Image subtraction is a method by which one image is matched against another by using a convolution kernel, so that they can be differenced to detect and measure variable objects. It has been demonstrated that constant optimal-kernel solutions can be derived over small sub-areas of dense stellar fields. Here we generalize the theory to the case of space-varying kernels. In particular, it is shown that the CPU cost required for this new extension of the method is almost the same as for fitting a

more »

... onstant kernel solution. It is also shown that constant flux scaling between the images (constant kernel integral) can be imposed in a simple way. The method is demonstrated with a series of Monte-Carlo images. Differential PSF variations and differential rotation between the images are simulated. It is shown that the new method is able to achieve optimal results even in these difficult cases, thereby automatically correcting for these common instrumental problems. It is also demonstrated that the method does not suffer due to problems associated with undersampling of the images. Finally, the method is applied to images taken by the OGLE II collaboration. It is proved that, in comparison to the constant-kernel method, much larger sub-areas of the images can be used for the fit, while still maintaining the same accuracy in the subtracted image. This result is especially important in case of variables located in low density fields, like the Huchra lens. Many other useful applications of the method are possible for major astrophysical problems; Supernova searches and Cepheids surveys in other galaxies, to mention but two. Many other applications will certainly show-up, since variability searches are a major issue in astronomy.