Splines應用於影像內插法之研究

A Study of Image Interpolation Methods Based on Splines

劉鴻明(Hang-Ming Liu)

指導教授 ： 張元翔

中原大學/工學院/資訊工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500259

摘要

隨著人們對影像品質要求的提昇，在數位影像縮放處理中，普遍存在的問題就是影像縮放後的失真現象。影像縮放的應用在很多地方都需要被使用到，但傳統的內插法皆沒有太好的效果。本篇論文將使用傾斜投影(oblique projection)演算法來實作影像縮放的處理，將它和最近相鄰內插法(nearest-neighbor interpolation)、雙線性內插法(bilinear interpolation)以及雙立方內插法(bicubic interpolation)相互作比較。傾斜投影演算法的處理程序中會使用到B-spline函數來實作影像的放大與縮小，它能提供僅次於正交投影(orthogonal projection)演算法的效能。雖然正交投影為最佳的處理方法，但是因計算複雜太高在實作上有些困難。傾斜投影演算法的主要優點在於它能提供與正交投影演算法幾乎同樣的結果，實作上更容易實現且速度又快。由實驗結果證實此傾斜投影演算法是一種極精確的內插法，而最近相鄰內插法、雙線性內插法以及雙立方內插法在性能上均明顯較差。

關鍵字

B-spline函數 ； 雙線性內插法 ； 雙立方內插法 ； 影像縮放

並列摘要

With the demand of image quality as requested by people in digital image processing, the general existing question is the distortion after image scaling. Image scaling is generally applied in many places, but traditional interpolation methods do not achieve a good effect. In this thesis, we propose to use the oblique projection algorithm to implementation image scaling and compare it with other methods such as nearest-neighbor interpolation、bilinear interpolation and bicubic interpolation. The process of the oblique projection algorithm is derived using B-spline function and can provide good effect that is only inferior to the orthogonal projection algorithm. Although the orthogonal projection is an optimal processing method, it is difficult to implement due to computation complexity. The oblique projection algorithm’s main advantage is that it can achieve almost same result with the orthogonal projection algorithm, while its implementation is easier and faster. It is shown by our experiment results that the oblique projection is a very precise interpolation. Nearest-neighbor interpolation、bilinear interpolation and bicubic interpolation tend to be inferior in performance.

並列關鍵字

bicubic inte ； B-spline function ； bilinear interpolation

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