In this study we propose a multiplicative regularization scheme to deal with the problem of the detection and imaging of homogeneous dielectric objects (the so-called binary objects). By considering the binary regularizer as a multiplicative constraint for the contrast source inversion (CSI) method we are able to avoid the necessity of determining the regularization parameter before the inversion process has been started. We present some numerical results for some representative two-dimensional configurations, but we also show the three-dimensional reconstruction for a full vectorial electromagnetic problem. We conclude that the binary CSI method is able to obtain reasonable reconstruction results even when a wrong estimate of the material parameter is used. Moreover, generalization of the method allows us to handle inversion of more than one homogeneous scatterer having different material parameters.