潘梅森, 江建軍, 周慧燦, 聶方彥

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尋優(yōu)方法在醫(yī)學(xué)圖像配準中性能比較研究

潘梅森1, 江建軍2, 周慧燦1, 聶方彥1

(1. 湖南文理學(xué)院 計算機科學(xué)與技術(shù)學(xué)院, 湖南 常德, 415000; 2. 湖南文理學(xué)院 圖書館, 湖南 常德, 415000)

醫(yī)學(xué)圖像配準是以相似性測度為目標函數(shù), 通過多參數(shù)優(yōu)化方法尋找最佳變換參數(shù)的過程. 本文以MI為相似性測度, 通過分別使用Powell算法和PSO法等方法尋優(yōu)得到最佳變換參數(shù), 并對它們的性能進行了比較. 實驗結(jié)果表明, Powell法適合于單、多模態(tài)配準; 雖然PSO法能成功配準, 但是尋優(yōu)效率有待提高, 有必要在精度和時間效率之間進行適當(dāng)折中.

醫(yī)學(xué)圖像配準; 互信息; 尋優(yōu)方法; 變換參數(shù)

醫(yī)學(xué)圖像配準是指對不同時間、不同場景、不同模態(tài)的多幅圖像進行空間幾何變換, 使得代表相同結(jié)構(gòu)的像素(體素)能夠達到空間上的一致[1-7]. 在過去的幾十年里, 醫(yī)學(xué)圖像配準技術(shù)取得了快速的發(fā)展, 學(xué)者們提出了很多實用有效的方法, 其中基于互信息量(Mutual Information,M)技術(shù)是目前在醫(yī)學(xué)圖像配準中廣泛使用的有效方法[8-11]. 它采用互信息量作為相似性測度, 是一種自動的、不需要對圖像作任何預(yù)處理而直接進行配準的方法. Paul 等人[12]通過使兩幅醫(yī)學(xué)圖像互信息量最大技術(shù)來獲取配準的平移和旋轉(zhuǎn)參數(shù), 由于互信息量函數(shù)包含了許多局部極值點, 使得獲取的旋轉(zhuǎn)角度并不是全局最優(yōu)值. Fei[13]、Slomka[14]和Radau[15]等人在采用互信息量作為相似性測度基礎(chǔ)上, 通過使用Powell法、單純形法等多參數(shù)尋優(yōu)方法來獲取平移和旋轉(zhuǎn)參數(shù)[16-17].

1 醫(yī)學(xué)圖像配準

1.1 醫(yī)學(xué)圖像配準過程

一般說來, 醫(yī)學(xué)圖像配準過程由4部分組成: 特征空間選擇、空間幾何變換、相似性測度、變換參數(shù)優(yōu)化, 如圖1所示, 其中, 變換參數(shù)優(yōu)化是這4個組成部分中非常關(guān)鍵的一環(huán).

圖1 醫(yī)學(xué)圖像配準過程

假設(shè)參考圖像和浮動圖像分辨率均為′像素,級灰度, 左上角像素點位置為(1, 1), 在點(,)的灰度值分別為(,)和(,),為將浮動圖像映射到參考圖像物理空間的幾何變換. 醫(yī)學(xué)圖像配準就是找到這樣一個空間幾何變換, 使得圖像和之間的相似性測度最大化的過程, 即:

其中是圖像相似性測度. 如果互信息作為圖像相似性測度, 則配準可以表示為:

式中()和()分別為參考圖像和浮動圖像的熵,(,)是圖像和的聯(lián)合熵, 其定義為:

在二維空間, 醫(yī)學(xué)圖像剛體變換實質(zhì)上包括了平移和旋轉(zhuǎn)變換, 即:

1.2 多參數(shù)優(yōu)化方法

1.2.1 Powell法

1.2.2 粒子群優(yōu)化算法

Kennedy和Eberhart提出的粒子群優(yōu)化(Particle Swarm Optimization, PSO)算法, 是一種新的群智能優(yōu)化技術(shù)[22-24]. 它模仿鳥類的覓食行為, 將問題的搜索空間類比于鳥類的飛行空間, 將每只鳥抽象為一個無質(zhì)量無體積的粒子, 用以表征問題的一個候選解, 優(yōu)化所需要尋找的最優(yōu)解則等同于要尋找的食物. PSO算法通過群體中粒子間的合作與競爭而產(chǎn)生的群體智能指導(dǎo)優(yōu)化搜索, 算法通用性較強, 具有全局尋優(yōu)的特點. 但PSO算法也存在局部搜索能力較差、搜索精度不夠高、不能保證搜索到全局最優(yōu)解、容易陷入局部極小解等缺點.

2 傾斜校正方法在互信息醫(yī)學(xué)圖像配準中的應(yīng)用

2.1 單模態(tài)醫(yī)學(xué)圖像配準

圖2 CT圖像

圖3 MR圖像

表1 單模態(tài)配準時浮動圖像實際變換參數(shù)

圖5 PSO

表2 單模態(tài)圖像配準性能比較

從表2可以看到, 在單模態(tài)配準時, 從配準精度來看, Powell法能成功配準4幅圖像, 精度較高, 但是我們發(fā)現(xiàn), 在配準CT1圖像時, 得到的平移參數(shù)誤差稍大; 整體上講, PSO法配準比Powell法精度高, 在配準CT1、CT2和MR2等3幅圖像時, 得到的平移參數(shù)和旋轉(zhuǎn)角接近實際變換參數(shù), 誤差小, 配準成功, 在MR1配準時, 雖然能成功配準, 但是旋轉(zhuǎn)角誤差略大. 至于配準耗費的時間, Powell法在配準4幅圖像所耗費時間較短, 尤其是在配準MR2圖像時速度最快; PSO法在配準時所耗費時間較長, 相對而言, 在配準CT2和MR1圖像時所耗費時間較短, 在配準CT1和MR2圖像時所耗費時間較長. 綜上所述, Powell法和PSO法均適合單模態(tài)配準; PSO法精度較高, 但是效率有待提高, 因此, 如果能在精度和時間效率之間進行適當(dāng)折中, PSO法應(yīng)該是一種較好的尋優(yōu)方法.

2.2 多模態(tài)醫(yī)學(xué)圖像配準

在本節(jié)實驗中, 我們選取patient_007頭部CT第4層圖像和MR_T1_rectified第4層圖像作為原始圖像, 經(jīng)過剛體變換后得到實驗圖像, 分辨率均為256×256像素, 灰度為256級. 實驗圖像分成2組: 第1組選擇CT1作為參考圖像, MR1作為浮動圖像, 如圖6所示; 第2組選擇MR2作為參考圖像, CT2作為浮動圖像, 如圖7所示. 每幅浮動圖像相對于參考圖像的實際變換參數(shù)如表3所示.

表3 多模態(tài)配準時浮動圖像實際變換參數(shù)

圖6 第1組

圖7 第2組

圖8 第1組配準結(jié)果

圖9 第2組配準結(jié)果

從表4可以看到, 在多模態(tài)配準時, 從配準精度來看, Powell法均能成功配準, 得到正確的平移參數(shù)和旋轉(zhuǎn)角度, 而且精度較高; PSO法在配準第1組圖像時, 得到的方向平移參數(shù)和實際變換參數(shù)相同, 但是方向平移參數(shù)誤差偏大, 配準基本成功, PSO在配準第2組圖像時, 得到的平移參數(shù)誤差較小, 但旋轉(zhuǎn)角誤差相對較大, 但是仍然能成功配準. 至于配準耗費的時間, Powell法相對較短, PSO法較長, 尋優(yōu)效率有待提高. 因此, Powell法適合多模態(tài)配準, PSO法需要在精度和時間效率之間進行折中.

表4 多模態(tài)圖像配準性能比較

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A performance comparison study of optimization methods for registration of medical images

PAN Mei-sen1, JIANG Jian-jun2, ZHOU Hui-can1, NIE Fang-yan1

(1. College of Computer Science and Technology, Hunan University of Arts and Science, Changde 415000, China; 2. Library of Hunan University of Arts and Science, Changde 415000, China)

Medical image registration, in essence, is the process that the similarity metric is referred to as the objective function, and the multi-parameter optimization method as the tool for obtaining the optimal transform parameters. In this paper, by use of the mutual information as the similarity metric, two optimization methods including the Powell method and the particle swarm optimization method (PSO) are exerted to explore the optimal transform parameters respectively, and their optimizing performances are evaluated and compared. The experimental results reveal that the Powell and PSO methods can cater to both the mono-modality and the multi-modality medical image registrations. Unfortunately, however, the running time of PSO is relatively longer and needs to be substantially reduced. So in order to improve the optimization efficiency, it is very necessary for PSO to counterbalance the registration accuracy and the running time.

medical image registration; mutual information; optimization method; transform parameters

10.3969/j.issn.1672-6146.2011.03.013

TP 391

1672-6146(2011)03-0044-06

2011-09-09

湖南省教育廳優(yōu)秀青年基金項目(No. 09B071).

潘梅森(1972-), 男, 教授, 博士, 研究方向為醫(yī)學(xué)圖像處理技術(shù). E-Mail: pmsjjj@126.com

(責(zé)任編校: 劉剛毅)