四項次遞迴平行計算Zernike矩

Parallel Computing Zernike Moments Using Four-Term Recurrence

鄧安文(An-Wen Deng) ； 郭枝盈(Chih-Ying Gwo)

《健行學報》 36卷3期 (2016/07) Pp. 1-24

摘要

Zernike 矩是由正交性的Zernike 多項式運算產生，矩與矩之間不會有訊息的重疊，同時Zernike 矩也有旋轉不變的特性，使得Zernike 矩被廣泛應用於圖形識別與影像分析等研究領域。然而運算Zernike 矩是極為複雜的程序，尤其計算高階矩時更為耗時，導致高階Zernike 矩的使用受到一定程度的限制。本論文探討高階Zernike 矩的平行計算，提出兩種平行化的演算法是基於Zernike Radial 多項式上的四項次遞迴式與結合平行化的技術。這兩種以執行緒為基礎(thread-level)的平行演算法，其一為，平行化使用同步化的技術，適用於階數高於350 的Zernike矩。另一則為，平行化是透過Reduction 法，適用於階數介於10 至350 的Zernike矩。根據實驗結果，在配以intel i7 四核心CPU 的電腦，大小為512x512 的灰階圖，執行計算所有階數小於等於500 的Zernike 矩，僅需時1.595 秒。這樣的速度是q-recursive 法的51.88 倍。本論文以眾所周知的10 張灰階影像為測試，實驗數據證實本方法計算高階Zernike 矩時，在執行速度以及精確度具有優於其他方法的實現。

關鍵字

Zernike矩 ； Zernike Radial多項式 ； 平行化 ； 四項次遞迴式 ； q-recursive法

並列摘要

Zernike Moments are broadly applied in the field of pattern recognition and image analysis due to their orthogonality and rotation invariance property. However, the computation of these moments is extremely time-consuming especially at high orders. The main purpose of this study is to propose two parallel algorithms for computing high-order Zernike moments. Two kinds of thread-level parallelization are discussed based on a four-term recurrence among Zernike radial polynomials. The parallelization by synchronization is applicable to greater than 350 order Zernike moments calculation. The other parallelization through the reduction method is suitable for computing Zernike moments order between 10 and 350. The experimental results showed that the proposed method only took 1.595 seconds to compute all Zernike moments up to order 500 of a 512x512 pixels image with an Intel i7 quad-core CPU. This is 51.88 times faster than the q-recursive method. In the experiment, ten well known testing images are used to evaluate the speed and accuracy of the proposed method.

並列關鍵字

Zernike Moments ； Zernike Radial Polynomials ； Parallelization ； Four-Term Recurrence ； q-recursive method