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Vander Lugt相關器已被廣泛使用在圖形辨識的應用上。但是其所能辨識
的圖形則必需和當初製作匹配濾波器時所用的圖形大小相等，否則便無法
達成辨識的目的。為此Casasent發表一序列利用Mellin Transform改進相
關器大小不變性的論文。原理為先將輸入的圖形經由Mellin Transform變
成和原圖形大小無關的圖形後，再輸入相關器做比較，如此即可得到一和
輸入圖形大小無關的相關器。但是Casasent在他的論文中，所使用的輸入
圖形都是具有中空和對稱的圖形，因此在運算過程中，巧妙的規避了
Mellin Transform所具有的基本限制。在我們的實驗中，由於所使用的圖
形為中文字，因此造成辨識上的困難。經由深入的討論後，我們可發現其
困難的來源乃是由於Mellin Trans- form的基本性質所造成的。原因為
Mellin Transform可分解為兩個步驟來完成。第一個步驟為對數轉換，而
第二個步驟為傅立葉轉換。在上述的兩個步驟中，要是使大小不同的兩個
圖形相等，只有在對數轉換這個步驟才有可能完成。但是要完成此一轉換
，則必需小心的將不同大小的圖形移至不同的位置，才有可能完成
Mellin Transform。而此一特性則給于 Mellin Transform一個基本的限
制。我們提出一個和Casasent不同的架構去應用Mellin Transform，以改
進相關器的大小不變性。雖然此一架構無法移除Mellin Transform的基本
限制，但是辨識率卻比Casasent的架構更成功。
The Vander Lugt correlator has been widely used to perform
pattern recognition. However , if the input pattern is
different in size from the pattern stored in memory then the
recognition is almost impossible . Casasent has published a
series of articles in which he claimed size-invariant pattern
recognition can be achieved by using Mellin transform to
preprocess both the input and the stored patterns. The Vander
Lugt correlator is then applied to the preprocessed patterns.
This thesis investi- gates his claim by using more complicated
patterns such as Chi- nese characters. The results were totally
unsuccessful. Upon further analysis, it has been found that the
limitation of Mellin transform is inherent in nature, which is
detailed as follows. The Mellin transform is composed of two
steps. The first step is log transform of the original object,
while the second step is the Fourier transform of the log-
transformed object. In these two steps, the only step possible
making different-size objects identical is the log-
transformation. In order to achieve this identical
transformation, one must be careful in placing the different
size objects with respect to each other in the coordinate
space. Thus, this operation imposes the limitation on the
cases that the Mellin transform can help in achieving scale-
invariant pattern recognition. We then propose an alternate
scheme by centering the objects then applying the Vander Lugt
Correlator directly on the log-trans- formed pattern. Although
we were unable to remove the fundamental limitation imposed by
the Mellin transform, we have found that the result is more
successful than the Casasent's scheme.
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