本稿は，体積のを視る授業内容による教授学習過程の効果を報告している。これは，面積のを視る授業（梶原，２０１７）で学習した直観の思考手続きの応用を目的とした実践である。 本授業内容は「x3」「x（x＋1）（x＋2）」「5πx2」を取り上げて，体積図を用いた次の思考手続きでの直観的理解を目指している。（１）「x3」の x の延長線上に⊿xをとる，（２）その場合，⊿y（体積の増加分）は体積図のどこになるか（⊿yの出どころ），（３）⊿xを０に近づけていくと⊿y/⊿xは最終的にどこに現れ出てくるか。このように頭の中で体積図を操作すれば，「x（x＋1）（x＋2）」「5πx2」の場合も，　瞬間の変化率（）を視ることができる。実践の結果，の公式の意味理解が欠落している現状（の事例がひとつも所有できていない現状）は，面積のを視る授業に続けて大きく改善され，事後質問でを直観できた生徒は，本授業の事例と類似性の大きい問題（（x＋1）（x＋2）（x＋3）），類似性の小さい問題（4πx3/3）双方で３０名（８１%）であった。これらの結果を含めて，本授業内容の成果と課題を本稿は報告している。

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In usual 3D measurement of shape by using stereo image, it is necesary to solve a correspondence problem which requires rather complicated image processing and high computational cost. Recently Ando developed the differential stereo vision system in which depth information can be derived from brightness values of image without solving the exact correspondence problem. However, this method has a weak point of narrow depth range in measurement. In this paper, we propose a method to solve a narrow depth range problem and to improve the accuracy of measurement for this method. Several examples of measurement are presented to demonstrate the effectiveness of the proposed method.

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This paper describes a method to solve the binocular stereo correspondance problem on an epipolar plane. In porposed method, a parametric curve is on the epipolar plane which is calcurated using world coordinates of lens centers and a image point. And a coordinate frame is set up on the epipoar plane(shn), and a transformation matrix between the world coordinate system and the coordinate frame (shn) is calcurated. Coordinates of the parametric curve is transformed from the coordinate frame (shn) to the world coordinate system. The parametric curve is projected to two cameras, and these projected lines have correspondance area on the images. Pixel values in area around these correspondance line on each images are compared to calcurate errors. And an error-function is defined the errors. Parameters of the curve are optimzed to let the error function be smaller. The laid parameteric curve is a polynominal and the polytope method is used as optimizing method. Pixel values of epipolar line on each two images are fitted each other on the images. A board shape object and a column shape object are used as experimentation. And the shape of the parametric curve is shown as a result.

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極方向に厚さが変化する扇形平板で変厚の始点が極座標の原点と一致しない, 一般の場合を本論文で扱った。板厚がrの代数関数で表わされる場合を主としてとりあげ基本方程式をたて, その解をベキ級数で求めることができた。例として厚さが直線的変化をなすような扇形平板の数値計算を行ない, 等厚のものおよび始点と原点の一致したものと, 比較することができた。

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An image measurement technique using the possibility of particle passing has been extended to obtain two-dimensional velocity field. Present paper describes the principle of the statistical analysis for the velocity field. An numerical simulation was carried out to examine the process of the present technique, and it shows that the degitalized image data may cause an error factor on the obtained velocity vector directions.

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