We address the problem of blind piecewise space-variant image deblurring where only part of the image is sharp, assuming a shallow depth of field which imposes significant defocus blur. We propose an automatic image recovery approach which segments the sharp and blurred sub-regions, iteratively estimates a non-parametric blur kernel and restores the sharp image via a variational non-blind space variant method. We present a simple and efficient blur measure which emphasizes the blur difference of the sub-regions followed by a blur segmentation procedure based on an evolving level set function. One of the contributions of this work is the extension to the space-variant case of progressive blind deconvolution recently proposed, an iterative process consisting of non-parametric blind kernel estimation and residual blur deblurring. Apparently this progressive strategy is superior to the one step deconvolution procedure. Experimental results on real images demonstrate the effectiveness of the proposed algorithm.