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Discontinuities in polarimetric SAR backscattered intensity (edges and point targets) can be characterized by a mathematical model. This paper presents a technique based on the Lipschitz regularity of an underlying singular function for detecting and interpreting such discontinuities. Numerical estimators of the Lipschitz parameters (exponent, swing and smoothing kernel variance) are implemented by a multi-voice wavelet frame transform. Local (one point in space) supervised estimates of the parameters and their dependence on polarization state are obtained by extracting the trajectory of the wavelet modulus maxima in the space scale-polarization domain and by a non-linear regression with respect to a theoretical trend with scale. Global image wide approximations of the Lipschitz parameters are also proposed, these aiming at a spatial description of the discontinuity's type, sharpness, and dependence on the polarization state. Examples are reported concerning experiments using simulated and real SAR polarimetric data.