Assessing the quality of polarization images is of significance for recovering reliable polarization information. Widely used quality assessment methods including peak signal-to-noise ratio and structural similarity index require reference data that is usually not available in practice. We introduce a simple and effective physics-based quality assessment method for polarization images that does not require any reference. This metric, based on the self-consistency of redundant linear polarization measurements, can thus be used to evaluate the quality of polarization images degraded by noise, misalignment, or demosaicking errors even in the absence of ground-truth. Based on this new metric, we propose a novel processing algorithm that significantly improves demosaicking of division-of-focal-plane polarization images by enabling efficient fusion between demosaicking algorithms and edge-preserving image filtering. Experimental results obtained on public databases and homemade polarization images show the effectiveness of the proposed method.