本研究基於TILT演算法模型，提出一套可高度自訂的幾何變換流程，作為TILT 操作中的影像轉換模組。傳統流程中常使用MATLAB內建的imtransform函數進行仿射 與投影轉換，但其參數形式固定，難以處理較為複雜或非線性的幾何變形。為此，我 們設計了新的影像轉換函數gsubtau，以一組參數向量τ 描述可調變換模型。該模型可 支援單應性矩陣、相機校準的旋轉與平移（RT），以及額外的曲線扭曲項，提供更高的 靈活度與應用擴展性。此外，我們重新設計了Jacobian計算方法，採用數值差分方式 估算參數偏導數，以因應τ結構可變的特性。初步實驗結果顯示，此方法可維持TILT 操作的收斂特性與變換方向，並支援多樣的變形組合。;This research presents a highly customizable geometric transformation workflow based on the TILT algorithm, serving as the image transformation module within the TILT opera tion. Traditional workflows often utilize MATLAB’s built-in imtransform function for affine and projective transformations; however, its fixed parameter format hinders handling complex or nonlinear geometric deformations. To address this, we designed a new image transformation function, gsubtau, described by a parameter vector τ. This model supports homography ma trices, camera calibration rotation and translation (RT), and additional curve distortion terms, offering greater flexibility and application scalability. Furthermore, we redesigned the Jacobian calculation method, employing numerical differentiation to estimate parameter partial deriva tives to accommodate the variable structure of τ. Preliminary experimental results indicate that this method maintains the convergence characteristics and transformation direction of the TILT operation while supporting diverse deformation combinations.
