形態內差法之研究

Abstract

形態內差法大致可以分為兩類，一種是分析物體外型的方法，另一種則是利用點到點之間的距離來做內差法，在這篇論文中，我們將深入探討利用距離來做形態內差的方法，並利用形態歐幾里德距離轉換來修改形態距離內差法的計算距離方式，使其在視覺上獲得更佳的效果。我們並修正形態距離內差法的演算法，使得在一些特殊的狀況下，內插法依然能夠正常的運作。最後，我們把距離內差法的二元影像演算法推廣到灰階影像演算法，其所花費的時間和二元影像演算法差不多。在應用方面，我們拿灰階影像的形態內差法來做自然影像的變形，或是臉部變形的應用。

Algorithms for morphological interpolation can be divided as shape-based morphological interpolation and distance-based morphological interpolation. Shape-based morphological interpolation would analyze object's shape by using weighted morphology or skeleton and distance-based morphological interpolation needs to calculate the distance between two points. In this thesis, our major aim is to discuss the distance-based morphological interpolation. We will modify the method of distance calculation for better visualization, the algorithm of distance-based morphological interpolation to fit some special cases. Finally, we will extend the binary distance-based morphological interpolation to grayscale distance-based morphological interpolation, and apply the proposed method to the image morphing of grayscale nature images and facial images.