高維空間中使用多棵K-D Trees搜尋最近鄰居

Nearest Neighbor Searching in High Dimensions Using Multiple K-D Trees

石兆宇(Chao-Yu Shih)

指導教授 ： 顏淑惠

淡江大學/工學院/資訊工程學系碩士班/碩士(2009年)

https://doi.org/10.6846/TKU.2009.00128

摘要

特徵比對在許多影像處理的應用中扮演著一個重要的角色，例如全景影像的產生、影像縫合、物件追蹤…等等。所謂的特徵比對即是在兩張不同的影像中找出最相似的特徵點組合，也就相當於找特徵點的最近鄰居。

在本篇論文提出了一個尋找最近鄰居的方法，利用將資料投射到不同的平面進行粗分類，同時建構數棵互補的K-D Tree進行最近鄰居的搜尋，且使用Best Bin First(BBF)的回溯機制平均的在各棵K-D Tree上搜尋以降低搜尋時間並提升正確率。文中以演算法分析時間複雜度，最後再以實驗證明我們的分析和執行的效能。

關鍵字

特徵比對 ； 最近鄰居搜尋 ； K-D樹 ； 回溯

並列摘要

Feature matching plays an important role in many image processing applications. To match a feature point in the query image is to find a correspondent feature point (i.e., the nearest neighbor) extracted from the target image. Edges, corners and DoG (difference of Gaussian) are most common adopted features in recent year. How to represent features is also very important in which SIFT (Scale Invariant Feature Transform) is one of the state-of-art. SIFT, proposed by Lowe [1], usually results feature vectors with high dimension such as 128. Thus how to efficiently find the nearest neighbor of a query feature point in the target image becomes essential. Kd- tree is often used to find the nearest neighbor in dimension higher than two. However, kd- tree needs many backtrackings to find the nearest neighbor when dimension gets higher. In this paper, we propose a multiple kd-trees method to efficiently search the nearest neighbor for high dimension feature points. First, we project feature points to three hyper-planes which have greatest variances. Second, for points projected on each splitting hyper-plane, two kd-trees are built that one is the conventional kd-tree and the other has first split on the hyper-plane with second largest variance. So total of six kd-trees are built. By this way, these kd-trees are searched for the nearest neighbor through different hyper-planes to compensate the deficiency of projection. The experiment showed that our method, under the same number of backtracks, indeed improves the accuracy rate of searching the nearest neighbor.

並列關鍵字

Feature matching ； Nearest neighbor search (NNS) ； K-D tree ； Backtrack

參考文獻

2. F. Isgrό and M. Pilu, “A Fast and Robust Image Registration Method Based on An Early Consensus Paradigm”, Pattern Recognition Letters vol. 25, pp. 943–954, 2004.

4. D. G. Lowe, “Distinctive Image Features from Scale-Invariant Keypoints”, Int’l J. Computer Vision, vol. 2, pp. 91-110, 2004.

5. H. J. Wolfson and I. Rigoutsos, “Geometric Hashing: An Overview”, IEEE Computational Science and Engineering, vol. 4, pp. 10–21, 1997.

6. A. Califano and R. Mohan, “Multidimensional Index for Recognizing Visual Shapes”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, pp. 373–392, 1994.

7. J. Bentley, “Multidimensional Binary Search Trees Used for Associative Searching”, Communications of the ACM, vol. 18, pp. 509–517, 1975.