數位影像內插放大:運用輻射基底函數及邊緣適應性演算法

Abstract

影像內插是將一張低解析度的影像轉為一個高解析度影像的過程，影像內插法在數位信號處理的領域中非常重要因為它的應用相當廣泛。 在這篇論文中，介紹了三種影像內插演算法。第一種是利用快速傅利業轉換來近似輻射基底函數的係數來內插影像，假如運用傳統方法來計算輻射基底函數的係數且輸入資料的數量為 ，會花費 計算時間，但利用快速傅利業轉換的方法來近似係數只需花費 。 第二種介紹的內插演算法是一種混合的邊緣方向的內插法。這個方法是依據低解析度影像及對應的高解析度影像的變異數之間有幾何的對偶性關係。為了節省時間花費及使得內插影像的邊緣清晰，這個演算法合併了以變異數為基礎的內插演算法以及雙線性內插演算法。 抵抗錯誤銳利邊緣模型是一種變形的雙線性內插法，這種方法依據經典的內插錯誤理論來解決鋸齒及棋盤效應。

Image interpolation concerns image resolution conversion that generates a high-resolution image from its given low-resolution image and has been an important issue in the digital of digital signal processing, since its applications are widespread. In this thesis, three interpolation algorithms are introduced. The algorithm interpolates images with the coefficients of the radial basis function (RBF) network and on the other hand, the fast computation of the RBF coefficients by using fast Fourier transform (FFT) is proposed. Computing coefficients of RBF network with this algorithm only cost computation time when the number of data is . The second interpolation algorithm is a hybrid edge-directed image interpolation algorithm. This algorithm is based on the geometric duality between the covariance of given low-resolution image and the covariance of the high-resolution result image. For computation complexity and the clarity of the edge regions, this algorithm combines bilinear interpolation and covariance-based interpolation. The error-amended sharp edge (EASE) scheme is an adapted bilinear method. EASE scheme solve the jagging and checkerboard effect according to the interpolation error theorem and the Sobel derivatives are utilized in the adapted bilinear interpolation model.