本研究主要目的是利用影像幾何校正於條紋反射法，透過幾何校正將受扭曲之影像修正近似與實際幾何形狀相同，以降低因幾何形狀不同所造成量測上誤差。
首先以有限元素法中形狀函數之特性，建立失真影像幾何形狀之數學模型。再由校正板透過影像處理，計算出黑點面積形心之位置，接著透過虛擬反矩陣(pseudo-inverse)獲得幾何轉換因子，並利用牛頓迭代法及影像灰階填補以重建校正後影像。本文應用四種幾何形狀誤差分析，在準確度考量下二次項轉換可達到所有誤差在0.5 個像素以內。
應用於條紋反射法上，實驗結果與形貌量測儀進行驗證比對以驗證正確性。比較影像校正前後之實驗量測值，可知經影像幾何校正法後可降低量測上誤差。

The main purpose of this thesis is to apply image correction to fringe reflection method. Geometric correction could both modify distortion images closely back to the original geometric shape and reduce the measure error cause by geometric differences.
First, we establish the mathematic model of the distortion geometric shape according to the characteristics of the shape function in finite-element theory. Then the position of black spot center is calculated through the image process of correction plate. At last, we can obtain geometric transfer factor with pseudo-inverse, and reconstruct the modified image with Newton’ iteration method and gray level image in-paint. Four geometric shape error analysis are introduced in this thesis. In the consideration of accuracy, quadratic
transformation can reach the total error within 0.5 pixel.
Applying to fringe reflection method, we compare the experiment result with surface roughness measuring instrument to testify the accuracy. Contrast the experiment data of the image before and after the correction, we can realize that the image geometric correction can reduce the measurement error.

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