Aperture masking interferometric data analysis involves measuring phases and amplitudes of fringes formed by interference between holes in the pupil mask. These fringe observables can be measured by computing an analytic model of the point spread function and fitting the relevant set of spatial frequencies directly in the image plane, without recourse to numerical Fourier transforms. The ImPlaneIA pipeline converts aperture masking images to fringe observables by fitting fringes in the image plane, calibrates data from a target of interest with one or more point source calibrators, and contains some basic model-fitting routines. The pipeline can accept different mask geometries, instruments, and observing modes.