理論上は
位置を時間で微分すると速度
速度を時間で微分すると加速度
ってなりますよね。
映像分析では、映像から任意の点の位置座標を算出することができますので、映像から加速度を求められないか試してみました。
映像の座標の単位
腕を真下から肩の高さくらいまで振るという単純な運動を行いました。
任意の点を自動追尾(トラッキング)を行います。
今回は同時に加速度計も使用したので、加速度計を自動追尾させました。
その点の位置情報を座標として表示。
さぁ、ここまではいいのですが、映像座標の単位って「ピクセル」ですよね…。
そこで、映像中に映っている加速度計の幅4.2cmを基準としcmで表示しました。
さらに原点は出発(開始)地点に設定。
得られた位置座標が
Excelで微分って…
なので、差分をとる方法で行いました。
映像は1/60秒での時間軸なので、誤差は大きくなりますが今回は試しなのでこのまま続行。
加速度計から得られた加速度データのX成分と、映像から得られた加速度のX成分を比較したのが下図です。
※赤線が加速度計、濃青が映像からのデータで30区間移動平均
加速度計は重力によるセンサ誤差がある?
今回はX成分のみで比較しました。
映像からのデータはただ差分をとっただけなので、バラつきが大きいことがわかります。
しかし、理論上から推測される加速度に近似するのは映像からのデータではないでしょうか。
映像からのデータはほぼ±1Gを振幅しています。
これに対し、加速度計のX成分は-1Gを極小とした振幅。
加速度のX成分の平均は計算するまでもなくマイナスとなるので、位置はどんどんマイナス方向に下がることになります。
ここで、重力の1Gを考慮しても波形は映像と異なります。
もっと単純な運動で違いができる原因を検討
今回は映像からのデータから加速度の値を求め、それがどれほど加速度計の値と相違するのかがぼんやりとわかりました。
次回はもっと単純な横だけの運動などで、さらに検討してみたいと思います。
ただ、加速度計も映像からも波形は似たものが出ているので、単位や重力の考慮など誤差がわかればいいのでは、と考えます。
映像は2次元平面ですが、加速度はX,Y,Zの3次元ですので、使い分けが必要ですね!
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