应用数学与计算数学学报
應用數學與計算數學學報
응용수학여계산수학학보
COMMUNICATION ON APPLIED MATHEMATICS AND COMPUTATION
2012年
4期
465-471
,共7页
图像分割%测地线活动轮廓模型%非线性共轭梯度
圖像分割%測地線活動輪廓模型%非線性共軛梯度
도상분할%측지선활동륜곽모형%비선성공액제도
image segmentation%geodesic active contour (GAC) model%nonlinear conjugate gradient (CG) method
从最优化理论的角度来看, 目前求解图像分割的测地线活动轮廓（geodesic active contour, GAC）模型大多采用固定步长的最速下降算法. 而众所周知, 该算法收敛速度较慢, 这在能量泛函的梯度较小时尤为明显. 对求解GAC模型的快速算法进行了研究. 首先, 回顾了GAC模型的演化方程; 随后, 将共轭梯度（conjugate gradient, CG）算法引入到GAC模型的求解中, 形成一种新的求解图像分割问题的数值方法, 即GAC模型的CG算法; 最后, 通过试验对比传统的数值方法, 表明CG算法具有良好的收敛性.
從最優化理論的角度來看, 目前求解圖像分割的測地線活動輪廓（geodesic active contour, GAC）模型大多採用固定步長的最速下降算法. 而衆所週知, 該算法收斂速度較慢, 這在能量汎函的梯度較小時尤為明顯. 對求解GAC模型的快速算法進行瞭研究. 首先, 迴顧瞭GAC模型的縯化方程; 隨後, 將共軛梯度（conjugate gradient, CG）算法引入到GAC模型的求解中, 形成一種新的求解圖像分割問題的數值方法, 即GAC模型的CG算法; 最後, 通過試驗對比傳統的數值方法, 錶明CG算法具有良好的收斂性.
종최우화이론적각도래간, 목전구해도상분할적측지선활동륜곽（geodesic active contour, GAC）모형대다채용고정보장적최속하강산법. 이음소주지, 해산법수렴속도교만, 저재능량범함적제도교소시우위명현. 대구해GAC모형적쾌속산법진행료연구. 수선, 회고료GAC모형적연화방정; 수후, 장공액제도（conjugate gradient, CG）산법인입도GAC모형적구해중, 형성일충신적구해도상분할문제적수치방법, 즉GAC모형적CG산법; 최후, 통과시험대비전통적수치방법, 표명CG산법구유량호적수렴성.
From the viewpoint of optimization, most methods to deal with the image segmentation problem based on the geodesic active contour (GAC) model adopt the steepest descent algorithm with constant step-size. It is well known that the steepest descent algorithm converges relatively slowly, especially when the gradient of the energy functional is small. The fast algorithm to solve the GAC model is studied. First, after recalling the GAC model and corresponding evolution equations, a discrete form of the evolution equations is proposed. Then, by introducing the conjugate gradient (CG) method to the model, a novel fast algorithm is proposed. Finally, several numerical experiments are conducted to compare with the traditional numerical method, which validates that the proposed CG algorithm has a better performance.
