  We develop a new process of image plane self-calibration for interferometric
imaging data. The process is based on Shape-Orientation-Size (SOS) conservation
for the principal triangle in an image generated from the three fringes made
from a triad of receiving elements, in situations where interferometric phase
errors can be factorized into element-based terms. The basis of the SOS
conservation principle is that, for a 3-element array, the only possible image
corruption due to an element-based phase screen is a tilt of the aperture
plane, leading to a shift in the image plane. Thus, an image made from any
3-element interferometer represents a true image of the source brightness,
modulo an unknown translation. Image plane self-calibration entails deriving
the unknown translations for each triad image via cross-correlation of the
observed triad image with a model image of the source brightness. After
correcting for these independent shifts, and summing the aligned triad images,
a good image of the source brightness is generated from the full array,
recovering source structure at diffraction-limited resolution. The process is
iterative, using improved source models based on previous iterations. We
demonstrate the technique in the high signal-to-noise context, and include a
configuration based on radio astronomical facilities, and simple models of
double sources. We show that the process converges for the simple models
considered, although convergence is slower than for aperture-plane
self-calibration for large-$N$ arrays. As currently implemented, the process is
most relevant for arrays with a small number of elements. More generally, the
technique provides geometric insight into closure phase and the
self-calibration process. The technique is generalizable to non-astronomical
interferometric imaging applications across the electromagnetic spectrum.
