Based on the duality theory of mathematical morphology and the relation between the mathematical morphological theory and linear shift invariant system, polarizationencoding method is introduced and a scheme is proposed to realize hitmiss transform by onechannel and zerothreshold value incoherent optical correlator. With polarization encoding, the scheme combines the foreground and background of an image into an encoded image, so the hitmiss transform can be completed by an erosion operator, onechannel realization. The experimental setup is simplified greatly, more compact, and the demand for adjusting light path is reduced. Because of the zero threshold, the error for the threshold of output image resulted from the ununiformity of optical intensity distribution and the imperfect linearity of CCD optoelectronic response is avoided. The experimental result proves the convenience, accuracy and validity of the scheme.