電腦硬體的發展日新月異，電腦在運算的能力有長足的提升，遠遠超過一般人腦的計算能力，隨著電腦的普及率大幅提高，電腦由以往為專業領域的工具轉變為家庭不可或缺的商品，一般大眾也成為電腦的使用者，與電腦溝通的技術（即人機介面）逐漸重要。在多樣人機介面當中，自然的人機介面尤為重要，在手持式計算裝置及平版電腦上的手寫或手勢是人機介面中較自然的方式，因此本論文將對手寫軌跡以及手勢辨識進行研究。由於此類的人機介面自由度較高，我們利用傅立葉描述元(Fourier descriptor)以及shape context，皆為平移、旋轉、縮放等rigid transformation下維持不變的方法。在手繪圖形，我們收集114位使用者的手繪資料，繪圖的過程中，依使用者直觀的方式，繪圖於電腦的觸控板，而這些使用者幾乎為首次使用觸控筆。當我們利用傅立葉描述元時，可達到67%辨識率；而使用shape context時，有90%的準確率。另外，我們將此技術應用於手勢辨識，收集348張手勢的照片，同樣使用傅立葉描述元以及shape context，其辨識率各為62%以及70%。 由於我們可以利用以上二方法定義出距離，即可使用K-Nearest Neighbor(KNN)為分類的方法。分別透過傅立葉描述元以及shape context所定義的距離，在辨識3D幾何物件約可達75%與95%，而在手勢辨識約有78%以及82%的辨識率。 / The cost of computing devices has dropped significantly in recent years, enabling diversified applications that require natural man-machine interaction such as pen-based computing and gesture-based communication. Whereas the automatic recognition of handwriting has been studied quite extensively, research on hand-drawn geometric shapes has received relatively little attention. In this thesis, we investigate an effective method to recognize hand-drawn geometric shapes and hand gesture. Due to the high degree of freedom of natural human-computer interface, we apply two methods, namely, Fourier descriptor (FD) and shape context (SC) to aid shape recognition. For hand-drawn shapes, we collect 114 users' free-hand drawings using Tablet PC. In this study, we achieve an accuracy of 67% by FD and 90% by SC. For gesture-based interface, we gather 348 pictures of hand gestures and obtain a classification rate of 62% by FD and 70% by SC. Since FD and SC are distance measures, we can use K-Nearest Neighbor (KNN) classifier to improve the recognition rate. The incorporation of KNN classifier has increased the precision to 75% and 95%, where distance is measured by FD and SC respectively. For hand gestures, the improved accuracy is 78% by FD and 82% by SC.