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Target detectors using polarimetry are often focused on single targets, since these can be characterized in a simpler and deterministic way. The algorithm proposed in this paper is aimed at the more difficult problem of partial-target detection (i.e., targets with arbitrary degree of polarization). The authors have already proposed a single-target detector employing filters based on a geometrical perturbation. In order to enhance the algorithm to the detection of partial targets, a new vector formalism is introduced. The latter is similar to the one exploited for single targets but suitable for complete characterization of partial targets. A new feature vector is generated starting from the covariance matrix and exploited for the perturbation method. Validation against L-band fully polarimetric airborne E-SAR and ALOS PALSAR data and X-band dual-polarimetric TerraSAR-X data is provided with significant agreement with the expected results. Additionally, a comparison with the supervised Wishart classifier is presented revealing improvements.