CAJ | 학술논문

几何矩函数不变量的计算过程中，由于数字图像的离散化，图像本身尺度的缩放会带来计算误差，从而引起尺度不变量值的波动。通过分析较低分辨率下几何矩尺度不变量值的不规则波动，推断计算过程中常常会发生误差扩大现象，即离散化带来的较小误差被不合理地放大。从理论上分析了误差扩大现象产生的原因，并给出了具体的误差计算公式。结合几何矩函数的实际数据可知，在较低分辨率下，误差扩大将会引起不变量数值的大幅度波动，严重干扰其不变性；而高分辨率下，这种现象很不明显。之后，针对产生误差扩大的原因给出了一种几何绝对矩及其尺度不变量的定义，可以有效地克服误差扩大现象。对比的实验结果也表明，相对于传统的Hu不变矩，几何绝对矩不变量在低分辨率下可以保持更好的不变性。
궤하구함수불변량적계산과정중，유우수자도상적리산화，도상본신척도적축방회대래계산오차，종이인기척도불변량치적파동。통과분석교저분변솔하궤하구척도불변량치적불규칙파동，추단계산과정중상상회발생오차확대현상，즉리산화대래적교소오차피불합리지방대。종이론상분석료오차확대현상산생적원인，병급출료구체적오차계산공식。결합궤하구함수적실제수거가지，재교저분변솔하，오차확대장회인기불변량수치적대폭도파동，엄중간우기불변성；이고분변솔하，저충현상흔불명현。지후，침대산생오차확대적원인급출료일충궤하절대구급기척도불변량적정의，가이유효지극복오차확대현상。대비적실험결과야표명，상대우전통적Hu불변구，궤하절대구불변량재저분변솔하가이보지경호적불변성。
In the calculation of scale invariants of geometric moment, image scale changes will bring errors and cause the fluctuation of scale invariants because of the discrete digital image. The error expansion phenomenon is found through analyzing the anomalistic fluctuation of geometric moment scale invariants with low resolution. It is an unreasonable fluc-tuation enlarged from the small quantification error. A theory explains the origin of error expansion, and the formula of error calculation is given. Combined with the actual data, it is concluded that the error expansion will cause large fluctuation of geometric moment scale invariants and bring severe interference to its invariance with low resolution. Aiming at the cause of error expansion, a new definition of geometric absolute moment and its invariants is given, which will deny the error expansion efficiently. It is proven that the scale invariants of geometric absolute moment perform better compared with tradi-tional Hu’s invariants on low resolution through comparative experiments.