在逆向工程以單聯結的臨界值改善實體與電腦模型密合度

Using Threshold of Single Linkage to Improve the Match Index Between Computer Model and Artifact

本研究主要是調查實際物體上不同位置量測點的精度是否會隨著量測點位置而改變。統計上來說，如果點的位置與該點重複量測所形成共變異矩陣有關，若兩個區域差異很大，其中一個區域上所量的點和另一個區域所量的點它們之間所形成的共變異矩陣一定是不相同的。本研究主要目的是根據這些量測點所形成的共變異矩陣間相似及相異程度來做一個歸納，並找出一個規則，即為在重複測量某一個位置所形成的點與點之間距離要相差多少時才會被判斷為不正常。所使用的量測工具是MicroScribe G2三維數位化儀，呈現圖形的軟體是使用Rhino，分析的工具是XploRe。本研究將共變異矩陣轉換為一個1*6的向量矩陣，並且藉由主成份分析（Principal components analysis）將該向量矩陣轉換為一個可以在二維圖形觀看的點。共有30個點分佈在測試的木雕上，希望能完全表達實體的曲面特性，藉著集群分析（cluster analysis）研究30個點中點與點之間的距離相似度，即可找出那些點具有相同的共變異矩陣，藉由這些共同的點可以計算聯合共變異矩陣（pooled covariance matrix），並由該矩陣算出2個模擬點的距離。重複模擬該距離2000次即可計算樣本平均值和標準差，並以平均值加上3倍標準差的上限值作為重複量測某一個位置所形成點與點之間合理距離的實驗上限值。

This paper investigates the relationship between geometric profile and measurement precision in repeated measurements of a wooden sculpture, christened as loving each other. Statistically, if the covariance matrix formed by the repeated measurement is dependent on the profile of the artifact, then given a large difference in the profile of two domains on the artifact, the corresponding covariance matrices would be significantly different. This study finds a rule of single linkage to discriminate outliers in repeated measurements based on similarities among them.The measurement tool is MicroScribe G2; the display software is Rhino; and the analysis tool is XploRe. We convert a covariance matrix into a 1x6 vector and by using principal components analysis the vector is projected into a 2D point. Thirty points are chosen among the domains to explore different profiles of the artifact. Next cluster analysis is applied to the 30 points in the 2D graph to find points which share the common covariance matrix. This further renders a pooled covariance matrix for points within a 0.2 mm square which inscribes the most crowded points in the projected 2D principal components. Then 2000 pairs of simulated points from the pooled covariance matrix are generated, and the distance between the pair points is calculated. The sample mean and standard deviation of the distance are obtained and the upper limit, mean plus the three standard deviations, is used as an empirical single linkage threshold.