Dynamic Partial Function（DPF）根據人類認知心理學（cognitive psychology），模擬人類比對的程序，貢獻了有效模擬人類感知的距離函數。當我們要比較兩張圖，使用DPF做比對時，由於DPF逼近人類的比對程序，因此相較於傳統的距離函數（如 Lp），它更能接近人類的感知。然而， 由於DPF是non-metric，不符合三角形不等式，而絕大部分的索引結構都要求距離函數必須metric，並且符合三角形不等式，所以這些索引結構無法運用在DPF上; 也因此，群聚技術（clustering technique）似乎是唯一的選擇; DPF能利用群聚技術，在Query-by-Example（QBE）的架構上，快速地搜尋 “可能的” k個相似的物件 （這意味著答案中可能存在一個圖片A，而A與被搜尋圖片Q的距離比另一個未在答案中的圖片B來的遠）。在這篇論文中，我們介紹一個新的技術，Closer，用來索引物件，並支援DPF搜尋 “精確的” k個物相似的圖片。當我們讀進索引結構時，我們利用一個metric的範圍函數（range function），緊密地評估出DPF的上下限，並且刪除掉不可能的答案，只留下少數可能的候選圖片，再進一步做答案驗證。我們展現出Closer能夠 “精確” 、快速地搜尋到k個相似的物件（在答案中不存在上述的圖片A），並且探討它能夠應用在relevance feedback架構上的可能性.

The essential contribution of Dynamic Partial Function (DPF) is to effectively quantify the perceptual similarity between images. This method closely models human cognitive activities when scrutinizing two images. However, due to DPF being non-metric and its violation of triangular inequality, most conventional index schemes that require metric-space properties fail to index images based on DPF. As a result, clustering techniques seem to be the only options for efficient, yet approximate retrievals of k nearest neighbors (kNN) to the query image in the Query-by-Example (QBE) paradigm. In this thesis, we introduce a novel technique, Closer, for the exact indexing of DPF. The idea utilizes a metric range function to tightly bound DPF along the traversal of index tree. Unpromising tree branches with their descendants can be efficiently disregarded from further consideration. Only a few surviving candidates are verified with DPF to finalize the kNN query. We show our scheme is correct, and demonstrate Closer can accurately search for true kNN with short delay, even in relevance feedback applications.

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