cameras. However, when shooting with a plurality of cameras, it is necessary to specify a common coordinate axis for each image by calibration or the like.
[0058]
In addition, when film is used as the recording means as a means for obtaining the position of the mark attached to the sphere from the photographed image, a primitive method for directly measuring the developed photograph with a ruler or the like, film, There is also a method in which a measurement cursor is placed on a computer screen and measured using an image input device such as a scanner that can capture a photographic image into the computer. Further, when an image memory is used as the recording means, there is a method of reading data in the image memory on a computer screen and measuring with a measurement cursor as described above. That is, the measuring means is not particularly limited as long as the two-dimensional position of each mark in the spherical image is obtained, and any of the above methods may be used.
[0059]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1A shows the configuration of a sphere rotation characteristic and flight characteristic measuring apparatus 10 for executing the method for measuring the rotation characteristic and flight characteristic of a sphere of the present invention.
The measuring device 10 creates a virtual sphere similar to a sphere in a three-dimensional coordinate space, a photographing means that can photograph the sphere from each direction, a recording means that records a two-dimensional image of the sphere obtained by photographing, Based on the virtual sphere and the two-dimensional image of the sphere, a three-dimensional posture and position of the sphere are specified, and calculation means for obtaining the rotation characteristics and flight characteristics of the sphere are provided.
[0060]
Further, the calculation means has a coordinate conversion program capable of deriving a relationship between the three-dimensional coordinates and the two-dimensional coordinates in advance using at least one photographing means, and two-dimensional of the sphere on the two-dimensional image The virtual sphere is displaced so that the video mark coordinate value matches the two-dimensional virtual mark coordinate value obtained by converting the mark position on the three-dimensional coordinate of the virtual sphere, and the reference posture of the virtual sphere And a posture recognition program for specifying the three-dimensional posture and position of the sphere based on the amount of posture displacement operation with respect to the reference position.
[0061]
As shown in FIG. 1B, the measuring apparatus 10 uses a CCD camera 11 as a photographing means and also uses two micro flashes 12-1 and 12-2. A sphere to be measured is photographed by the CCD camera 11, and sequentially obtained images are stored in the image memory 15b as recording means. The image memory 15b is installed in the computer 15 which is a calculation means.
[0062]
At the time of video shooting, the microflashes 12-1 and 12-2 are emitted one by one at a required time interval, and then the accumulation in the image memory 15b is terminated, whereby two spheres are formed in one two-dimensional video. Individual images are obtained in the image memory 15b. In addition, the trigger signal by photoelectric tube switch 16-1, 16-2 and the retarder 17 is utilized for the timing which light-emits microflash 12-1, 12-2.
[0063]
In addition to the image memory 15b described above, the computer 15 included in the measuring apparatus 10 includes a central processing unit (CPU), a memory, a hard disk 15a that is a storage device, and the like. It has a posture recognition program and an optimization program for calculating the reference posture and the amount of posture displacement operation with respect to the reference position according to the genetic algorithm.
[0064]
The posture recognition program, the coordinate conversion program, and the optimization program are basically assembled based on the flowchart of FIG.
That is, a virtual sphere is formed in a virtual three-dimensional space based on the sphere to be measured, and the virtual sphere is marked in the same manner as the real measurement symmetry, and the arbitrary posture and position of the formed virtual sphere are set as a reference posture. And set as a reference position.
Converting a mark position on a three-dimensional space coordinate of a virtual sphere into a two-dimensional image using a relationship between three-dimensional coordinates and two-dimensional coordinates derived in advance using at least one photographing means. To obtain a two-dimensional virtual mark coordinate value. Further, a two-dimensional video mark coordinate value of a sphere existing on the video is obtained.
Posture displacement operation (movement, rotation, etc.) is limited to the rotation amount and flight range of the virtual sphere that can be predicted with respect to the reference posture and the reference position so that the virtual mark coordinate value matches the video mark coordinate value. Then, the three-dimensional posture and position of the sphere are specified for each two-dimensional image of the sphere based on the amount of the posture displacement operation. The two-dimensional image of the sphere is subjected to a posture displacement operation (movement, rotation, etc.) limited to a predictable range, and the rotation amount and position of the sphere are obtained from the rotational movement amount of the posture displacement operation.
Based on the three-dimensional posture and position at a certain time specified for each two-dimensional image and the three-dimensional posture and position at another time, the rotation characteristics and flight characteristics of the sphere are calculated.
In addition to the processing described above, binarization processing for converting a captured two-dimensional image into a white and black display is also included. In the present invention, the measurement is performed with the details limited within a certain range of the three-dimensional space.
[0065]
The displacement amount associated with the virtual sphere posture displacement operation as described above is programmed in an optimization program that calculates according to the genetic algorithm so as to be specified using the calculation based on the genetic algorithm. The identification of the three-dimensional posture is performed for each spherical image photographed in obtaining the rotation characteristics and flight characteristics of the sphere. In addition, the search range of the angle and position for coordinate transformation and movement transformation using a genetic algorithm is set so that the sphere can be physically rotated or / and moved, and optimization calculation of the genetic algorithm is performed. Is defined using a value of a predetermined fitness.
[0066]
Hereinafter, a method for measuring the rotation characteristics and flight characteristics of a sphere using the measurement apparatus for the rotation characteristics and flight characteristics of the sphere will be described in more detail.
[0067]
First, a golf ball is used as a sphere to be measured, and black marks 21 (all not shown) are attached to the surface of the golf ball 20 as shown in FIG. Specifically, 12 points are randomly placed on the circumferential line C1 (y = 0) of the longitude 90 ° and 270 ° of the golf ball 20 and on the circumferential line C2 (x = 0) of the longitude 0 ° and 180 °. 12 points are randomly added, 6 points are randomly added on the circumferential line C3 in a direction in which the equator (z = 0) is inclined by 45 °, and 12 points marks 21 are randomly assigned on the equator C4.
Further, when the golf ball 20 is rotated about the rotation axis J at an angle obtained by dividing 360 degrees by 1, the mark 21 is attached so as to be symmetric only once before and after the rotation. That is, it has one-time rotational symmetry with respect to the rotation operation.
[0068]
Further, the three-dimensional coordinate value of each mark is read by using a three-dimensional measuring device or the like for the golf ball 20 with the mark 21 as described above. At this time, polar coordinates (radial direction coordinate value r, meridian direction angle θ, azimuth direction angle φ) are adopted as coordinates used for reading, as shown in FIG.
[0069]
Next, as shown in FIG. 5, the virtual golf ball 30 similar to the actual golf ball 20 is formed in the virtual three-dimensional coordinate space S on the computer by the posture recognition program in the computer 15, and this virtual golf ball A mark 31 is attached to the numerical position of the polar coordinates (r, θ, φ) read as described above so that the surface of 30 is similar to the golf ball 20. In the posture recognition program described above, the calculation is performed by converting into orthogonal coordinates. In addition, an arbitrary posture of the virtual golf ball 30 formed in this way is set as a reference posture.
[0070]
Next, using at least one photographing means, the relationship between the three-dimensional coordinates and the two-dimensional coordinates is derived and grasped in advance, and the mark position relationship between the virtual sphere mark position and the camera film surface (two-dimensional) A method for obtaining the value will be described. That is, the coordinates are converted from space coordinates to camera coordinates.
[0071]
FIG. 6 shows the positional relationship between the coordinates on the three-dimensional real space and the coordinates on the two-dimensional image. Below is a detailed explanation of the variables.
Arbitrary coordinate axes are set in the real space, and point P (X, Y, Z) and lens center coordinate O (X ₀ , Y ₀ , Z ₀ ) are set.
The distance between the surface including the point P and perpendicular to the optical axis and the center of the lens is L, and the distance between the file surface and the lens center is F.
Arbitrary coordinate axes are also set on the film surface, and the coordinates of Q, which is an image of the point P, on the film surface are (U, V), and the coordinates of the intersection of the optical axis and the film surface are (U _0). , V ₀ ).
Considering a coordinate system (X'Y'Z ') with the lens center O as the origin, the Z axis parallel to the optical axis, and the X / Y axes parallel to the U / V axes, the real space coordinates (XYZ A conversion matrix from coordinates) to X′Y′Z ′ is M (m _ij : i = 1 to 3, j = 1 to 3). However, since this transformation matrix obeys Euler's theorem, M is as shown in Equation 1 below.
[0072]
[Expression 1]

[0073]
In order to directly represent the relationship between the point P in the real space and the image Q, the relationship between the two must be represented in the same coordinate system. Therefore, Formula 2 is obtained from the real space defined above using a transformation matrix M into a coordinate system having the X axis and the Y axis parallel to the image axis U and V axis, with the optical axis as the Z axis.
[0074]
[Expression 2]

[0075]
Since OP and OQ are collinear with each other and the length ratio is L: F, Equation 3 is obtained.
[0076]
[Equation 3]

[0077]
By substituting Equation 2 into Equation 3, L is obtained from one of the three equations, and by substituting L into the other two equations, the following Equation 4 is obtained.
[0078]
[Expression 4]

[0079]
By summarizing the variables in Equation 4 and organizing U, V, X, Y, and Z, Equation 5 is obtained.
[0080]
[Equation 5]

[0081]
In order to obtain 11 coefficients, two sets of (X, Y, Z) and (U, V) can be calculated by substituting into Equation 5 for two cameras. In order to suppress, it is desirable to measure six or more sets of known real space coordinates. In addition, one camera requires 12 or more (X, Y, Z) and (U, V). With 3 cameras, the number is 4 or more.
[0082]
By the above method, the relationship between the known real space coordinates and the coordinates on the two-dimensional image can be grasped. Using this relationship, as shown in FIG. 7, the coordinates of the virtual sphere mark on the computer can be obtained as the two-dimensional coordinates on the film surface of the camera. That is, the position of the mark 30 on the three-dimensional space coordinates of the virtual golf ball 30 can be converted into a two-dimensional image.
[0083]
Next, when a mark on a virtual three-dimensional sphere is projected onto two-dimensional coordinates, a method for determining whether or not the mark exists on the film image (whether the mark exists on the front side or the back side) Will be described.
[0084]
A method for determining whether the mark shown in the flowchart shown in FIG. The eleven coefficients defined by Equation 5 can be obtained, and the three-dimensional coordinates of the camera lens are calculated using these coefficients.
[0085]
As shown in FIG. 8, assuming that the lens center O (X ₀ , Y ₀ , Z ₀ ) and the virtual sphere center of gravity P (G _X , G _Y , G _Z ), the vector OP is as shown in Equation 6.
[0086]
[Formula 6]

[0087]
Using the vector OP and the diameter R of the sphere, the tangent length l from the lens center to the sphere is expressed by Equation 7.
[0088]
[Expression 7]

[0089]
When the hatched portion of the virtual sphere is projected two-dimensionally, it is defined as a mark that can actually be photographed (front side), and the other marks are defined as the back side. Assuming that the length of the center of the lens and the mark on the virtual sphere is L, L is determined by the position of the center of gravity of the virtual sphere and the known positional relationship of each mark.
[0090]
L <l: The mark on the sphere is the image direction (front side) that can actually be measured, and is used for GA calculation.
L ≧ l: A mark on the sphere is a direction of the image that cannot actually be measured (back side) and is not used for GA calculation.
[0091]
By the above method, it is possible to determine whether or not all marks on a virtual sphere are marks that can be used for GA calculation. However, it is necessary to obtain the lens center position O (X ₀ , Y ₀ , Z ₀ ). Therefore, the center position of the lens is determined using Equation 4 and Equation 5 above. When these expressions are compared, the following relational expression (Formula 8) is established.
[0092]
[Equation 8]

[0093]
Equation 8 has 12 variables, but there are only 11 equations, so X ₀ , Y ₀ and Z ₀ cannot be calculated as they are. Therefore, by calculating the determinant of the transformation matrix M and adding the relational expression of Equation 9, 12 variables can be obtained from Equation 12, and X ₀ , Y ₀ , and Z ₀ can be obtained.
[0094]
[Equation 9]

[0095]
Next, the CCD camera 11 is disposed at a position where the actual golf ball 20 can be imaged in a rotating state, and the distance from the golf ball 20 and the magnification of the camera lens are adjusted as appropriate.
[0096]
When the golf ball 20 passes in front of the CCD camera 11 in the above arrangement state, the microflash is emitted twice at a predetermined time interval, and a still image in which two golf balls 20 are captured in one two-dimensional image. Is obtained in the image memory 11b. The two-dimensional image obtained here is shown in FIG. The video data thus photographed is binarized into white and black by a binarization processing program, and then a two-dimensional coordinate value is read for each mark 21 on the display screen 18 and the read value is obtained. It is recorded on the hard disk 15a.
[0097]
Using the posture recognition program, the mark position on the three-dimensional spatial coordinates of the virtual golf ball 30 is converted into a two-dimensional image using the relationship between the three-dimensional coordinates and the two-dimensional coordinates derived in advance by the above method. The two-dimensional virtual mark coordinate value obtained in this way and the two-dimensional video mark coordinate value of the actual golf ball 20 existing on the image obtained by the above photographing are respectively moved and rotated. It is carried out.
Thereby, the attitude | position and position with respect to the reference | standard attitude | position of the virtual golf ball 30 and a reference | standard position are specified. The amount of the movement operation and the rotation operation is calculated using a genetic algorithm which is a kind of optimization method.
The operation range is limited in the posture displacement operation, and the search range of the angle and position for coordinate conversion and movement conversion using a genetic algorithm is limited to a range in which the sphere can be physically rotated. Specifically, the search for the entire range from 0 ° to 360 ° is limited to a rotatable range. Furthermore, the position is limited rather than the entire space in which the ball flies. The specific limited range is as described above.
[0098]
The conditions for optimization using the genetic algorithm (GA) of this embodiment are shown below.
A total of six items including rotation angles (α, β, γ) around each axis of three-dimensional orthogonal coordinates set arbitrarily, and barycentric coordinates (X ₀ , Y ₀ , Z ₀ ) of the virtual golf ball 30 in a three-dimensional space. Design variables. These six items are six variables. In the optimization by GA, it is necessary to code the design variables, but each variable (real value) of α, β, γ, X ₀ , Y ₀ , Z ₀ is converted to a 10-bit binary system. Is used as code.
[0099]
In addition, basic setting values for optimization by GA according to the present embodiment are shown below.
Number of individuals: 50
Chromosome length: 60 bits Number of design variables: 6 variables (10 bits per variable)
Termination condition (termination if the maximum value of fitness is -0.002 or more)
Number of marks: 42
[0100]
The pattern matching is performed between the two-dimensional projection obtained by performing the above operation using a computer and the photographed two-dimensional projection. The similarity of the pattern at this time is defined by the following formula 10, and the maximum value is searched by a genetic algorithm using this as an objective function.
[0101]
[Expression 10]

[0102]
In Equation 10, Xi is the two-dimensional coordinates of the mark of the photographed projection (the origin is the center coordinate of the sphere (ball)), and Yi is the three-dimensional space of the ball after being rotated by the value obtained by the genetic algorithm. Are the two-dimensional coordinates (the origin is the center coordinates of the sphere) of the mark of the projected view obtained from the position of the center of gravity using the relationship between the known real space coordinates and the coordinates on the two-dimensional image.
Further, distance (a, b) represents the distance between the two points a and b, min _j represents the minimum value with respect to j (j = 1 to n, n is the number of marks), and Σ is i (i = 1). N, n means the sum of the number of marks). N is the number of marks. For each image, the minimum value of the distance between the marks is calculated for all the marks, and the sum is used as the fitness.
[0103]
The calculation of the objective function is performed for all the individual individuals arranged, and the fitness for each individual is obtained from these calculations.
As an end condition for the optimization calculation of the genetic algorithm, a fitness value that can correctly calculate the rotation angle or position of the sphere is derived in advance from the measurement result in advance, and the fitness value is used. As described above, if the fitness is −0.002 or more, the optimization calculation is terminated. It is judged that the value of the six variables possessed by the individual whose fitness is −0.002 or more is the optimum solution for the posture displacement of the virtual golf ball, and the three-dimensional posture and position of the golf ball 20 are determined by this individual. I have identified. Note that a method other than the above may be used as a method for terminating the generational change simulation of the genetic algorithm.
[0104]
The rotation of the point on the three-dimensional coordinate may be performed by applying a 3 × 3 rotation matrix to the point coordinate. This rotation matrix is determined when the values of α, β, and γ are determined. Therefore, by obtaining this rotation matrix, it is possible to determine the amount of rotation of the golf ball from the reference position in each image. In the optimization calculation, the golf ball is rotated by varying α, β, and γ, and α, β, and γ are determined so that the deviation from the captured image is minimized.
In addition, the rotation matrix in each video can be obtained by the above method, but in order to obtain how much rotation between two videos, the rotation matrix of one video is added to the rotation matrix of one video. The inverse matrix of Based on the rotation matrix determined here, the rotation axis vector and the rotation angle are calculated.
[0105]
Specifically, a rotation matrix of three rows and three columns is calculated from numerical values of rotation angles (α, β, γ) around the X axis, Y axis, and Z axis of the three-dimensional coordinate space possessed by individuals satisfying the end condition of the fitness. This rotation matrix is a matrix that determines the posture of the golf ball 20. That is, the rotation matrices Rx, Ry, and Rz that are rotated around the X-axis, Y-axis, and Z-axis are expressed as follows.
[0106]
[Expression 11]

[0107]
On the other hand, a rotation matrix R that is a matrix that specifies the posture and position of the golf ball 20 specified by the posture recognition program from the reference posture and reference position of the virtual golf ball is a rotation matrix Rx, Ry, Rz around each axis. It is expressed as follows.
[0108]
[Expression 12]

[0109]
In addition, the same calculation and fitness evaluation as described above are performed for the other golf ball 20 images, and the golf ball 20 is rotated from rotation angles (α ′, β ′, γ ′) that specify the posture and position of the golf ball 20. I'm looking for a matrix.
[0110]
As described above, R1 is a rotation matrix that specifies the posture of the golf ball 20 at a certain time specified by Formula 12, and R2 is a rotation matrix that specifies the posture of the golf ball 20 at another time. Is a rotation matrix that matches the posture of the golf ball 20 at other times with R12, the rotation matrix R12 is obtained by the following equation.
[0111]
[Formula 13]

[0112]
The direction (u1, u2, u3) of the rotation axis (coordinate axis) and the rotation angle Ψ at the time of coordinate conversion shown in FIG. 10 according to the rotation matrix R12 obtained by the above equation are obtained by the following equations 14 and 15. .
[0113]
[Expression 14]

[0114]
[Expression 15]

[0115]
The amount of rotation of the golf ball 20 and the rotation axis method from one time to another are obtained from the obtained rotation angle Ψ and the time interval between the two images.
In order to obtain the amount of rotation between two or more images, the amount of rotation between the images is obtained from the images before and after each successive image, and the amount of rotation of the sphere is continuously obtained. ing.
[0116]
Further, by obtaining the three component moving speeds of the center of gravity of the golf ball in each image by the above method, the flight characteristics including the flight path such as the launch angle and the swing angle can be calculated. Specifically, assuming that the gravity center positions Gx (t), Gy (t), and Gz (t) of the ball at a certain time, the three component moving speeds Vx, Vy, Vz, and the ball speed V Is required.
[0117]
[Expression 16]

[0118]
Further, the launch angle and the deflection angle are obtained by the following Expression 17. However, the advancing direction of the ball is the X axis, the left and right direction is the Y axis, and the height direction is the Z axis.
[0119]
[Expression 17]

[0120]
Examples of the present invention will be described in detail below.
(Experiment 1)
The golf ball 40 is teeed up so that the equator / longitude 0 ° and 180 ° directions face the front, and a mark 41 is attached to the golf ball 40 in the same manner as in FIG. 3, and as shown in FIG. ) Is measured by the two HS measurement sensors 42 (42A, 42B), and the golf ball 40 that rotates and receives an external force with the first camera 43A and the second camera 43B is photographed at intervals of 3 ms. did. The first camera 43A took a picture with the strobe emitting 3.2 ms after the impact using the second sensor 42B as a trigger signal. In the second camera 43B, the second sensor 42B was used as a trigger signal, and the strobe light was emitted 6.2 ms after the impact. Different indoor conditions.
[0121]
For golf ball back spin (1000 rpm to 4000 rpm), side spin (-3000 rpm to 3000 rpm), and axial spin (-500 rpm to 500 rpm), the flight direction is the Y axis, the left and right direction is the X axis, and the direction perpendicular to these two axes is When it was defined as the Z axis, the rotation angles around the X axis, the Y axis, and the Z axis were measured with the first camera and the second camera. The results are shown in Table 1.
It has been experimentally found that the spin amount when hitting a driver at a head speed of 40 m / s becomes the above-mentioned back spin amount, side spin amount, and axial spin amount, and the data was referred to. For example, at the rotation angle (around the X axis) of the golf ball after hitting the ball at 1000 rpm (3.2-1.75) = 1.45 ms,
1000 rpm × 2π / 60 (rad / s) × 360 / 2π (deg / s) × 1.45 × 10 ⁻³ (s) = 8.7 deg. Others were calculated similarly.
[0122]
[Table 1]

[0123]
As shown in Table 1, it was confirmed that the rotation angle range of the golf ball photographed by the first camera and the rotation angle range photographed by the second camera can be limited. That is, the range in which the golf ball can physically rotate is −90 to 90 [deg] around the Y axis, 5 to 120 [deg] around the X axis, and around the Z axis with respect to an arbitrary reference position of the golf ball. It was confirmed that it was in the range of -15 to 15 [deg].
[0124]
(Experiment 2)
Ten ball hit tests were performed by a driver, and comparison of calculation time was verified by the two measurement methods of Example 1 and Comparative Example 1. The measurement was performed under the condition that the same result was obtained using either method except for the portion related to the calculation time. The results are shown in Table 2.
The personal computer used was a PC equivalent to Pentium (R) IV 1.5 GHz memory 2G.
[0125]
[Table 2]

[0126]
(Example 1)
By the same method as in the above embodiment, the rotation amount, swing angle, launch angle, and ball speed of back spin and side spin were calculated by the measurement method of the present invention. That is, the measurement was performed by limiting the search range of the genetic algorithm and adding marks only within that range.
[0127]
(Comparative Example 1)
Although the calculation was performed by an optimization method using a genetic algorithm, the search range of the genetic algorithm was not limited and the mark addition position was not limited.
[0128]
As shown in Table 2, it was confirmed that the calculation time of Example 1 was significantly shortened compared to Comparative Example 1 in any of the 10 different hitting ball patterns, and the measurement result could be obtained instantaneously.
[0129]
【The invention's effect】
As is clear from the above description, according to the present invention, a plurality of two-dimensional images of the sphere are obtained in a state where the amount of rotation of the sphere can be predicted, and the operation range is limited with respect to the reference posture and the reference position. The posture displacement is operated. Therefore, the search range such as the rotation angle and position in the posture displacement operation can be limited, and the amount of calculation such as the rotation angle, the swing angle, and the launch angle can be drastically reduced. Therefore, the calculation time can be greatly shortened, and the rotation characteristics and flight characteristics of the sphere can be measured instantaneously in a short time.
[0130]
Also, since the 3D posture and position of the sphere are specified, the rotation speed of the sphere and the rotation axis direction, etc. can be determined from the relationship between the 3D posture and position at a certain time and the 3D posture and position at another time. Flight characteristics such as characteristics, flight path and flight speed can be measured easily and with high accuracy. Therefore, it is most suitable for the measurement of the spin amount of a golf ball that is a rotating sphere without receiving an external force, the launch angle and the deflection angle of a hit ball, and in particular, the accuracy of the measurement of the deflection angle can be improved.
[0131]
In addition, if the target sphere is properly photographed, it is calculated according to the program in the computer based on the image of the sphere, and the rotation characteristics and flight characteristics of the sphere can be measured automatically, greatly reducing the measurement effort. be able to.
[0132]
Furthermore, the termination condition for the optimization calculation of the genetic algorithm is defined using a predetermined fitness value. As described above, the calculation time can be shortened by defining the optimization calculation based on the fitness and ending the calculation.
[Brief description of the drawings]
FIG. 1A is a diagram showing a configuration of a measuring apparatus for rotational characteristics and flight characteristics of a sphere of the present invention, and FIG. 1B is a schematic perspective view.
FIG. 2 is a flowchart of a method for measuring the rotational characteristics and flight characteristics of a sphere according to the present invention.
FIG. 3 is a diagram illustrating a position where a mark is attached to a sphere.
FIG. 4 is a diagram illustrating polar coordinates of a sphere.
FIG. 5 is a schematic view of a virtual sphere with marks.
FIG. 6 is a diagram illustrating a positional relationship between coordinates on a three-dimensional space and coordinates on a two-dimensional image.
FIG. 7 is a diagram illustrating a method for converting a mark position on a three-dimensional space coordinate of a virtual sphere onto a two-dimensional image.
FIG. 8 is a diagram illustrating a relationship between a lens center and a sphere.
FIG. 9 is a diagram showing a two-dimensional image of a sphere.
FIG. 10 is a diagram illustrating a rotation axis direction and a rotation angle.
FIG. 11 is a diagram for explaining a shooting situation of a golf ball in Experiment 1;
12A and 12B are two-dimensional ball images obtained by a conventional measuring method.
13A is a schematic diagram of another conventional measuring apparatus, and FIG. 13B is a ball image by the apparatus of FIG.
14A is a perspective view of another conventional measuring apparatus, and FIG. 14B is a perspective view of a three-dimensional region showing a golf ball that has passed through the measurement region.
[Explanation of symbols]
10 Measuring Device 15 Computer 20 Golf Ball 21 Mark 30 Virtual Golf Ball

Claims (5)

A rotating sphere with a plurality of marks on the surface is photographed a plurality of times with a predetermined time interval to obtain a plurality of two-dimensional images of the sphere, while a virtual sphere with a mark on the surface as with the sphere is obtained. Created on the three-dimensional space coordinates of the computer, set the arbitrary posture and arbitrary position of the virtual sphere as the reference posture and reference position of the virtual sphere,
Using at least one imaging means, the relationship between the three-dimensional coordinates and the two-dimensional coordinates is derived in advance,
Using the above relationship, the mark position on the three-dimensional space coordinate of the virtual sphere is converted to a two-dimensional image to obtain a two-dimensional virtual mark coordinate value, and the sphere existing on the video is Find the 2D image mark coordinate value,
And the virtual mark coordinate values, as the video marked coordinates and matches, the virtual sphere, with respect to the reference posture and the reference position, predict the photographing time interval of the moving speed and the image of the rotating spheres When the rotation direction of the rotating sphere is defined as the Y axis, the left and right direction is defined as the X axis, and the direction perpendicular to these two axes is defined as the Z axis, to the rotatable range, -90~90 [deg] to the Y axis with respect to the reference posture, 5-120 to X-axis [deg], the range of -15~15 [deg] to the Z axis Limited to the above-mentioned virtual sphere posture displacement operation, and by the amount of the posture displacement operation, for each two-dimensional image of the sphere, specify the three-dimensional posture and position of the sphere,
A sphere characterized in that the rotation characteristics and flight characteristics of the sphere are calculated from the three-dimensional attitude and position at a certain time and the three-dimensional attitude and position at another time specified for each of the two-dimensional images. Of measuring the rotation characteristics and flight characteristics of the aircraft. The amount of posture displacement operation with respect to the reference posture and the reference position is obtained by calculation according to an optimization method called a genetic algorithm,
2. The rotation characteristics and flight characteristics of a sphere according to claim 1, wherein a search range of angles and positions for coordinate conversion and movement conversion using the genetic algorithm is limited to a range in which the sphere can be physically rotated or moved. Measuring method. A first camera and a second camera are provided. These first and second cameras have a function of photographing a moving sphere with a moving speed of 40 m / s to 90 m / s, and the first camera has a reference position for the sphere. The second camera shall shoot from 1.5 ms to 8.0 ms after the sphere moves from the reference position.
The range in which the sphere is physically movable is 50 mm to 100 mm in the Y-axis direction, −100 mm to 100 mm in the X-axis direction, and Z-axis direction in the case of an image taken by the first camera with respect to the reference position of the sphere. In the case of an image taken by the second camera, the Y-axis direction is 150 mm to 300 mm, the X-axis direction is -300 mm to 300 mm, and the Z-axis direction is 0 mm to 300 mm. Item 3. A method for measuring rotational characteristics and flight characteristics of a sphere according to Item 2. The end condition of the optimization calculation of the genetic algorithm is defined using a value of the degree of fitness that has been derived in advance from a measurement result obtained in advance and a degree of fitness that can calculate the rotation angle or position of the sphere. 4. A method for measuring the rotational characteristics and flight characteristics of a sphere according to claim 2 or claim 3 . The method for measuring rotational characteristics and flight characteristics of a sphere according to any one of claims 1 to 4, wherein the sphere is a golf ball .

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