Many voxel-based models for quantifying analysis of diffusion-weighted images have been proposed, which require the diffusion-weighted images across various b-value images aligned. Any motion of the patient during scan such as normal respiratory and cardiac motion leads to images misaligned. Respiratory-triggered acquisition method can alleviate the effect of motion in the cost of more acquisition time, but may fail in irregular breathing patterns and result in displacement between different b-value images. Thus motion correction is a precondition for precise parameter estimation. For the deformation, the rigid and affine transformation registration [1-2] could not describe perfectly the characteristics of motion in abdomen. Free-form deformation (FFD) [3] registration has been widely used but would lead to unwanted bias in the registration of different b-value images to b₀ image, especially high-b-value images, due to signal attenuation dependent on b values. In this study, we propose a method that utilizes a fitting accuracy to guide the step in FFD for finding the optimal transformation based on the similarity measures of mutual information [4]. The step changed at different positions depends on the fitting accuracy, which allows small displacement at high fitting accuracy and large displacement at low fitting accuracy.The object function was $$$E(T)=-E_{MI}(A,T(B))+\lambda *E_{smooth}(T)$$$ where $$$E_{MI}$$$ is mutual information similarity between reference image $$$A$$$ and the transformed image $$$T(B)$$$, $$$E_{smooth}(T)$$$ is the smoothness of the transformation and $$$λ$$$ is trade-off parameter which was set to 0.01. The gradient vector of the object function was calculated as $$$\triangledown E=\frac{\partial E(T^l)}{\partial E(T^l)}$$$ with the non-rigid transformation parameter $$$T$$$ after the $$$l$$$-th iteration. Based on the exponential weighted FFD, the transformation $$$T$$$ can be updated by $$$T^{l+1}=T^l+\mu *\omega(R^2)*\frac{\triangledown E}{|\triangledown E|}$$$ where $$$T^l$$$ is the $$$l$$$-th transformation, $$$T^{l+1}$$$ is the updated transformation, $$$μ$$$ is the step size and $$$\omega(R^2)$$$ is a weighted matrix. $$$SS_e$$$ is the sum of squares of the distances between observed data and fitting data and $$$SS_T$$$ is the average of the observed data. Fitting accuracy is expressed as the following equation in accordance with the former defined variables: $$$R^2=1-\frac{SS_e}{SS_T}$$$ . $$$R^2$$$ exponential function weighted equation is $$$\omega (R^2)=e^{-h*R^2}$$$ with the coefficient $$$h$$$ which was set to 2.0, amplifying the difference between weighted factors and the fitting accuracy which has been calculated. Data Acquisition: Free breathing diffusion datasets were acquired on a 3.0T Philips scanner using a single-shot spin-echo echo-planar imaging (EPI) sequence with TR/TE 1600/62 ms, matrix 256×256,in-plane resolution 1.46×1.46 mm² slice gap 0 mm,32 slices and b-values = 0, 10, 30, 60, 100, 150, 200, 400, 600 and 1000 s/mm².Figure.1 shows the registration results of the FFD and the proposed $$$R^2$$$-FFD. The red lines represent the edges of b₀ image. Both of methods align the different b-value images to b₀ image in the edge of liver. The mis-registration pointed by white arrows at high-b-value images (g, j) appear with FFD, while it does not happen at $$$R^2$$$-FFD. Figure.2 shows the comparison of the registration and deformation results acquired from FFD and $$$R^2$$$-FFD of b₄₀₀ and b₁₀₀₀ images. There are mis-registration (b, d) pointed by red arrows and some folding effect (f, h) in deformed mesh with the FFD, while the registration results are without mis-registration (c, e) and the deformed meshes are smooth (g, i) with the $$$R^2$$$-FFD. Figure.3 shows the comparison of the mapping before and after registration with our proposed method. After registration, fitting accuracy $$$R^2$$$ is raised that pointed by the white arrows. And the mapping D is homogeneous and its periphery is clear in liver parenchyma.FFD registration method can describe non-grid deformation but the same step in different positions would fail in finding the optimal transformation. Our proposed method introduces the fitting accuracy to guide the step for finding the accurate transformation, which allows small displacement at high fitting accuracy and large displacement at low fitting accuracy. We can obtain accuracy parameters form the IVIM model by using our proposed registration method. Further evaluation of the proposed method on more subjects is warranted in a future study.