離散小波轉換在PCB邊緣影像檢測上之應用

Abstract

本論文的目標是要發展一套適用於PCB的影像邊緣自動檢測技術。此技術是以小波轉換為基礎，利用向量空間(vector space)的觀念將影像中物件的輪廓（影像邊緣），擷取出來。有別於以差分(difference)找影像邊緣的傳統方法，此種影像邊緣檢測方法為一嶄新的觀念。此外，此新方法能提供優良的影像邊緣品質，與提升成功率。 由於訊號處理，或說影像處理，的工作中的第一步便是做某種基底轉換。且小波轉換為有別於傅力業轉換(Fourier Transform)的另類基底。因此，本論文以離散小波轉換(Discrete Wavelet Transform,DWT)為信號轉換的工具。經過離散小波轉換之後，可得到各頻帶(frequency band)的小波轉換係數，因此可經由適當地調整這些頻帶係數，得到理想的PCB邊緣影像。 調整頻帶係數是本論文另一個重要課題。首先取得一張標準的PCB邊緣影像（由設計檔，或用人工影像處理法）。然後利用小波轉換將PCB數位灰階影像中物件的影像邊緣擷取出來，並得到一張PCB邊緣影像。然後再求得兩張邊緣影像間的誤差。以這個誤差為指標，並搭配最佳化演算法(optimization algorithms)調整此誤差。若誤差過大，則繼續調整各頻帶係數的權重值(weighting)，直到誤差小到可以接受的範圍之內為止。

To develop an appropriate algorithm for PCB (Printed Circuit Board) image edge detection is the main subject of this thesis. The algorithm proposed in this thesis can be applied only on digital gray-level images of PCBs. Instead of the conventional idea of difference, DWT (Discrete Wavelet Transform), an alternative and novel method for basis change despite Fourier Transform, is employed. In this thesis, digital gray-level images of PCB are considered as vectors existing in the vector space constructed by selected basis that are the dilations and translations of Harr function and box function. By using DWT, image-edge-related information in digital gray-level images can be extracted easily. Not only DWT but also optimization algorithms are involved. Two well-known optimization algorithms, gradient method and one-dimensional Newton's method, are adopted for tuning the result into the best condition. The purpose of adopting two-stage optimization algorithm, gradient method and one-dimensional Newton's method, is to diminish the elapsing time in etermining the weighting vectors by searching the maximum step-size in the determined descent direction. Step-size and descent direction are determined by one-dimensional Newton's method and gradient method, respectively. When the weighting vectors are obtained, the two-stage optimization can be abandoned. Only are the weighting vectors and DWT used for PCB image edge detection in the rest of PCBs.