運用形態學及模糊推理作彩色影像內插之研究

Abstract

彩色影像內插廣泛應用在影像擷取及影像縮放等方面，在多媒體訊號處理上是一個重要課題。形態學提供簡單但功能很強的數學運算，在影像處理上是被常用的一種工具。其基本運算如擴張、侵蝕、開啟和關閉，皆能保留影像特徵，譬如形狀。另一方面, 模糊理論在機械控制及其他工業上已被廣泛使用，近來，更被運用在雜訊消除、紋理分類及邊緣偵測等影像處理上。我們將這兩種運算工具運用在彩色影像內插中, 尤其針對彩色影像放大及影像感測器的彩色內插。 首先，我們用基本形態學開啟運算內插法來作影像內插。基於我們所針對的應用，我們發展了所需的結構元件。在影像放大應用上，我們看到在大部分影像樣本中，除了在小範圍的亮點上，產生了些微的局部擴散問題之外，大致上有不錯表現。在影像感測器的彩色內插上，則產生了不正確的色彩。 其次, 我們用邊緣分類開啟運算內插法。我們使用形態學梯度運算，根據所得形態學梯度將一張影像分為陡峭及平緩兩區域。之後，在陡峭區域我們使用形態學開啟運算內插法，而在平緩區域，我們使用雙線性內插法。結果減少了在影像感測器彩色內插上所產生的不正確色彩。而在影像放大上所產生局部擴散現象，也獲得了一些改善。 之後，我們使用邊緣分類模糊內插法。同樣將影像分類後，我們在陡峭區域使用模糊內插法，結果在局部擴散和不正確色彩兩個問題上都獲得了改善。 影像處理的優劣主要取決於主觀視覺判斷，不過最後，我們仍將這幾種內插法所產生的均方差作一比較。發現，大體而言，形態學開啟運算內插法所得到的均方差最大，此乃因開啟運算所產生誤差的點數較少，但單一誤差值較大的緣故。

Color image interpolation finds application in image capture and image rescaling and as such, it is an important topic in multimedia signal processing. Mathematical morphology possesses simple but effective operators and is a well-known tool in image processing. The basic operations such as dilation, erosion, opening and closing retain the structuring features of an image such as shape. On the other hand, fuzzy logic has been popular in machine control and other industrial applications. Recently, it has also been considered for image processing such as noise removal, texture classification and edge detection. We consider their use in color image interpolation. In particular, we consider the problems of color image zoom-in and CCD/CMOS sensor color recovery. Firstly, we consider color image interpolation by simple morphological opening operation. Base on the properties of our target applications, we develop the structuring element for this purpose. For image zoom-in application, we see that the interpolation results are reasonable for most of the experimented image patterns. However, there is a little enlargement effect for small, high-intensity areas, which is undesirable. For CCD/CMOS sensor color recovery, it produces false colors. Secondly, we consider edge-classified morphological opening interpolation. We use a morphological gradient operation to classify the images into sharp and smooth areas according to the morphological gradients. After it, we use a morphological opening operator in the sharp areas and the bilinear interpolator in the smooth areas. We see that the false colors are reduced in CCD/CMOS sensor color recovery. For the enlargement effect in image zoom-in, it produces a little improvement. Finally, we consider edge-classified fuzzy interpolation, in which, after classifying the pixels in an image, we use fuzzy interpolation in sharp areas. We see that it reduces the enlargement effect and false colors. The performance of the image processing is mainly judged from human subjectivity. For reference, we list the mean square errors of the different interpolation methods. We see that the morphological opening interpolator has the most mean square errors in most patterns. That is because, opening interpolator has less error points, but the error values at the error points are larger.