在三維點雲中使用隨機取樣一致算法偵測二次曲面

Abstract

近幾年電腦圖學的進步，使得相關的研究發展快速，譬如辨識、三維重建、切割等相關議題都有許多的探討，其中我們針對形狀辨識有相關的研究，為了使三維物件可以簡化的表達，減少儲存空間的使用，本論文利用三維形狀與基本參數表達模型，基於我們認為僅用圓形類形狀與平面，無法完全表達所有物體，因此，我們延伸更多的形狀，使得我們可以偵測更多的形狀，我們的系統增加了橢圓柱、橢圓椎、橢球、雙曲面等，並增加了更多的參數，基於octree的資料結構，隨機取點，由本論文提供的形狀參數算法，得出形狀的參數，並透過隨機抽樣一致算法，取得最佳的形狀參數，再使用符合最佳形狀的點數，重新調整參數，以得到偵測形狀與參數。以本論文與已知文獻結果做比較，本論文可以偵測出更複雜的形狀，未來也可以增加其他模型，以增加系統偵測形狀的多樣性。

In recent years, the advance of computer vision has led to the rapid development of related research areas, such as shape recognition, 3D reconstruction, and shape segmentation. In order to simplify the presentation of a 3D model and to reduce the storage space, it is a common practice to use simple 3D shapes and their parameters to interpret real world models. As a result, 3D shape recognition has become a research topic of importance and interest in many real-world applications. Existing work in the literature deals mostly with simple circular-shapes. In order to better cope with more complex shapes in existence in the real-world, our work extends the research on shape recognition by incorporating additional shapes of quadric surfaces including elliptic cylinders, elliptic cones, ellipsoids, circular-hyperboloids of one sheet, and circular-hyperboloids of two sheets. We use RANSAC (RANdom SAmple Consensus) algorithm to randomly choose sample points and to find the parameters repeatedly and finally find the best solution based on the octrees. At the end, we also use a re-fitting method to improve the accuracy of the parameters of the shape. In comparison with existing result in the literature, our work is able to detect more complex shapes. In the future, we plan to add additional shape models, increasing the versatility of our system.