《确定性扰动pv插值算法及其性能分析》由会员分享，可在线阅读，更多相关《确定性扰动pv插值算法及其性能分析（6页珍藏版）》请在金锄头文库上搜索。
1、Vol.31, No.4ACTA AUTOMATICA SINICAJuly, 2005Deterministic Perturbation Partial Volume Interpolation: Algorithm and Analysis1)FENG LinYAN LiangSUN TaoHUANG De-GenTENG Hong-Fei(Institute of Mechanical Engineering, Dalian University of Technology, Dalian116024) (E-mail: )AbstractThis paper discusses th
2、e performance of some existing interpolation algorithms, and presents a deterministic perturbation partial volume interpolation algorithm. This algorithm dis- tributes the contribution of intensity of the transformed point to nine entries in the joint histogram, imports and determines the perturbati
3、on to calculate the weights. Then it is analyzed and compared with other algorithms. The results of experiments indicate that this algorithm can avoid the localextremes on grid points and non-grid points, and effectively smooth the object function.Key wordsInterpolation, partial volume interpolation
4、, perturbation, deterministic perturbation, image registration, mutual information1Introduction Essentially, image registration based on mutual information is a problem of multi-parameter optimization1. Therefore, the target function is usually unsmooth. This cumbers registration badly. Local extrem
5、es are always ascribed to two facts2. One is that there may be misregistrations between images; the other is that voxels would not coincide completely with the sample grid and interpolation is needed. Then local extremes appear easily during interpolating. Therefore, a good interpolation algorithm i
6、s as important as a good optimization to the result of registration. There are common interpolation methods3such as nearest neighbor (NN) interpolation, linear interpolation and partial volume (PV) interpolation. Pluim4analyzed the reason of local extremes in the linear and PV interpolations. Likar5
7、presented random re-sampling, and Jeffrey Tsao6presented NN with JIT. Liu7presented a method of average. It considers the inter-complement between the linearand PV interpolations, but it is usually difficult to assure that the average of the two mutual information values could keep smooth. Consideri
8、ng the characteristics of PV interpolation and perturbation, we present a deterministic perturbation partial volume interpolation algorithm (DPPV).2Partial volume interpolation and perturbation 2.1Partial volume interpolation For a point P0(i,j) in a floating image F, transfer it to P = T(P0); let t
9、he neighbor grid points be O,A,B,C (as Fig.2). When apply PV interpolation to P, the contribution of intensity of P0in F will be distributed to its four neighbors (in a 2D situation), using weights shown in Fig.1.Fig. 1 PV InterpolationFig. 2 Coordinates for DPPV1) Supported by National Natural Scie
10、nce foundation of P.R. China (50275019) and the Research Fund for the Dectoral Program of Ministry of Education (20010441005) Received October 21, 2003; in revised form January 3, 2005No.4FENG Lin et al.: Deterministic Perturbation Partial Volume Interpolation: Algorithm 5852.2Perturbation algorithm
11、s Perturbation algorithms include: 1) Random resampling Each grid point (i,j) is slightly transformed into (i + i,j + j) by randomly selecting two real transformations i and j in the interval 1/2,1/2 using a uniform probability distribution. The grey value of each transformed point is determined by
12、the bilinear interpolation form the four neighboring points. In this way, a new image Fis obtained. 2) Nearest neighbor with JIT For every voxel to be interpolated, its coordinates are jittered by adding a normally distributedrandom offset (mean=0, standard deviation=0.5). The intensity at the jitte
13、red coordinates is interpo- lated by NN interpolation. 3) Random perturbationPerturb each transformed grid point in the transformed floating image instead of creating a new image, using the same distribution as random resampling.3Deterministic perturbation partial volume interpolation For a transfor
14、med grid point (x,y), let the nearest grid point acquired using nearest neighbor (NN) interpolation be the origin O(0,0), and the point P(x,y). Then we form the coordinates shown in Fig.2. Obviously, x,y (1/2,1/2. The coordinates could be divided into 4 quadrants, and we willonly describe the algori
15、thm in detail when P in the first quadrant. In order to avoid the coincidence of lots of grid points, we apply a perturbation to point P with x and y in 1/2,1/2, using a uniform probability distribution. Then use partial volume (PV) interpolation to update the joint histogram for each voxel pair com
16、posed of a perturbed point and the corresponding point of P. Considering the fact that perturbed points could appear in four quadrantsand P could affect the histogram entries of nine grid points, we distribute the contribution of the image intensity f(P) of the sample of P to the histogram over the intensity of all 9 neighbor grid points in a 2D situation or 27 neighbor grid points in a 3D situation. We present a deterministic perturbationappr
