摘要：數(shù)字圖像處理與分析領(lǐng)域里的一個重要研究方向是對圖像形狀特征的表達(dá)。我們可以從一幅數(shù)字圖像計算而得到的一系列矩值，這些矩值通常表達(dá)了圖像形狀的全局特征，由矩函數(shù)可以得到一系列的不變量，它在圖像發(fā)生平移，縮放，或旋轉(zhuǎn)變換后，仍然保持不變，從而可以作為目標(biāo)的特征向量被廣泛地應(yīng)用于圖像的識別中。此外，如何用數(shù)學(xué)的手段構(gòu)造更好，更實用的矩來滿足目前圖像分析的需要仍是有待解決的問題。非正交連續(xù)矩、徑向連續(xù)正交矩、直角連續(xù)正交矩以及直接離散正交矩是最具有代表性的四種矩。本文通過討論此四種矩來研究和比較各種矩的縮放不變量的構(gòu)造。

關(guān)鍵詞:矩; 不變量; 縮放

Abstract: In digital image processing and analysis domain，an important research direction is the expression method of  an image shape. We can obtain a series of moment from a digital image, which usually express the overall features of an image. Then a series of invariants can achieved from these moments. They can keep invariant under the transform of translation, scale and rotation. Hence, invariants of moments were widely applied as the global features in the image recognition. In addition, how uses mathematics method to construct a better, a more practical moment is still a pending solution question. The non-orthogonal continual moment, the radial direction continual orthogonal moment, the orthogonal continual moment and the discrete orthogonal moment is the most representative four kinds of moments. This article discusses these four kinds of moments, and we compare three kinds of scale invariants of them. 

Key words: Geometric Moment; Zernike Moments; Legendre Moments; Tchebichef Moments, Invariant of moments; scale invariants;