Diffusion-weighted MRI of the body has the potential to provide important new insights into physiological and microstructural properties. The intra-voxel incoherent motion (IVIM) model relates the observed DW-MRI signal decay to parameters that reflect perfusivity (D*) and its volume fraction (f), and diffusivity (D). However, the commonly used voxel-wise fitting of the IVIM model leads to parameter estimates with poor precision, which has hampered their practical usage. In this work, we increase the estimates' precision by introducing a model of spatial homogeneity, through which we obtain estimates of model parameters for all of the voxels at once, instead of solving for each voxel independently. Furthermore, we introduce an efficient iterative solver which utilizes a model-based bootstrap estimate of the distribution of residuals and a binary graph cut to generate optimal model parameter updates. Simulation experiments show that our approach reduces the relative root mean square error of the estimated parameters by 80% for the D* parameter and by 50% for the f and D parameters. We demonstrated the clinical impact of our model in distinguishing between enhancing and nonenhancing ileum segments in 24 Crohn's disease patients. Our model detected the enhanced segments with 91%/92% sensitivity/specificity which is better than the 81%/85% obtained by the voxel-independent approach.